Microfluidics Based Microsystems: Fundamentals and Applications (NATO Science for Peace and Security Series A: Chemistry and Biology) 9048190312, 9789048190317

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Microfluidics Based Microsystems

NATO Science for Peace and Security Series This Series presents the results of scientific meetings supported under the NATO Programme: Science for Peace and Security (SPS). The NATO SPS Programme supports meetings in the following Key Priority areas: (1) Defence Against Terrorism; (2) Countering other Threats to Security and (3) NATO, Partner and Mediterranean Dialogue Country Priorities. The types of meeting supported are generally "Advanced Study Institutes" and "Advanced Research Workshops". The NATO SPS Series collects together the results of these meetings. The meetings are coorganized by scientists from NATO countries and scientists from NATO's "Partner" or "Mediterranean Dialogue" countries. The observations and recommendations made at the meetings, as well as the contents of the volumes in the Series, reflect those of participants and contributors only; they should not necessarily be regarded as reflecting NATO views or policy. Advanced Study Institutes (ASI) are high-level tutorial courses intended to convey the latest developments in a subject to an advanced-level audience Advanced Research Workshops (ARW) are expert meetings where an intense but informal exchange of views at the frontiers of a subject aims at identifying directions for future action Following a transformation of the programme in 2006 the Series has been re-named and re-organised. Recent volumes on topics not related to security, which result from meetings supported under the programme earlier, may be found in the NATO Science Series. The Series is published by IOS Press, Amsterdam, and Springer, Dordrecht, in conjunction with the NATO Public Diplomacy Division. Sub-Series A. B. C. D. E.

Chemistry and Biology Physics and Biophysics Environmental Security Information and Communication Security Human and Societal Dynamics

http://www.nato.int/science http://www.springer.com http://www.iospress.nl

Series A: Chemistry and Biology

Springer Springer Springer IOS Press IOS Press

Microfluidics Based Microsystems Fundamentals and Applications edited by

S. Kakaç TOBB University of Economics and Technology Sögütözü, Ankara, Turkey

B. Kosoy State Academy of Refrigeration Odessa, Ukraine

D. Li University of Waterloo Waterloo, Ontario, Canada and

A. Pramuanjaroenkij Kasetsart University Chalermphrakiat Sakonnakhon Province Campus Sakonnakhon, Thailand

Published in cooperation with NATO Public Diplomacy Division

Proceedings of the NATO Advanced Study Institute on Microfluidics Based Microsystems: Fundamentals and Applications Çeşme-Izmir, Turkey August 23–September 4, 2009

Library of Congress Control Number: 2010930508

ISBN 978-90-481-9031-7 (PB) ISBN 978-90-481-9028-7 (HB) ISBN 978-90-481-9029-4 (e-book)

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All Rights Reserved © Springer Science + Business Media B.V. 2010 No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work.

CONTENTS Preface

ix

Convective Heat Transfer Correlations in Some Common Micro-Geometries O. Aydin and M. Avci

1

Convective Heat Transfer in Microscale Slip Flow A. Guvenc Yazicioglu and S. Kakaç Direct and Inverse Problems Solutions in Micro-Scale Forced Convection C. P. Naveira-Cotta, R. M. Cotta, H. R. B. Orlande, and S. Kakaç

15

39

Conjugated Heat Transfer in Microchannels J. S. Nunes, R. M. Cotta, M. R. Avelino, and S. Kakaç

61

Mechanisms of Boiling in Microchannels: Critical Assessment J. R. Thome and L. Consolini

83

Prediction of Critical Heat Flux in Microchannels J. R. Thome and L. Consolini

107

Transport Phenomena in Two-Phase Thermal Spreaders H. Smirnov and B. Kosoy

121

An Investigation on Thermal Conductivity and Viscosity of Water Based Nanofluids I. Tavman and A. Turgut

139

Formation of Droplets and Bubbles in Microfluidic Systems P. Garstecki

163

Transport of Droplets in Microfluidic Systems P. Garstecki

183

The Front-Tracking Method for Multiphase Flows in Microsystems: Fundamentals M. Muradoglu

v

203

vi

CONTENTS

The Front-Tracking Method for Multiphase Flows in Microsystems: Applications M. Muradoglu

221

Gas Flows in the Transition and Free Molecular Flow Regimes A. Beskok

243

Mixing in Microfluidic Systems A. Beskok

257

AC Electrokinetic Flows A. Beskok

273

Scaling Fundamentals and Applications of Digital Microfluidic Microsystems R. B. Fair

285

Microfluidic Lab-on-a-Chip Platforms: Requirements, Characteristics and Applications D. Mark, S. Haeberle, G. Roth, F. Von Stetten, and R. Zengerle

305

Microfluidic Lab-on-a-Chip Devices for Biomedical Applications D. Li Chip Based Electroanalytical Systems for Monitoring Cellular Dynamics A. Heiskanen, M. Dufva, and J. Emnéus

377

399

Perfusion Based Cell Culture Chips A. Heiskanen, J. Emnéus, and M. Dufva

427

Applications of Magnetic Labs-on-a-Chip M. A. M. Gijs

453

Magnetic Particle Handling in Microfluidic Systems M. A. M. Gijs

467

AC Electrokinetic Particle Manipulation in Microsystems H. Morgan and T. Sun

481

Microfluidic Impedance Cytometry: Measuring Single Cells at High Speed T. Sun and H. Morgan

507

CONTENTS

vii

Optofluidics D. Erickson

529

Vivo-Fluidics and Programmable Matter D. Erickson

553

Hydrophoretic Separation Method Applicable to Biological Samples S. Choi and J.-K. Park

577

Programmable Cell Manipulation Using Lab-on-a-Display H. Hwang and J.-K. Park

595

Index

615

PREFACE This volume contains an archival record of the NATO Advanced Study Institute on Microfluidics Based Microsystems – Fundamentals and Applications held in Çeşme-Izmir, Turkey, August 23–September 4, 2009. ASIs are intended to be high-level teaching activity in scientific and technical areas of current concern. In this volume, the reader may find interesting chapters and various microsystems fundamentals and applications. As the world becomes increasingly concerned with terrorism, early onspot detection of terrorist’s weapons, particularly bio-weapons agents such as bacteria and viruses are extremely important. NATO Public Diplomacy division, Science for Peace and Security section support research, Advanced Study Institutes and workshops related to security. Keeping this policy of NATO in mind, we made such a proposal on Microsystems for security. We are very happy that leading experts agreed to come and lecture in this important NATO ASI. We will see many examples that will show us Microfluidics usefulness for rapid diagnostics following a bioterrorism attack. For the applications in national security and anti-terrorism, microfluidic system technology must meet the challenges. To develop microsystems for security and to provide a comprehensive state-of-the-art assessment of the existing research and applications by treating the subject in considerable depth through lectures from eminent professionals in the field, through discussions and panel sessions are very beneficial for young scientists in the field. Microfluidics are great tools for security and anti-terrorism with many applications. New and better diagnostic technology must be developed in order to be prepared for an act of bio-terrorism. The subject will be treated through lectures by experts on biosensors, microsystems, bio micro-electromechanical devices, and nanofluidics. To establish the objectives of this Institute, important lectures by prominent expert on the field are presented and are included in this volume of the Institute. Basics of Electrokinetic Microfluidics, Lab-on-a-Chip Devices for Biomedical Applications, Microfluidic Biological Application Specific Integrated Circuits, Integrated Optofluidics and Nanofluidics, Cell Culture Revolution via Dynamical Microfluidic Controls, Fundamentals of droplet flow in microfluidics, Implementation of fluidic functions in digital microfluidics, Chip architecture and applications for digital microfluidics, Mixing in microfluidic systems are presented and discussed in detail. In addition more presentations such as Optofluidics – Fusing Nanofluidics and Nanophotonics, Programmable Matter – Micro and milliscale fluid dynamics of reconfigurable assembly for control of living systems, An Overview on Microfluidic

ix

x

PREFACE

Platforms for Lab-on-a-Chip Applications, Centrifugal Microfluidics for Lab-on-a-Chip Applications are also given. Transport of droplets and bubbles in microfluidic systems – from flow through a simple pipe to logic gates and automated chips for chemical processing, Analytical, Synthesis and Bio-Medical Applications of Microchip Technology, Hydrophoretic separation method for blood sample analysis, Magnetophoretic multiplexed immunoassays in a microchannel, programmable particle manipulation using lab-on-a-display are discussed in details with fundamentals and applications. During the 10 working days of the Institute, the invited lecturers covered fundamentals and applications of Microsystems in various fields including the security. The sponsorship of the NATO Science for Peace and Security Section (SPS) is gratefully acknowledged; in person, we are very thankful to Dr. Fausta Pedrazzini director of the ASI programs and the executive secretary, Ms Alison Trapp who continuously supported and encouraged us at every phase of our organization of this Institute. We are appreciative to TOBB University of Economics and Technology and International Centre of Heat and Mass Transfer for their sponsorships. We are also very grateful to Annelies Kersbergen, publishing editor of Springer Science; our special gratitude goes to Drs. Nilüfer Eğrican, Şepnem Tavman, Almıla Yazıcıoğlu, Ahmet Yozgatlıgil, Derek Baker, Selin Aradağ, Nilay S. Uzol for coordinating sessions and we are very thankful to Büryan Apaçoğlu, Gizem Gülben, Sezer Özerince, and Cahit C. Köksal for smooth running of the Institute. S. Kakaç B. Kosoy D. Li A. Pramuanjaroenkij

CONVECTIVE HEAT TRANSFER CORRELATIONS IN SOME COMMON MICRO-GEOMETRIES ORHAN AYDIN AND METE AVCI Department of Mechanical Engineering Karadeniz Technical University, 61080 Trabzon, Turkey, [email protected]

Abstract. This work summarizes some of our recent theoretical studies on convective heat transfer in micro-geometries. Only pure analytical solutions are presented here. At first, forced convection is studied for the following three geometries: microtube, microchannel between two parallel plates and microannulus between two concentric cylinders. Constant heat flux is assumed to be applied at walls. Then mixed convection in a vertical parallel-plate microchannel with symmetric wall heat fluxes is investigated. Steady and laminar internal flow of a Newtonian is analyzed. In the analysis, the usual continuum approach is coupled with the two main characteristics of the microscale phenomena, the velocity slip and the temperature jump. In the forced convection problems, viscous dissipation is also included, while it is neglected for the mixed convection problem. Internal velocity and temperature distributions are obtained for varying values of governing parameters. Finally, fully analytical Nusselt number correlations are developed for the cases investigated.

1. Introduction Microelectromechanical systems (MEMS) have gained a great deal of interest in recent years. Such small devices typically have characteristic size ranging from 1 mm to 1 μm, and may include sensors, actuators, motors, pumps, turbines, gears, ducts and valves. Microdevices often involve mass, momentum and energy transport. Modeling gas and liquid flows through MEMS may necessitate including slip, rarefaction, compressibility, intermolecular forces and other unconventional effects [1]. The interest in the area of microchannel flow and heat transfer has increased substantially during the last decade due to developments in the electronic industry, microfabrication technologies, biomedical engineering, etc. In general, there also seems to be shift in the focus of published articles, S. Kakaç et al. (eds.), Microfluidics Based Microsystems: Fundamentals and Applications, DOI 10.1007/978-90-481-9029-4_1, © Springer Science + Business Media B.V. 2010

1

2

O. AYDIN AND M. AVCI

from descriptions of the manufacturing technology to discussions of the physical mechanisms of flow and heat transfer [2]. Readers are referred to see the following recent excellent reviews related to transport phenomena in microchannels. Ho and Tai [3] summarized discrepancies between microchannel flow behavior and macroscale Stokes flow theory. Palm [2], Sobhan and Garimella [4] and Obot [5] reviewed the experimental results in the existing literature for the convective heat transfer in microchannels. Rostami et al. [6, 7] presented reviews for flow and heat transfer of liquids and gases in microchannels. Gad-el-Hak [1] broadly surveyed available methodologies to model and compute transport phenomena within microdevices. Guo and Li [8, 9] reviewed and discussed the size effects on microscale single-phase fluid flow and heat transfer. In a recent study, Morini [10] presents an excellent review of the experimental data for the convective heat transfer in microchannels in the existing literature. He critically analyzed and compared the results in terms of the friction factor, laminar-to-turbulent transition and the Nusselt number. It is shown that fluid flow and heat transfer at microscale differ greatly from those at macroscale. At macroscale, classical conservation equations are successfully coupled with the corresponding wall boundary conditions, usual no-slip for the hydrodynamic boundary condition and no-temperaturejump for the thermal boundary condition. These two boundary conditions are valid only if the fluid flow adjacent to the surface is in thermal equilibrium. However, they are not valid for gas flow at microscale. For this case, the gas no longer reaches the velocity or the temperature of the surface and therefore a slip condition for the velocity and a jump condition for the temperature should be adopted. The Knudsen number, Kn is the ratio of the gas mean free path, λ, to the characteristic dimension in the flow field, D, and, it determines the degree of rarefaction and the degree of the validity of the continuum approach. As Kn increases, rarefaction become more important, and eventually the continuum approach breaks down. The following regimes are defined based on the value of Kn [11]: (i) (ii) (iii) (iv)

Continuum flow (ordinary density levels) Kn ≤ 0.001 Slip-flow regime (slightly rarefied) 0.001 ≤ Kn ≤ 0.1 Transition regime (moderately rarefied) 0.1 ≤ Kn ≤ 10 Free-molecule flow (highly rarefied) 10 ≤ Kn ≤ ∞

Viscous dissipation is another parameter that should be taken into consideration at microscale. It changes temperature distributions by playing a role like an energy source induced by the shear stress, which, in the following, affects heat transfer rates. The merit of the effect of the viscous dissipation depends on whether the pipe is being cooled or heated.

CONVECTIVE HEAT TRANSFER CORRELATIONS

3

In this work, heat and fluid flow in some common micro geometries is analyzed analytically. At first, forced convection is examined for three different geometries: microtube, microchannel between two parallel plates and microannulus between two concentric cylinders. Constant wall heat flux boundary condition is assumed. Then mixed convection in a vertical parallel-plate microchannel with symmetric wall heat fluxes is investigated. Steady and laminar internal flow of a Newtonian is analyzed. Steady, laminar flow having constant properties (i.e. the thermal conductivity and the thermal diffusivity of the fluid are considered to be independent of temperature) is considered. The axial heat conduction in the fluid and in the wall is assumed to be negligible. In this study, the usual continuum approach is coupled with the two main characteristics of the microscale phenomena, the velocity slip and the temperature jump. Effects of the main governing dimensionless parameters on the momentum and heat flow transfer will be analyzed. Pure analytical correlations for Nusselt number as a function of the Brinkman number and the Knudsen number are developed for both hyrodynamically and thermally fully developed flow. In fact, this work will be a summary view of our recent studies [12–15]. 2. Nu Correlations In this part, three different geometries are considered and corresponding results for the Nusselt number these geometries are given respectively in the following. 2.1. FORCED CONVECTION IN A MICROPIPE

For this geometry, the fully developed velocity profile taking the slip flow condition at the wall is u 2(1 − (r / r0 ) 2 + 4 Kn) = um (1 + 8 Kn)

(1)

where um is the mean velocity and Kn is the Knudsen number, Kn = λ / Dh . The Nusselt number correlation for this geometry is obtained as follows [12]: Nu =

Brq

2 Brq

1 + 16 Brq 1 ⎛ 16γ Kn ⎞ 1 + + + + 1+ ⎜ ⎟ 4 3 4 ⎝ γ + 1 Pr ⎠ 3(1 + 8 Kn) (1 + 8 Kn) 24(1 + 8 Kn) 2 6(1 + 8 Kn)

(2)

O. AYDIN AND M. AVCI

4

where Brq, represents the modified Brinkman number, whose value is determined from μ um2 (3) Brq = D qw′′

2.2. FORCED CONVECTION IN A MICROCHANNEL BETWEEN TWO PARALLEL PLATES

The fully developed velocity profile for this microchannel is: u 3 ⎡1 − ( y / w) 2 + 4 Kn ⎤ = ⎢ ⎥ um 2 ⎣ 1 + 6 Kn ⎦

(4)

where Kn is the Knudsen number, Kn = λ / 2w . In terms of the modified Brinkman number, Brq, the Nusselt number receives the following form [13]: Nu =

2 2Brq 11Brq 2(1 + 21Brq ) 1 ⎛ 12γ Kn ⎞ 2 1+ + + + + ⎜ ⎟ 4 3 2 3 ⎝ γ + 1 Pr ⎠ 35(1 + 6Kn) 35(1 + 6Kn) 105(1 + 6Kn) 15(1 + 6Kn)

(5)

where Brq =

μ um2

w qw

(6)

2.3. FORCED CONVECTION IN A MICROANNULUS BETWEEN TWO CONCENTRIC CYLINDERS

The dimensionless velocity distributions is obtained as [14]: u = 2 (1 − R 2 + 2rm*2 ln ( R ) + A ) / B um

where A and B are, respectively:

(7)

CONVECTIVE HEAT TRANSFER CORRELATIONS

5

A = 4 Kn (1 − r * )(1 − rm*2 )

(8)

⎛ ⎞ ⎛1 ⎞ r *2 ln ( r * ) ⎟ + 8Kn (1 − r * )(1 − rm*2 ) ⎟⎟ B = ⎜⎜ 1 − r *2 − 4rm*2 ⎜ + *2 ⎝ 2 1− r ⎠ ⎝ ⎠

(9)

Here Kn is Knudsen number ( Kn = λ Dh ) and rm* designates the dimensionless radius where the maximum velocity occurs (∂u / ∂r = 0) . It is given by [14] 1/ 2

⎛ ⎞ ⎜ ⎟ 2 rm ⎜ ⎟ (1 − r * )(1 + 4 Kn) * rm = = ⎜ ⎟ 2 * ro ⎜ ⎛ r −1 ⎞ 2 ln(1 / r * ) − 4 Kn ⎜ * ⎟ ⎟ ⎜ r ⎟⎟ ⎜ ⎝ ⎠⎠ ⎝

(10)

For this geometry, two different forms of the thermal boundary conditions are applied, which are shown in Fig. 1. In the following, these two different cases are treated separately [14]: insulated

qw

ro

Flow

ri

r z

qw

insulated

(a) Case A

(b) Case B

Figure 1. Schematic of the problem [14].

For the Case A, the dimensionless temperature distribution is obtained as follows [14]:

O. AYDIN AND M. AVCI

6

θ ( R) =

T − Ts qw′′ro / k

*2 2 *2 2 a ⎛⎜ −3 − A + 2rm + R (1 + A − 2rm + R / 2) ⎞⎟ = ⎟ 2B ⎜ − ln R (1 + 2 A − 2rm*2 (1 + ln R ) ) ⎝ ⎠ Br 2 + 2 (1 − R2 )(1 + R2 − 8rm*2 ) + 4ln R (1 − 4rm*2 ) − 8rm*4 ( ln R ) + ln R B

(

where a=

(11)

)

−2 B 2 r * + 8Br ( r *2 − 1)(1 − 4rm*2 + r *2 ) + 32 Br rm*4 ln ( r * )

(

B (1 + 2 A − 2rm*2 − r *2 )( r *2 − 1) + 4 rm*2 r *2 ln ( r * )

)

(12)

and Br =

μ um2

(13)

qw′′ ro

Similarly, the dimensionless temperature distribution is obtained for the Case B as in the following [14]: θ ( R) =

T − Ts qw′′ ro / k

2 *2 *2 2 *2 * *2 a ⎛⎜ ( R − r )(1 + A − 2rm ) − ( R − r ) − ( ln R − ln r )(1 + 2 A − 2rm ) ⎞⎟ = ⎟ 2 B ⎜ +2rm*2 ( R 2 ln R − r *2 ln r * ) ⎝ ⎠ ⎛ ( R 2 − r *2 ) 8rm*2 − ( R 2 + r *2 ) + 4 ( ln R − ln r * )(1 − 4rm*2 ) ⎞ Br ⎜ ⎟ + 2⎜ ⎟ B ⎜ −8r *4 ( ln R )2 − ( ln r * )2 ⎟ ⎝ m ⎠

(

(

)

(14)

)

where a=

−2 B 2 r * + 8Br ( r *2 − 1)(1 − 4rm*2 + r *2 ) + 32 Br rm*4 ln ( r * )

(

B (1 + 2 A − 2rm*2 − r *2 )( r *2 − 1) + 4 rm*2 r *2 ln ( r * )

)

(15)

After performing necessary substitutions, the Nusselt number is obtained as follows [14]:

CONVECTIVE HEAT TRANSFER CORRELATIONS Nu =

7

qw Dh 2 = − * (1 − r * ) (Tw − Tm ) k θ m

(16)

2.4. MIXED CONVECTION IN A VERTICAL PARALLEL-PLATE MICROCHANNEL WITH SYMMETRIC WALL HEAT FLUXES

For this problem under the above mentioned assumptions, therefore, the dimensionless velocity profile is obtained as [15]:

U = C1eξ Y cos(ξ Y ) + C2 e −ξ Y cos(ξ Y ) + C3eξ Y sin(ξ Y ) + C4 e −ξ Y sin(ξ Y )

(17)

where 1/ 4

⎡ Gr ⎤ ξ = ⎢ q U⎥ ⎣ Re ⎦

(18)

By applying the boundary conditions given in Eq. (10), the four unknown constants C1, C2, C3 and C4 can be obtained. Some typical values of these constants for different values of Grq/Re and Kn are tabulated in Table 1. TABLE 1. Typical values of constants C1, C2, C3, and C4 [15].

Grq/Re 1

50

100

Kn 0.00 0.02 0.06 0.10 0.00 0.02 0.06 0.10 0.00 0.02 0.06 0.10

C1 2.87634 2.39220 1.82928 1.51201 0.82091 0.69563 0.55026 0.46847 0.59553 0.50312 0.39610 0.33599

C2 −2.87634 −2.19857 −1.41051 −0.96634 −0.82091 −0.49796 −0.12322 0.08763 −0.59553 −0.30136 0.03930 0.23064

C3 −8.90402 −7.16036 −5.13293 −3.99024 −0.42563 −0.30682 −0.16895 −0.09137 −0.11637 −0.05680 0.01218 0.05093

C4 15.15670 12.25113 8.87272 6.96858 3.39702 2.82999 2.17201 1.80179 2.88858 2.44242 1.92576 1.63556

After several steps of derivations, the Nusselt numbers is obtained as [15]: Nu1 = −

1

θ m*

(19)

O. AYDIN AND M. AVCI

8

where 0.5

∫ Uθ dY *

θ m* =

Tm − T1 = ( q Dh / k )

0 0.5

(20)

∫ UdY 0

and θ* = =

(T − Ts ,1 ) (Ts ,1 − T1 ) T − T1 = + q2 Dh / k q2 Dh / k q2 Dh / k

(

Re 2ξ 2 e −ξ Y ( (C4 − C3 )eξ Y + (C3e 2ξ Y − C4 ) cos(ξ Y ) + (C2 − C1e 2ξ Y )sin(ξ Y ) ) Grq

)

(21)

− β t Kn(q1 / q2 )

3. Results and Discussion

Here, only summary results are given for three different geometries considered separately. 3.1. FORCED CONVECTION IN A MICROPIPE

Figure 1 shows the variation of the Nusselt number with the Knudsen number for different values of the modified Brinkman number. For Brq = 0, an increase at Kn decreases Nu due to the temperature jump at the wall. Viscous dissipation, as an energy source, severely distorts the temperature profile. Positive values of Brq correspond to wall heating (heat is being supplied across the walls into the fluid) case (qw > 0), while the opposite is true for negative values of Brq. In the absence of viscous dissipation the solution is independent of whether there is wall heating or cooling. However, viscous dissipation always contributes to internal heating of the fluid, hence the solution will differ according to the process taking place. Nu decreases with increasing Brq for the hot wall (i.e. the wall heating case). As expected, increasing dissipation increases the bulk temperature of the fluid due to internal heating of the fluid. For the wall heating case, this increase in the fluid temperature decreases the temperature difference between the wall and the bulk fluid, which is followed with a decrease in heat transfer. When wall cooling is applied, due to the internal heating effect of the viscous dissipation on the fluid temperature profile, temperature difference is increased with the increasing Brq (Fig. 2). For more details, readers are referred to Ref. [12].

CONVECTIVE HEAT TRANSFER CORRELATIONS

9

8

7

Br q -----------0.1 -0.01 0.0 0.01 0.1

Pr=0.7

Nu

6

5

4

3

2 0,00

0,02

0,04

0,06

0,08

0,10

Kn

Figure 2. The variation of Nu with Kn at different values of Brq [12].

3.2. FORCED CONVECTION IN A MICROCHANNEL BETWEEN TWO PARALLEL PLATES

For this geometry, Fig. 3 illustrates the variation of the Nusselt number with the Knudsen number for different values Brinkman numbers. As seen, an increase at Kn decreases Nu due to the temperature jump at the wall. The effect of the viscous dissipation is discussed above. For more details, readers are referred to Ref. [13]. 5,6 5,2

Br q -------------

Pr=0.7 4,8

-0.1 -0.01 0.0 0.01 0.1

4,4

Nu

4,0 3,6 3,2 2,8 2,4 2,0 0,00

0,02

0,04

0,06

0,08

0,10

Kn

Figure 3. The variation of Nu with Kn at different values of Brq [13].

10

O. AYDIN AND M. AVCI

3.3. FORCED CONVECTION IN A MICROANNULUS BETWEEN TWO CONCENTRIC CYLINDERS

Figure 4 illustrates the variation of the Nusselt number with the aspect ratio of the annulus, r* for different values of the Knudsen number at Cases A and B without viscous dissipation (Br = 0), respectively. For the both cases, the influence of the increasing Kn is to decrease the heat transfer rates. As expected, for the Case A, an increase in r* increases Nu, while it decreases Nu for the Case B. However, this Nu-dependence on r* becomes negligible with increasing Kn. The variation of the Nusselt number with the Knudsen number for different values of the Brinkman number at r* = 0.2 for Cases A and B, respectively, is shown in Fig. 5. An increase at Kn decreases the Nu due to the temperature jump at the wall. Nu decreases with increasing Br for the hot wall (i.e. the wall heating case). For this case, the wall temperature is greater than that of the bulk fluid. Viscous dissipation increases the bulk fluid temperature especially near the wall since the highest shear rate occurs in this region. Hence, it decreases the temperature difference between the wall and the bulk fluid, which is the main driving mechanism for the heat transfer from wall to fluid. However, for the cold wall (i.e. the wall cooling case), the viscous dissipation increases the temperature differences between the wall and the bulk fluid by increasing the fluid temperature more. Therefore, increasing Br in the negative direction increases Nu. As seen from the figure, the behavior of Nu versus Kn for lower values of the Brinkman number, either in the case of wall heating (Br = 0.01) or in the case of the wall cooling (Br = −0.01) is very similar to that of Br = 0. In addition, as observed from the figure, Br is more effective on Nu for lower values of Kn than for higher values of Kn. For more details, readers are referred to Ref. [14]. 3.4. MIXED CONVECTION IN A VERTICAL PARALLEL-PLATE MICROCHANNEL WITH SYMMETRIC WALL HEAT FLUXES

For this problem, the variation of Nu with Grq/Re is plotted for different values of Kn in Fig. 6. As expected, increasing Grq/Re increases Nu while increasing Kn decreases Nu. Because of the lower values of the Grq/Re present at microscale, the aiding effect of the buoyancy forces on the inertia forces are not much. Therefore, increasing Grq/Re in this limited range will not have a profound effect on Nu. For example, at Kn = 0.02, increasing Grq/Re from 1 to 200 will lead to an increase of about 2% in Nu. For more details, readers are referred to Ref. [15].

CONVECTIVE HEAT TRANSFER CORRELATIONS

11

6 Br = 0.00 Pr = 0.71

5

Kn = 0.00

Nu

Kn = 0.02

4

Kn = 0.04 Kn = 0.06 Kn = 0.08

3

2 0.2

Kn = 0.10

0.3

0.4

0.5

0.6

0.7

0.8

r*

(a)

10 Br = 0.00 Pr = 0.71

8

Nu

Kn = 0.00

6 Kn = 0.02 Kn = 0.04

4

Kn = 0.06 Kn = 0.08 Kn = 0.10

2 0.2

0.3

0.4

0.5 r

0.6

0.7

0.8

*

(b) Figure 4. The variation of Nu with r* at different values of Kn for Br = 0.0, (a) Case A, (b) Case B.

O. AYDIN AND M. AVCI

12

7 Br = -0.10 Br = -0.01 Br = 0.00 Br = 0.01 Br = 0.10

6

5 Nu

r* = 0.2 Pr = 0.71

4

3

2 0.00

0.02

0.04

0.06

0.08

0.10

Kn

(a) 16 Br = -0.10 Br = -0.01 Br = 0.00 Br = 0.01 Br = 0.10

14 12

r* = 0.2 Pr = 0.71

Nu

10 8 6 4 2 0.00

0.02

0.04

0.06

0.08

0.10

Kn

(b) Figure 5. The variation of Nu with Kn at different values of Br for r* = 0.2, 0.5 and 0.8, (a) Case A, (b) Case B.

CONVECTIVE HEAT TRANSFER CORRELATIONS

13

9 Kn = 0.00

8

Nu (Nu1=Nu2)

7

Kn = 0.02

6

Kn = 0.04

5

Kn = 0.06 Kn = 0.08

4

Kn = 0.10

Pr = 0.7 rq = 1.0

3 0

50

100

150

200

Grq / Re

Figure 6. The variation of the Nu with the Grq/Re at different values of Kn.

Acknowledgment

The first author of this work is indebted to the Turkish Academy of Sciences (TUBA) for the financial support provided under the Programme to Reward Success Young Scientists (TUBA-GEBIT).

References 1. Gad-el-Hak, M., Flow physics in MEMS, Mec. Ind., vol. 2, pp. 313–341, 2001. 2. Palm, B., Heat transfer in microchannels, Microscale Thermophysical Engineering, vol. 5, pp. 155–175, 2001. 3. Ho, C.M. and Tai, C.Y., Micro-electro-mechanical systems (MEMS) and fluid flows, Annu. Rev. Fluid Mech., Vol. 30, pp. 579–612, 1998. 4. Sobhan, C.B. and Garimella, S.V., A comparative analysis of studies on heat transfer and fluid flow in microchannels, Microscale Thermophysical Engineering, vol. 5, 293–311, 2001. 5. Obot, N.T., Toward a better understanding of friction and heat/mass transfer in microchannels-A literature review, Microscale Thermophysical Engineering, vol. 6, pp. 155–173, 2002. 6. Rostami, A.A., Saniei, N. and Mujumdar, A.S., Liquid flow and heat transfer in microchannels: A review, Heat Technol., Vol. 18, pp. 59–68, 2000. 7. Rostami, A.A., Mujumdar, A.S. and Saniei, N., Flow and heat transfer for gas flowing in microchannels: A review, Heat Mass Transfer, vol. 38, pp. 359– 367, 2002.

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O. AYDIN AND M. AVCI

8. Guo, Z.Y. and Li, Z.X., Size effect on microscale single-phase flow and heat transfer, International Journal of Heat and Mass Transfer, vol. 46, pp. 59– 149, 2003. 9. Guo, Z.Y. and Li, Z.X., Size effect on single-phase channel flow and heat transfer at microscale, International Journal of Heat and Fluid Flow, vol. 24 (3), pp. 284–298, 2003. 10. Morini, G.L., Single-phase convective heat transfer in microchannels: a review of experimental results, International Journal of Thermal Sciences, vol. 43, pp. 631–651, 2004. 11. Beskok, A. and Karniadakis, G.E., Simulation of heat and momentum transfer in complex micro-geometries, J. Thermophysics Heat Transfer, vol. 8, pp. 355–370, 1994. 12. Aydın, O. and Avcı, M., Heat and Fluid Flow Characteristics of Gases in Micropipes, Int. J. Heat Mass Transfer, vol. 49, pp. 1723–1730, 2006. 13. Aydın, O. and Avcı, M., Analysis of Laminar Heat Transfer in MicroPoiseuille Flow, Int. J. Thermal Sci., vol. 46, pp. 30–37, 2007. 14. Avcı, M. and Aydın, O., Laminar forced convection slip flow in a micro-annulus between two concentric cylinders, Int. J. Heat and Mass Transfer, vol. 51, pp. 3460–3467, 2008. 15. Avcı, M. and Aydın, O., Mixed convection in a vertical parallel-plate microchannel with asymmetric wall heat fluxes, J. Heat Transfer, vol. 129, pp. 1091–1095, 2007.

CONVECTIVE HEAT TRANSFER IN MICROSCALE SLIP FLOW A. GUVENC YAZICIOGLU1 AND S. KAKAÇ2 1

Orta Doğu Teknik Üniversitesi, Makine Mühendisliği Bölümü, Ankara, 06531 Turkey, [email protected] 2 TOBB Ekonomi ve Teknoloji Üniversitesi, Makine Mühendisliği Bölümü, Söğütözü Cad.No:43, Söğütözü, Ankara, 06560 Turkey

Abstract. In this lecture, steady-state convective heat transfer in different microchannels (microtube and parallel plates) will be presented in the slip flow regime. Laminar, thermally and/or hydrodynamically developing flows will be considered. In the analyses, in addition to rarefaction, axial conduction, and viscous dissipation effects, which are generally neglected in macroscale problems, surface roughness effects, and temperature-variable thermophysical properties of the fluid will also be taken into consideration. Navier–Stokes and energy equations will be solved and the variation of Nusselt number, the dimensionless parameter for convection heat transfer, along the channels will be presented in tabular and graphical forms as a function of Knudsen, Peclet, and Brinkman numbers, which represent the effects of rarefaction, axial conduction, and viscous dissipation, respectively. The results will be compared and verified with available experimental, analytical, and numerical solutions in literature.

1. Introduction Devices having the dimensions of microns have been used in many fields such as; biomedicine, diagnostics, chemistry, electronics, automotive industry, space industry, and fuel cells, to name a few. With the increase of integrated circuit density and power dissipation of electronic devices, it is becoming more necessary to employ effective cooling devices and cooling methods to maintain the operating temperature of electronic components at a safe level. Especially when device dimensions get smaller, overheating of microelectronic components may be a serious issue. Microchannel heat sinks, with hydraulic diameters ranging from 10 to 1,000 μm, appear to be the ultimate solution for removing these high amounts of heat. This pressing requirement of cooling of electronic devices has initiated extensive research in microchannel heat transfer. Many analytical and experimental studies have been performed to have a better understanding of heat transfer at the S. Kakaç et al. (eds.), Microfluidics Based Microsystems: Fundamentals and Applications, DOI 10.1007/978-90-481-9029-4_2, © Springer Science + Business Media B.V. 2010

15

16

A. GUVENC YAZICIOGLU AND S. KAKAÇ

microscale. Both liquids and gases have been investigated. However, none of them has been able to come to a general conclusion. For example, there are controversial results in the literature about the boundary conditions, for liquids flows. It is not clear whether discontinuity of velocity and temperature exists on the wall or not. The pioneering conclusion drawn by Tuckerman and Pease in 1982 [1] that the heat transfer coefficient for laminar flow through microchannels may be greater than that for turbulent flow, accelerated research in this area. Many experimental [2–6], numerical [7–10], and analytical [11–14] studies have been performed, with some focusing on the effects of roughness [15–21] and temperature-variable thermophysical properties of the fluid [22–26]. Some of these works have been compiled in review articles such as those by Gad-El-Hak [27], Morini [28], Bayazitoglu [29], Hetsroni [30], Yener [31], Cotta [32], and Rosa [33]. The reader is also referred to excellent books by Karniadakis [34], Sobhan [35], and Yarin [36]. Several conflicting results may be drawn from the above-mentioned studies. First, some investigators reported laminar fully-developed friction factors and Poiseuille numbers lower than the conventional values, some reported higher values, while others reported agreement with conventional values. Another conflict occurs in laminar to turbulent transition Re values, varying between 3,000 and 6,000. A similar conclusion can be made about the laminar regime Nusselt number (Nu = hD/k, h being the convection heat transfer coefficient, and D the hydraulic diameter) and the effect of energy dissipation on heat transfer. However, it should also be noted that as the precision and reliability of the experimental set-ups and measurement devices increase, the deviation margin of theoretical and experimental results obtained from similar experiments conducted by different investigators reduces. In any case, future research is still needed for fundamental understanding, as pointed out in Refs. [28–33, 37, 38]. 2. General Considerations For the effective and economical design of microchannel heat sinks, some key design parameters should be considered and optimized. These are, the pressure required for pumping the cooling fluid, the mass flow rate of the cooling fluid, the hydraulic diameter of the channels, the temperature of the fluid and the channel wall, and the number of channels. In order to understand the effect of these parameters on the system, the dynamic behavior and heat transfer characteristics of fluids at the microscale must be well-understood. There are two major approaches to modeling fluid flow at the microscale: In the first model, the molecular model, the fluid is assumed to be a collection of molecules whereas in the second model, the continuum model, the fluid

CONVECTIVE HEAT TRANSFER IN MICROSCALE SLIP FLOW

17

is assumed to be continuous and indefinitely divisible. In macroscale flows, the continuum approach is generally accepted. The velocity, density, pressure, etc., for the fluid are defined at every point and time in space. Conservation of mass, momentum, and energy are applied and a set of nonlinear partial differential equations (Navier–Stokes and energy equations) are obtained. These equations are solved to obtain the fluid flow and heat transfer characteristic parameters at the macroscale. However as the dimensions of the channels get smaller, the continuum assumption starts to break. For microscale slip flow regime, the continuum approach is still valid, and Navier–Stokes and energy equations may still be used, but with a modification of boundary conditions. One important dimensionless parameter characterizing the flow regime is the Knudsen number (Kn). Knudsen number, which signifies the degree of rarefaction in the flow and the degree of validity of the continuum model, is defined as the ratio of the mean free path of the molecules, λ, to the characteristic length, L (Kn = λ/L). The different Kn regimes are determined empirically and are therefore only approximate for a particular flow geometry. For example, for gases, below L ≈ 100 nm, the rarefaction effect seems to be significant, while for liquids, below L ≈ 0.3 nm, the interfacial electro-kinetic effects near the solid–liquid interface become important. In general, the following is a commonly used scale for Kn to differentiate flow regimes [34]: Kn < 0.001 0.001 < Kn < 0.1 0.1 < Kn < 10 Kn > 10

Continuum flow Slip-flow (slightly rarefied) Transition flow (moderately rarefied) Free-molecular flow (highly rarefied)

When the flow is in the higher Kn regime (transition and free-molecular), a molecular approach, such as direct simulation Monte Carlo method using the Boltzmann equation should be employed. For L  λ, the continuum approach will be applicable with traditional no-slip, no-temperature jump boundary conditions. However as this condition is violated, the linear relation between stress and the rate of strain, thus the no-slip velocity condition will not be valid. Similarly, the linear relation between heat flux and temperature gradient, thus the no-temperature jump condition at the solid–fluid interface will no longer be accurate [39]. The fluid and solid particles cannot retain thermodynamic equilibrium at the surface, thus the fluid molecules close to the surface do not have the velocity and temperature of the surface. Therefore, the slip-flow regime may be modeled with classical Navier–Stokes and energy equations by making some modifications in the boundary conditions for velocity and temperature at the wall, because the rarefaction effect is not small enough to be negligible in the slip-flow regime. As a result, fluid molecules at the wall will have finite slip-velocity and temperature-jump at

18

A. GUVENC YAZICIOGLU AND S. KAKAÇ

the wall. These modified conditions depend on the Kn value, some thermophysical properties of the fluid, and accommodation factors. Besides the Knudsen number, some other dimensionless parameters become important in microscale flow and heat transfer problems. The first such number is the Peclet number (Pe), which is the product of Reynolds (Re) and Prandtl (Pr) numbers (Pe = Re·Pr), and signifies the ratio of rates of advection to diffusion. Peclet number enumerates the axial conduction effect in flow. In macro-sized conduits, Pe is generally large and the effect of axial conduction may be neglected. However as the channel dimensions get smaller, it may become important. Brinkman number is the dimensionless parameter representing the relative importance of heat generated by viscous dissipation (work done against viscous shear) to heat transferred by fluid conduction across the microchannel cross-section in the flow. Its definition varies with the boundary condition at the wall. For example, for constant wall temperature, Br = μum2/kΔT and for constant wall heat flux, Br = μum2/qwR, where μ is the fluid dynamic viscosity, um is the mean flow velocity, k is the fluid thermal conductivity, ΔT is the fluid inlet-to-wall temperature difference, R is the hydraulic radius of the channel, and qw is the wall heat flux. Br is usually neglected in lowspeed and low-viscosity flows through conventionally-sized channels of short lengths. However in flows through conventionally-sized long pipelines, Br may become important. For flows in microchannels, the length-to-diameter ratio can be as large as for flows through conventionally-sized long pipelines, thus Br may become important in microchannels as well. In this lecture, the effects of the abovementioned dimensionless parameters, namely, Knudsen, Peclet, and Brinkman numbers representing rarefaction, axial conduction, and viscous dissipation, respectively, will be analyzed on forced convection heat transfer in microchannel gaseous slip flow under constant wall temperature and constant wall heat flux boundary conditions. Nusselt number will be used as the dimensionless convection heat transfer coefficient. A majority of the results will be presented as the variation of Nusselt number along the channel for various Kn, Pe, and Br values. The lecture is divided into three major sections for convective heat transfer in microscale slip flow. First, the principal results for microtubes will be presented. Then, the effect of roughness on the microchannel wall on heat transfer will be explained. Finally, the variation of the thermophysical properties of the fluid will be considered. 3. Microtubes The geometry of the problem for microtubes is shown in Fig. 1. Steadystate, two-dimensional, incompressible, laminar, and single-phase gas flow is considered. An unheated section is provided, where the velocity profile

CONVECTIVE HEAT TRANSFER IN MICROSCALE SLIP FLOW

19

develops. As mentioned before, in the slip flow regime, slip-velocity and temperature-jump boundary conditions should be applied to the momentum and energy equations. These are:

us = −

2 − Fm ⎛ du ⎞ λ⎜ ⎟ Fm ⎝ dr ⎠ r = R

Ts − Tw = −

(1)

2 − Ft 2γ λ ⎛ ∂T ⎞ ⎜ ⎟ Ft γ + 1 Pr ⎝ ∂r ⎠ r =R

Velocity entrance length

(2)

Tw or qw = constant u (η,Kn) R

r x

Tw or qw = constant Figure 1. The problem geometry for microtubes.

In Eq. (1), Fm is the momentum accommodation factor and has a value close to unity for the gas–solid couples used most commonly in engineering, and is also taken so in this work. In Eq. (2), Ts is the temperature of the fluid molecules at the wall, Tw is the wall temperature, γ is the ratio of the specific heats of the fluid, and Ft is the thermal accommodation factor. Ft may take a value in the range 0.0–1.0, depending on the gas and solid surface, the gas temperature and pressure, the temperature difference between the gas and the surface, and is determined experimentally. Using the slip-velocity boundary condition, the fully developed velocity profile may be written as [40]

(

)

u 2 1 − η2 + 8Kn = , um 1 + 8Kn

(3)

where η = r/R is the nondimensional radial coordinate. Figure 2 presents the variation of the nondimensional velocity along the radial distance as a function of rarefaction in the flow. As can be observed therein, for continuum (Kn = 0), the no-slip velocity is present at the wall while as the degree of rarefaction increases, so does the slip velocity at the wall [41].

A. GUVENC YAZICIOGLU AND S. KAKAÇ

20

3.1. CONSTANT WALL TEMPERATURE

For this boundary condition, the nondimensional energy equation and the boundary conditions for the flow inside a microtube, including axial conduction and viscous dissipation are

Dimensionless Radius (η= r/R)

1,0

Kn=0(continuum) Kn=0.02 Kn=0.04 0,5

Kn=0.06 Kn=0.08 Kn=0.10 0,0 0,0

0,5

1,0

1,5

2,0

Dimensionless Velocity (u/um)

Figure 2. Velocity profile variation with Kn along the radial direction. 2

⎛ ∂u * ⎞ u * ∂θ 1 ∂ ⎛ ∂θ ⎞ 1 ∂ 2θ ⎟⎟ , = ⎜⎜ η ⎟⎟ + 2 2 + Br ⎜⎜ 2 ∂ξ η ∂η ⎝ ∂η ⎠ Pe ∂ξ ⎝ ∂η ⎠

η = 0,

∂θ = 0, ∂η

⎛ ∂θ ⎞ η = 1, θ = −2κKn⎜⎜ ⎟⎟ , ⎝ ∂η ⎠ η=1 ξ = 0, θ = 1 .

(4)

(5) (6) (7)

In Eqs. (4–7), the following parameters have been used for nondimensionalization: T − Tw μu 2m x r u θ= , Br = , ξ= , η = , u* = , (8) Ti − Tw k (Ti − Tw ) PeR R um

CONVECTIVE HEAT TRANSFER IN MICROSCALE SLIP FLOW

21

and κ is a parameter that accounts for temperature jump at the wall as κ=

2 − Ft 2 γ 1 . Ft γ + 1 Pr

(9)

The energy equation has been solved numerically [40] and analytically, using general Eigen functions expansion [42], and the details can be found in related references. Using the temperature distribution, the local Nusselt number may be determined as

Nu x =

hxD =− k

2

∂θ ∂η η=1

4 γ Kn ∂θ θm − γ + 1 Pr ∂η η=1

,

(10)

where θm is the nondimensional mean temperature defined by 1

∫

θ m ( ξ) = 2 u * θ( η, ξ)ηdη .

(11)

0

3.2. CONSTANT WALL HEAT FLUX

In this case, the nondimensional energy equation and the boundary conditions become [40],

(

)

Gz 1 − η2 + 4 Kn ∂θ 1 ∂ ⎛ ∂θ ⎞ 1 ∂ 2θ 32 Br = η2 , ⎜⎜ η ⎟⎟ + 2 2 + 2(1 + 8Kn ) ∂ζ η ∂η ⎝ ∂η ⎠ Pe ∂ζ (1 + 8Kn )2 ∂θ η = 0, = 0, ∂η ∂θ η = 1, = 1, ∂η ξ = 0, θ = 1 .

(12)

(13) (14) (15)

A. GUVENC YAZICIOGLU AND S. KAKAÇ

22

In Eqs. (12–15) the following additional parameters have been used for non-dimensionalization: θ=

k (T − Ti ) μu 2 2R , Br = m , Gz = Re Pr , qwR qwD L

(16)

The temperature profile is determined numerically, and using the temperature distribution, local Nusselt number may be determined as [40], Nu x =

hxD =− k

2 θs +

4 γ Kn − θm γ + 1 Pr

,

(17)

where θs is the nondimensional temperature of the fluid at the surface. 3.3. RESULTS

In this section, the results will be presented in tabular and graphical forms, for Nusselt number for both constant wall temperature and constant wall heat flux cases with variable Kn, Br, Pe values to investigate the effects of rarefaction, viscous dissipation, and axial conduction in the slip-flow regime for microtubes. Table 1 presents the effect of rarefaction on laminar flow fully developed Nu values for constant wall temperature (NuT) and constant wall heat flux (Nuq) cases, where viscous dissipation and axial TABLE 1. Laminar flow fully-developed Nu values for the present work for constant wall temperature (NuT) and constant wall heat flux (Nuq) cases, compared with analytical results from Ref. [43] (Pr = 0.6).

Kn

NuT [43]

NuT

Nuq [43]

Nuq

0.00

3.6751

3.6566

4.3627

4.3649

0.02

3.3675

3.3527

3.9801

4.0205

0.04 0.06 0.08 0.10

3.0745 2.8101 2.5767 2.3723

3.0627 2.8006 2.5689 2.3659

3.5984 3.2519 2.9487 2.6868

3.6548 3.3126 3.0081 2.7425

CONVECTIVE HEAT TRANSFER IN MICROSCALE SLIP FLOW

23

conduction effects have been neglected. The table serves as a verification of the solution procedure, as comparisons with analytical solutions from literature [43] are also provided. To observe the effect of viscous dissipation on heat transfer, in Table 2, the fully developed Nusselt number is presented for constant wall temperature and constant wall heat flux cases with and without viscous dissipation. For all cases, the fully developed Nusselt number decreases as Kn increases. For Tw = constant, for the no-slip condition (Kn = 0), when Br = 0.01, Nu = 9.5985, while it drops down to 3.8227 for Kn = 0.1, a decrease of 60.2%. Similarly for qw = constant, for the no-slip condition, when Br = 0.01, Nu = 4.1825, while it drops down to 2.9450 for Kn = 0.1, with a decrease of 29.6%. This is due to the fact that the temperature jump, which increases with increasing rarefaction, reduces heat transfer, as can be observed from Eqs. (10) and (17). A negative Br value for the constant wall heat flux condition refers to the fluid being cooled, therefore Nu takes higher values for Br < 0 and lower values for Br > 0 compared with those for no viscous heating. TABLE 2. Laminar flow fully-developed Nu with and without viscous dissipation for Tw = constant and qw = constant cases (Pr = 0.7).

Kn 0.00 0.02 0.04 0.06 0.08 0.10

Tw = constant Br = 0.00 Br = 0.01 3.6566 9.5985 3.4163 7.4270 3.1706 6.0313 2.9377 5.0651 2.7244 4.3594 2.5323 3.8227

qw = constant Br = 0.00 4.3649 4.1088 3.8036 3.4992 3.2163 2.9616

Br = 0.01 4.1825 4.0022 3.7398 3.4598 3.1912 2.9450

Br = −0.01 4.5640 4.2212 3.8695 3.5395 3.2419 2.9784

In Fig. 3, the variation of local Nusselt number along the constant wall temperature tube is presented as a function of Peclet number, representing axial conduction in the fluid. For Pe = 50, which represents a case with negligible axial conduction, the solution of the classical Graetz problem, Nu = 3.66, is reached [44], while for Pe = 1, Nu = 4.03 [45] is obtained as the fully developed values of Nu. The temperature gradient at the wall decreases at low Pe values, thus the local and fully developed Nu values increase with decreasing Pe.

A. GUVENC YAZICIOGLU AND S. KAKAÇ

24 10

Kn = 0, Br = 0

Local Nu

8

Decreasing Pe (50, 10, 5, 1)

6

4.03 3.66

4

2 0.01

0.1

1.0

10

x = x / (R Pe) Figure 3. Variation of local Nu with Pe when Kn = 0 and Br = 0.

Figure 4 presents the local Nusselt number variation along the microtube for the constant wall temperature boundary condition for cases where both viscous dissipation and axial conduction effects have been considered. A positive Br for this boundary condition refers to the fluid being cooled as it flows along the tube. Local Nu value first decreases due to temperature jump at the wall, then increases to its fully-developed value because of the heating due to the viscous dissipation effect. Before the increase, the values of local Nu match those for the Br = 0 case presented in Fig. 3 [10, 42]. However, because of the definition of Pe, local Nu curves deviate from those for Br = 0 as the minima are approached. This effect results in the overall increase in the average Nu in the tube, thus we can conclude that average Nu increases as the effect of axial conduction is more prominent. Also, the amount of viscous dissipation does not affect the fully developed Nu value.

CONVECTIVE HEAT TRANSFER IN MICROSCALE SLIP FLOW

25

Figure 4. Variation of local Nu with Pe when viscous dissipation is present (Br > 0, Kn = 0).

When the fluid is being heated along the tube, i.e., the fluid inlet temperature is less than that of the wall, for the constant wall temperature case, Br is negative and the local Nu variation is as shown in Fig. 5. As can be observed therein, local Nu reaches an asymptotic value when the fluid temperature is equal to the wall temperature, when viscous dissipation and axial conduction are included. Thermal development continues after this point, and the fully developed Nu is reached. Similar to positive Br cases, the amount of viscous dissipation effects the location where the sudden change in local Nu occurs, but the fully developed Nu is the same for all non-zero Br values. Table 3 summarizes a majority of the results for fully developed Nu for slip-flow in microtubes presented in this section for constant wall temperature boundary condition, and provides comparisons with available results from literature. Here, κ = 0 refers to no temperature jump while κ = 1.667 refers to temperature jump for air flow. The present results show excellent agreement with literature.

A. GUVENC YAZICIOGLU AND S. KAKAÇ

26 20

Br = - 0.1 Br = - 0.01

Decreasing Pe (10, 5, 2, 1)

Local Nu

15

10

9.60

Decreasing Pe (10, 5, 2, 1)

5

Br = 0, Pe Æ •

3.66

Kn = 0 0 0.01

0.1

1.0

10

x = x / (R Pe) Figure 5. Variation of local Nu with Pe when viscous dissipation is present (Br < 0, Kn = 0). TABLE 3. Comparison of fully developed Nu with results from literature.

Kappa Pe = 1.0 Pe = 5.0 (κ) Nu* Nu Nu** Nu 0 4.028 4.030 3.767 3.767 1.667 4.028 4.030 3.767 3.767 0 4.358 – 4.131 – 1.667 3.604 – 3.387 – 0 4.585 – 4.386 – 1.667 3.093 – 2.949 – Nu: Present results Nu*: Results from Ref. [45]

Pe = 10 Pe → ∞ Nu Nu* Nu Nu*** 3.695 3.697 3.656 3.656 3.695 3.697 3.656 3.656 4.061 – 4.020 4.020 3.325 – 3.292 3.292 4.319 – 4.279 4.279 2.909 – 2.887 2.887 Nu**: Results from Ref. [46] Nu***: Results from Ref. [9]

Kn 0.00 0.04 0.08

4. Roughness Effect

The effect of surface roughness may be particularly important in microchannel flows. Roughness characteristics of microchannels are strictly dependent on the manufacturing process. Since the random distribution and small size of the roughness peaks along a surface are quite difficult to define, most investigators neglect this effect in their studies. There is a limited number of publications in open literature compared to other effects in microscale. In one of the first experimental studies in this area water flow through rough

CONVECTIVE HEAT TRANSFER IN MICROSCALE SLIP FLOW

27

fused silica and stainless steel microtubes was investigated, and deviations from theoretical predictions; such as higher friction factor, and early transition from laminar to turbulent flow, were found [15]. Later, heat transfer characteristics were also investigated and due to the surface roughness effect, smaller Nu values were determined [47]. Different models were proposed to represent the effects of surface roughness; such as roughness-viscosity model [15], porous medium layer model [48], and the explicit model [17, 18]. Roughness can reduce or increase Nu depending on the distribution, spacing, and geometry of the obstructions. However one common conclusion is that roughness is more effective at low Kn values. In this case, steady-state, laminar, developing air flow in a parallel-plate microchannel with one rough wall is considered. As shown in the channel schematic in Fig. 6, the roughness is modeled as two-dimensional equilateral triangular elements placed on the bottom wall surface. The relative surface roughness of the wall may be determined by ε = e/D, where e is the height of the roughness elements and D the hydraulic diameter of the channel. In most of the studies in literature, it is stated that silicon microchannels generally have a relative roughness value in the range 0–4%. Thus, in this work, ε = 1.325%, 2.0% are considered [49, 50]. Solid smooth wall, Tw = T u=Ui v=0 T=Ti

H=D/2

y x

e Solid rough wall, Tw = T

Figure 6. Schematic of the rough microchannel.

The equations to be solved are similar to those in the previous section with some minor differences due the change in geometry (parallel-plate microchannel versus microtube). In the solution, slip boundary conditions given in Eqs. (1) and (2) are applied and finite element method is used to solve for the velocity profile and the temperature distribution. Then, from the temperature profile, the local Nu is determined. For the continuum case (Kn = 0), without viscous dissipation, local Nu has a wavy pattern, as shown in Fig. 7, similar to the observations in Refs. [17, 20] for triangular roughness elements. Velocity and temperature gradients are higher at the peaks of the elements, thus local Nu is larger there, while at the bottom corners, the low gradients result in minimum local Nu.

A. GUVENC YAZICIOGLU AND S. KAKAÇ

28 25

Local Nu

20

(a)

smooth e = 1.325%

15 10 5 0 1.9 25

Local Nu

20

1.95

2 x

2.05

2.1

smooth e = 2.0%

(b)

15 10 5 0

1.9

1.95

2

x

2.05

2.1

2.15

Figure 7. Local Nu variation over the roughness elements for Kn = 0, Re = 100 and Br = 0 when (a) ε = 1.325%, (b) ε = 2.0%.

Graphical results are presented in Fig. 8 for the channel averaged Nu (including smooth inlet–outlet sections), including axial conduction and viscous dissipation (Br = 0.1). Without the rarefaction effect, roughness reduces heat transfer. However, with the rarefaction effect, an increase in the average Nu with respect to smooth channel values is observed. Due to the reduced interaction between the gas molecules and channel walls at high Kn values, the increase is less pronounced at high Kn values and more at low Kn values. Moreover, when rarefaction is considered, the average Nu values increase with increasing Pe and relative surface roughness height. In Table 4, average Nu values for the rough section of the channel (representing a channel with a completely rough wall from the inlet to the outlet) are presented for cases where axial conduction and viscous dissipation (Br = 0.1) are both included, compared to smooth channel values. For this case, average Nu takes higher values, except Kn = 0 cases, where the reduction in local Nu between roughness elements is dominant and cannot be compensated by the higher local Nu computed at the other parts of the channel. The

CONVECTIVE HEAT TRANSFER IN MICROSCALE SLIP FLOW

29

general trend is similar to the channel averaged cases presented in Fig. 8; at low Kn, the effect of surface roughness is more prominent and average Nu increases with increasing roughness height. As the flow becomes more rarefied, the importance of relative surface roughness height is reduced and yields nearly the same average Nu values for the considered relative roughness heights. 25 21

21

19

19

17

17

15 13 11 9

smooth e = 1.325% e = 2.0%

23

Nu

Nu

25

smooth e = 1.325% e = 2.0%

23

15 13 11

Pe = 3.5 Br = 0.1

7 0.00

0.02

9 7 0.04

0.06

0.08

0.10

Pe = 70 Br = 0.1 0.00

0.02

Kn

0.04

0.06

0.08

0.10

Kn

Figure 8. Channel averaged Nu compared with fully developed smooth channel values when axial conduction and viscous dissipation (Br = 0.1) are included. TABLE 4. Rough section averaged Nu compared with fully developed smooth channel values when axial conduction and viscous dissipation are included (Br = 0.1).

17.484 13.680 16.450 12.289 9.782 8.090

Rough 1.325% 11.389 26.499 17.768 13.160 10.466 8.662

Rough 2.0% 11.175 29.783 16.450 12.289 9.782 8.090

17.547 13.775 11.298 9.563 8.280 7.295

11.585 28.354 18.330 13.820 11.062 9.184

11.384 32.332 20.324 15.345 12.340 10.295

Pe

Kn

Smooth

3.5

0.00 0.02 0.04 0.06 0.08 0.10

70

0.00 0.02 0.04 0.06 0.08 0.10

30

A. GUVENC YAZICIOGLU AND S. KAKAÇ

5. Temperature-Variable Thermophysical Properties

The earliest studies related to thermophysical property variation in tube flow conducted by Deissler [51] and Oskay and Kakac [52], who studied the variation of viscosity with temperature in a tube in macroscale flow. The concept seems to be well-understood for the macroscale heat transfer problem, but how it affects microscale heat transfer is an ongoing research area. Experimental and numerical studies point out to the non-negligible effects of the variation of especially viscosity with temperature. For example, Nusselt numbers may differ up to 30% as a result of thermophysical property variation in microchannels [53]. Variable property effects have been analyzed with the traditional no-slip/no-temperature jump boundary conditions in microchannels for three-dimensional thermally-developing flow [22] and two-dimensional simultaneously developing flow [23, 26], where the effect of viscous dissipation was neglected. Another study includes the viscous dissipation effect and suggests a correlation for the Nusselt number and the variation of properties [24]. In contrast to the abovementioned studies, the slip velocity boundary condition was considered only recently, where variable viscosity and viscous dissipation effects on pressure drop and the friction factor were analyzed in microchannels [25]. Because of the limited number of studies conducted in this area, simultaneously developing, steady-state, single phase gaseous flow and heat transfer in parallel plate microchannels in the slip flow regime (with slip-flow and temperature-jump boundary conditions) is studied numerically by taking into account the effects of rarefaction, viscous dissipation, and viscosity and thermal conductivity variation with temperature. The geometry is similar to the rough channel geometry, but without the roughness elements. Temperature dependent thermal conductivity is approximated by using a third-order polynomial function k ( T ) = a 0 T 3 + a 1T 2 + a 2 T + a 3 ,

(18)

where ai are constants. Temperature dependent dynamic viscosity is modeled by using Sutherland’s formula μ( T ) = μ 0

T0 + C ⎛ T ⎞ ⎜ ⎟ T + C ⎜⎝ T0 ⎟⎠

3/ 2

,

(19)

where μ0 is the dynamic viscosity evaluated at the reference temperature T0 (273 K), and C is the Sutherland constant (111 K for air). Energy and momentum equations are solved in a coupled manner to account for the viscosity variation. Coupled solutions are made for pressure

CONVECTIVE HEAT TRANSFER IN MICROSCALE SLIP FLOW

31

and velocity for investigating simultaneously developing flow. Variation of specific heat (Cp) and density (ρ) with temperature is not included, since these properties vary in negligible amounts within the studied temperature range (from 20°C, the inlet temperature, to 85°C, the wall temperature). The results, grouped into two categories as variable property (vp) and constant property (cp) are presented in Figs. 9–12. Both negative (fluid heating along the channel) and positive (fluid cooling along the channel) Brinkman values are analyzed, with Tinlet/Twall = 0.75 for heating and Tinlet/Twall = 1.5 for fluid cooling. Moreover Kn = 0.0 and 0.1, and Br = 0.001, 0.01, and 0.1 are considered [54]. An examination of Figs. 9–12 shows that the variation of Nu for cp and vp cases differ up to a certain distance in the channel and there is no significant difference in the fully developed Nu values. Both for the cooling and heating cases, the difference due to variable properties is non-negligible for part of the channel length. The difference in the cp and vp local Nu values decreases with increasing Br. An increase in Br, the nondimensional number representing viscous dissipation, results in the development of the flow in a shorter distance, and in return, the temperature gradients decrease. Since the temperature gradients directly affect the variation in properties, an increase in viscous dissipation reduces the difference due to variable properties. Moreover, the difference in the cp and vp local Nu values also decreases slightly with increasing Kn, representing the degree of rarefaction in the flow. As Kn increases, the flow is less affected by the wall conditions. As the heat transfer at the wall decreases, temperature gradients are reduced, and the difference due to variable properties decreases, as explained above. 17

17

15

15

Nu

13

13

Br � - - - - - - - constant properties variable properties

11 9 7

11 9 7

5

5 0

5

10 15 Dimensionless Length(x/H)

20

Figure 9. Local Nu variation with positive Br = 0.001, 0.01, 0.1 (fluid cooling) values along the microchannel for Kn = 0.01 (Tinlet/Twall = 1.5).

A. GUVENC YAZICIOGLU AND S. KAKAÇ

32 12

12

11

11 - - - - - - - constant properties variable properties

10

Nu

9

10 9

8

8

7

7 Br 

6

6

5

5 0

5

10 15 Dimensionless Length(x/H)

20

Figure 10. Local Nu variation with positive Br = 0.001, 0.01, 0.1 (fluid cooling) values along the microchannel for Kn = 0.1 (Tinlet/Twall = 1.5).

25

25

Br 

20

20 15

Nu

15

-------

10 5

Br 

constant properties variable properties

10 5 0

0 0

5

10 15 Dimensionless Length(x/H)

20

Figure 11. Local Nu variation with negative Br = −0.001, −0.01, −0.1 (fluid heating) values along the microchannel for Kn = 0.01 (Tinlet/Twall = 0.75).

CONVECTIVE HEAT TRANSFER IN MICROSCALE SLIP FLOW 12

12

Br 

10

Nu

33

10

8

8

6

6

4

Br 

- - - - - - - constant properties

4

variable properties

2

2 0

0

5

10 15 Dimensionless Length(x/H)

20

0

Figure 12. Local Nu variation with negative Br = −0.001, −0.01, –0.1 (fluid heating) values along the microchannel for Kn = 0.1 (Tinlet/Twall = 0.75).

6. Conclusions

In this lecture, a variety of results for convective heat transfer in microtubes and microchannels in the slip flow regime under different conditions have been presented. Both constant wall temperature and constant wall heat flux cases have been analyzed in microtubes, including the effects of rarefaction, axial conduction, and viscous dissipation. In rough microchannels the abovementioned effects have also been investigated for the constant wall temperature boundary condition. Then, temperature-variable dynamic viscosity and thermal conductivity of the fluid were considered, and the results were compared with constant property results for microchannels, with the effects of rarefaction and viscous dissipation. The conclusions drawn for microscale slip flow may be summarized as follows: 1. For high values of rarefaction (high Kn) and temperature jump (high κ), the effect of axial conduction is negligible. However for lower rarefaction and temperature jump values, as Pe decreases (axial conduction effect

34

2.

3.

4. 5.

6.

A. GUVENC YAZICIOGLU AND S. KAKAÇ

increases), the fully developed Nu increases more significantly. It may be concluded from these observations that the effect of axial conduction should not be neglected for low-rarefied flows and with low values of temperature jump. Regardless of the effect of axial conduction, for a given Kn and κ value, the flow reaches the same fully developed Nu value for all values of Br. When the fluid is cooled (Br > 0 for constant wall temperature and Br < 0 for constant wall heat flux) Nu takes higher values. The increase in fully developed Nu value with the added effect of viscous dissipation suggests that this effect should not be neglected for long channels. Since micro conduits have high length-to-diameter ratios, even for low values of Br, viscous dissipation effect must be considered. In general, for constant wall temperature and constant wall heat flux conditions, velocity slip and temperature jump affect the heat transfer in opposite ways: a large slip on the wall will increase the convection along the surface. On the other hand, a large temperature jump will decrease the heat transfer by reducing the temperature gradient at the wall. Therefore, neglecting temperature jump will result in the overestimation of the heat transfer coefficient. When viscous dissipation is neglected, the effect of axial conduction should be included for Pe < 100. When viscous dissipation is included in the analysis, axial conduction is significant for Pe < 100 for short channels. When surface roughness is considered, the fully developed Nu increases with respect to the smooth channel value for rarefied flows, but not for continuum, for all values of Peclet number. The increase in Pe increases Nu more for low values of rarefaction. It appears that, for the range Kn considered in this work, the maximum heat transfer is observed for Kn = 0.02. When viscous dissipation effect is included, in either fluid heating or fluid cooling, Nu increases, and more significantly with higher relative roughness values. The variation of thermophysical properties affects the temperature profile, but not the velocity field. For both fluid heating cooling cases, the variation in local Nu due to temperature-variable properties is significant in the developing region. However the fully developed Nu is almost invariant for constant and variable properties cases due to reduced temperature gradients in this region.

Acknowledgement

The authors would like to thank the Turkish Scientific and Technical Research Council, TUBITAK, Grant No. 106M076, for financial support.

CONVECTIVE HEAT TRANSFER IN MICROSCALE SLIP FLOW

35

References 1. D.B. Tuckerman and R.F. Pease, Optimized convective cooling using micromachined structure, Journal of the Electrochemical Society 129, P. C 98 (1982). 2. P.Y. Wu and W.A. Little, Measurement of heat transfer characteristics of gas flow in fine channels heat exchangers used for microminiature refrigerators, Cryogenics 24, 415–420 (1984). 3. S.B. Choi, R.F. Barron, and R.O. Warrington, Fluid flow and heat transfer in microtubes, Micromechanical Sensors, Actuators, and Systems, ASME DSC 32, 123–134 (1991). 4. C.P. Tso and S.P. Mahulikar, Experimental verification of the role of Brinkman number in microchannels using local parameters, International Journal of Heat and Mass Transfer 43, 1837–1849 (2000). 5. J.Y. Jung and H.Y. Kwak, Fluid flow and heat transfer in microchannels with rectangular cross section, Heat Mass Transfer 44, 1041–1049 (2008). 6. H.S. Park and J. Punch, Friction factor and heat transfer in multiple microchannels with uniform flow distribution, International Journal of Heat and Mass Transfer 51, 4535–4543 (2008). 7. R.F. Barron, X.M. Wang, R.O. Warrington, and T.A. Ameel, The Graetz problem extended to slip flow, International Journal of Heat and Mass Transfer 40, 1817–1823 (1997). 8. T.A. Ameel, R.F. Barron, X.M. Wang, and R.O. Warrington, Laminar forced convection in a circular tube with constant heat flux and slip flow, Microscale Thermophysical Engineering 1, 303–320 (1997). 9. B. Cetin, H. Yuncu, and S. Kakac, Gaseous flow in microconduits with viscous dissipation, International Journal of Transport Phenomena 8, 297– 315 (2006). 10. B. Cetin, A. Guvenc Yazicioglu, and S. Kakac, Fluid flow in microtubes with axial conduction including rarefaction and viscous dissipation, International Communications in Heat and Mass Transfer 35, 535–544 (2008). 11. G. Tunc and Y. Bayazitoglu, Heat transfer in microtubes with viscous dissipation, International Journal of Heat and Mass Transfer 44, 2395–2403 (2001). 12. G. Tunc and Y. Bayazitoglu, Convection at the entrance of micropipes with sudden wall temperature change, Proceedings of IMECE, November 17–22, 2002, New Orleans, Louisiana. 13. S.P. Yu and T.A. Ameel, Slip-flow heat transfer in rectangular microchannels, International Journal of Heat and Mass Transfer 44, 4225–4235 (2001). 14. H.-E. Jeong and J.-T. Jeong, Extended Graetz problem including streamwise conduction and viscous dissipation in microchannel, International Journal of Heat and Mass Transfer 49, 2151–2157 (2006). 15. Gh.M. Mala and D. Li, Flow characteristics of water in microtubes, International Journal of Heat and Fluid Flow 20, 142–148 (1999). 16. C. Kleinstreuer and J. Koo, Computational analysis of wall roughness effect for liquid flow in micro-conduits, Journal of Fluids Engineering 126, 1–9 (2004). 17. G. Croce and P. D’Agaro, Numerical analysis of roughness effect on microtube heat transfer, Superlattices and Microstructures 35, 601–616 (2004).

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18. G. Croce and P. D’Agaro, Numerical simulation of roughness effect on microchannel heat transfer and pressure drop in laminar flow, Journal of Physics D: Applied Physics 38, 1518–1530 (2005). 19. G. Croce, P. D’Agaro, and C. Nonini, Three-dimensional roughness effect on microchannel heat transfer and pressure drop, International Journal of Heat and Mass Transfer 50, 5249–5259 (2007). 20. G. Croce, P. D’Agaro, and A. Filippo, Compressibility and rarefaction effects on pressure drop in rough microchannels, Heat Transfer Engineering 28, 688– 695 (2007). 21. Y. Ji, K. Yuan, and J.N. Chung, Numerical simulation of wall roughness on gaseous flow and heat transfer in a microchannel, International Journal of Heat and Mass Transfer 49, 1329–1339 (2006). 22. Z. Li, X. Huai, Y. Tao, and H. Chen, Effects of thermal property variations on the liquid flow and heat transfer in microchannel heat sinks, Applied Thermal Engineering 27, 2803–2814 (2007). 23. S.P. Guidice, C. Nonino, and S. Savino, Effects of viscous dissipation and temperature dependent viscosity in thermally and simultaneously developing laminar flows in microchannels, International Journal of Heat and Fluid Flow 28, 15–27 (2007). 24. J.T. Liu, X.F. Peng, and B.X. Wang, Variable-property effect on liquid flow and heat transfer in microchannels, Chemical Engineering Journal 141, 346– 353 (2008). 25. M.S. El-Genk and I. Yang, Numerical analysis of laminar flow in micro-tubes with a slip boundary, Energy Conversion and Management 50, 1481–1490 (2009). 26. N.P. Gulhane and S.P. Mahulikar, Variations in gas properties in laminar micro-convection with entrance effect, International Journal of Heat and Mass Transfer 52, 1980–1990 (2009). 27. M. Gad-El-Hak, The fluid mechanics of microdevices, Journal of Fluids Engineering 121, 5–33 (1999). 28. G.L. Morini, Single-phase convective heat transfer in microchannels: A review of experimental results, International Journal of Thermal Sciences 43, 631–651 (2004). 29. Y. Bayazitoglu and S. Kakac, Flow regimes in microchannel single-phase gaseous flow, Microscale Heat Transfer – Fundamentals and Applications in Biological Systems and MEMS, edited by S. Kakac, L. Vasiliev, Y. Bayazitoglu, and Y. Yener (Kluwer Academic Publishers, The Netherlands 2005). 30. G. Hetsroni, A. Mosyak, E. Pogrebnyak, and L.P. Yarin, Heat transfer in micro-channels: Comparison of experiments with theory and numerical results, International Journal of Heat and Mass Transfer 25–26, 5580–5601 (2005). 31. Y. Yener, S. Kakac, M. Avelino, and T. Okutucu, Single phase forced convection in microchannels – State-of art-review, Microscale Heat TransferFundamentals and Applications in Biological Systems and MEMS, edited by S. Kakac, L. Vasiliev, Y. Bayazitoglu, and Y. Yener (Kluwer Academic Publishers, The Netherlands 2005). 32. R.M. Cotta, S. Kakaç, M.D. Mikhailov, F.V. Castellos, and C.R. Cardoso, Transient flow and thermal analysis in microfluidics, Microscale Heat TransferFundamentals and Applications in Biological Systems and MEMS, edited by

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S. Kakac, L. Vasiliev, Y. Bayazitoglu, and Y. Yener (Kluwer Academic Publishers, The Netherlands 2005). P. Rosa, T.G. Karayiannis, and M.W. Collins, Single-phase heat transfer in microchannels: The importance of scaling, Applied Thermal Engineering 29, 3447–3468 (2009). G. Karniadakis, A. Beskok, and N. Aluru, Microflows and Nanoflows: Fundamentals and Simulation (Springer, New York, 2005). C.B. Sobhan and G.P. Peterson, Microscale and Nanoscale Heat Transfer: Fundamentals and Engineering Applications (CRC Press, Florida, 2008). L.P. Yarin, A. Mosyak, and G. Hetsroni, Fluid Flow, Heat Transfer and Boiling in Micro-Channels (Springer, New York, 2008). Y. Bayazitoglu, G. Tunc, K. Wilson, and I. Tjahjono, Convective heat transfer for single phase gases in microchannel slip flow: Analytical solutions, Microscale Heat Transfer – Fundamentals and Applications in Biological Systems and MEMS, edited by S. Kakac, L. Vasiliev, Y. Bayazitoglu, and Y. Yener (Kluwer Academic Publishers, The Netherlands 2005). N.T. Obot, Toward a better understanding of friction and heat/mass transfer in microchannels – A literature review, Microscale Thermophysical Engineering 6, 155–173 (2002). A. Beskok, G.E. Karniadakis, and W. Trimmer, Rarefaction, compressibility effects in gas microflows, Journal of Fluids Engineering 118, 448–456 (1996). W. Sun, S. Kakac, and A. Guvenc Yazicioglu, A numerical study of singlephase convective heat transfer in microtubes for slip flow, International Journal of Thermal Sciences 46, 1084–94 (2007). B. Cetin, Analysis of single phase convective heat transfer in microtubes and microchannels, M.Sc. Thesis, Middle East Technical University, Ankara, Turkey (2005). M. Barisik, Analytical solution for single phase microtube heat transfer including axial conduction and viscous dissipation, M.Sc. Thesis, Middle East Technical University, Ankara, Turkey (2008). G. Tunc and Y. Bayazitoglu, Heat transfer in microtubes with viscous dissipation, International Journal of Heat and Mass Transfer 44, 2395–2403 (2001). S. Kakac and Y. Yener, Convective Heat Transfer (CRC Press, Florida, 1994). R.K. Shah and A.L. London, Laminar flow forced convection in ducts, Advances in Heat Transfer, edited by T.F.Jr. Irvine, and J.P. Hartnett (Academic Press, New York 1978), pp. 78–152. J. Lahjomri and A. Oubarra, Analytical solution of the Graetz problem with axial conduction, Journal of Heat Transfer 121, 1078–1083 (1999). W. Qu, Gh.M. Mala, and D. Li, Heat transfer for water flow in trapezoidal silicon microchannels, International Journal of Heat and Mass Transfer 43, 3925–3936 (2000). J. Koo and C. Kleinstreuer, Analysis of surface roughness effects on heat transfer in micro-conduits, International Journal of Heat and Mass Transfer 48, 2625–2634 (2005). M.B. Turgay and A. Guvenc Yazicioglu, Effect of surface roughness in parallelplate microchannels on heat transfer, Numerical Heat Transfer 56, 497–514 (2009).

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50. M.B. Turgay, Effect of surface roughness in microchannels on heat transfer, M.Sc. Thesis, Middle East Technical University, Ankara, Turkey (2008). 51. R.G. Deisler, Analytical investigation of turbulent flow in smooth pipes with heat transfer, with variable fluid properties for Prandtl number of 1, NACA Technical Note 2242 (1950). 52. R. Oskay and S. Kakac, Effect of viscosity variations on forced convection heat transfer in pipe flow, METU Journal of Pure and Applied Sciences 6, 211–230 (1973). 53. H. Herwig and S.P. Mahulikar, Variable property effects in single-phase incompressible flows through microchannels, International Journal of Thermal Sciences 45, 977–981 (2006). 54. C. Gozukara, Heat transfer analysis of single phase forced convection in microchannels and microtubes with variable property effect, M.Sc. Thesis, Middle East Technical University, Ankara, Turkey (2010).

DIRECT AND INVERSE PROBLEMS SOLUTIONS IN MICRO-SCALE FORCED CONVECTION C.P. NAVEIRA-COTTA1, R.M. COTTA1, H.R.B. ORLANDE1, AND S. KAKAÇ2 1

Laboratory of Transmission and Technology of Heat, LTTC Mechanical Engineering Department, COPPE & POLI, Cx. Postal 68503 CEP 21945-970, Universidade Federal do Rio de Janeiro, RJ, Brasil, [email protected] 2 TOBB University of Economics & Technology, Ankara, Turkey

1. Introduction The analysis of internal flows in the slip-flow regime gained an important role along the last two decades in connection with micro-electromechanical systems (MEMS) applications and in the thermal control of microelectronics, as reviewed in different sources [1–5]. Several steady-state incompressible flow situations in laminar regime within simple geometries, such as circular micro-tubes and parallel-plate micro-channels, developed for the slip flow regime, have been employed in the heat transfer analysis of micro-systems [6, 7]. Also recently in Refs. [8–12], the analytical contributions were directed towards more general steady and transient problem formulations, including viscous dissipation, axial diffusion in the fluid and three-dimensional flow geometries. In this context, the first goal of this lecture is thus to illustrate the results obtained from a fairly general hybrid numerical–analytical solution for temperature distributions in a fluid flowing through two- or three-dimensional micro-channels, taking into account the velocity slip and temperature jump at the walls surfaces. For this purpose, a flexible approach was employed [13], based on formal solutions of the energy equation as obtained via the classical integral transform method [14], in association with the Generalized Integral Transform Technique, GITT [15–18], which was used for the solution of the required eigenvalue problem [19–21]. This method is here applied for illustration purposes in the integral transformation of the energy equation for thermally developing flow within parallel-plates micro-channels under the slip flow regime. This combination of solution methodologies provides a very effective eigenfunction expansion solution, through the fast converging analytical representation in all the space coordinates, together

S. Kakaç et al. (eds.), Microfluidics Based Microsystems: Fundamentals and Applications, DOI 10.1007/978-90-481-9029-4_3, © Springer Science + Business Media B.V. 2010

39

40

C.P. NAVEIRA-COTTA ET AL.

with a flexible and reliable numerical–analytical approach for the Sturm– Liouville eigenvalue problem solution. The accuracy of such analytic-type solutions for the direct forced convection problem in micro-channels are however dependent on the also accurate determination of the momentum and thermal accommodation coefficients, as required by the slip and temperature jump boundary conditions inherent to the slip flow model that accounts for non-continuum effects at the fluid–surface interactions. Fundamental experimental work on rarefied gas dynamics have offered measurements of the tangential momentum accommodation coefficient, requiring, for instance, high vacuum and molecular beams impinging on carefully prepared substrates, such as recently reviewed in Ref. [22], but very few results are available for the actual conditions of the flow configuration within micro-channels and their actual bounding walls [23, 24]. The experiments indicate that the tangential momentum accommodation coefficient generally assumes values between 0.2 and 1.0, with the lower limit being associated with exceptionally smooth surfaces and the upper limit with very rough or highly oxidized surfaces [4]. Similar considerations are pertinent to the measurement of thermal accommodation coefficients [25], where an even more limited experimental database is available, and apparently no previous work seems to be available on the identification of this coefficient in actual heat and fluid flow conditions within specific pressure and temperature levels pertinent to MEMS applications, and in addition for actual morphology and finishing of the microchannel walls. Thus, we take advantage of the accuracy, robustness and efficiency of the direct problem solution, to tackle the associated inverse heat transfer problem analysis [26, 27] towards the simultaneous estimation of momentum and thermal accommodation coefficients in micro-channel flows with velocity slip and temperature jump. A Bayesian inference approach is adopted in the solution of the identification problem, based on the Monte Carlo Markov Chain method (MCMC) and the Metropolis–Hastings algorithm [28–30]. Only simulated temperature measurements at the external faces of the channel walls, obtained for instance via infrared thermography [30], are used in the inverse analysis in order to demonstrate the capabilities of the proposed approach. A sensitivity analysis allows for the inspection of the identification problem behavior when the external wall Biot number is also included among the parameters to be estimated. 2. Direct Problem Solution The approach here employed in the direct problem solution for forced convection in micro-channels, is borrowed from a recent work on diffusion in heterogeneous media, with arbitrarily space variable thermophysical

DIRECT AND INVERSE PROBLEMS SOLUTIONS

41

properties [13]. In this sense, the dimensionless velocity fields are mathematically equivalent to space variable thermal capacitances, and the solution procedure is here briefly described. For a general purpose automatic implementation, it is quite desirable to employ a flexible computational approach to handle eigenvalue problems with arbitrarily variable coefficients. Thus, the Generalized Integral Transform Technique (GITT) is here employed in the solution of the Sturm–Liouville problem via the proposition of a simpler auxiliary eigenvalue problem, and expanding the unknown eigenfunctions in terms of the chosen basis [19]. Also, the variable equation coefficients may themselves be expanded in terms of known eigenfunctions [13], so as to allow for a fully analytical implementation of the coefficients matrices in the transformed system. The equation coefficients of the auxiliary problem are simpler forms of the original coefficients, chosen so as to allow for an analytical solution of the auxiliary problem [13, 19]. Then, the resulting algebraic problem can be numerically solved to provide results for the eigenvalues and eigenvectors, which will be combined to provide the desired eigenfunctions of the original eigenvalue problem, as described in further detail in Ref. [13]. In order to illustrate both the direct and inverse problems solutions, we consider the two-dimensional situation of parallel-plates micro-channels, with steady thermally developing laminar flow under the slip flow regime. The fluid is assumed to enter the channel with a fully developed velocity profile and a uniform temperature, exchanging heat by convection with the surroundings with an external heat transfer coefficient that might not be known a priori in the inverse problem analysis. Thermophysical properties are assumed to be constant, while axial conduction and viscous dissipation are neglected. Although more involved formulations could be handled by the proposed approach, the direct problem solution is here illustrated for the parallel-plates channel incompressible flow case, previously solved in Ref. [6, 7] for the prescribed wall temperature boundary condition, and here written in a more general form including the external wall convection effect:

W (Y )

∂θ (Y , Z ) ∂ 2θ (Y , Z ) , 0 < Y < 1, Z > 0 = ∂Z ∂Y 2

θ (Y ,0) = 1, ∂θ (Y , Z ) ∂Y

Y =0

= 0,

∂θ (Y , Z ) ∂Y

Y =1

=−

0 ≤ Y ≤1 Bi θ (1, z ), Z > 0 1 + 2 Knβt Bi

where the corresponding dimensionless groups are given by

(1a) (1b) (1c,d)

C.P. NAVEIRA-COTTA ET AL.

42

Y=

T ( y, z ) − T∞ αz y ; Z= ; θ (Y , Z ) = ; 2 y1 uav y1 T0 − T∞ W (Y ) =

hy λ u( y) ; Bi = 1 ; Kn = uav kf 2 y1

(2a–f)

and,

βt =

(2 − α t ) 2γ 1 α t (γ + 1) Pr

(2g)

is the wall temperature jump coefficient and αt is the thermal accommodation coefficient, λ is the molecular mean free path, γ=cp/cv, while cp is specific heat at constant pressure, cv specific heat at constant volume and Pr is the Prandtl number. The dimensionless velocity profile is given as [6]: W (Y ) =

6 Knβ v + 3(1 − Y 2 ) / 2 1 + 6 Knβ v

(3a)

where,

βv =

(2 − α m )

(3b)

αm

is the wall velocity slip coefficient and αm is the tangential momentum accommodation coefficient. The ratio of the boundary conditions coefficients is also of interest, and given as β = βt/βv. The solution of the dimensionless problem (1) is then a special case from the general solution given in Ref. [13], written as [6]: ∞

θ (Y , Z ) = ∑ f iψ% i (Y )e − μ Z , with f i = − 2 i

i =1

ψ% i' (1) μi2

(4a,b)

where ψi(Y) are eigenfunctions of the following Sturm–Liouville problem, with the corresponding normalization integral and normalized form of the eigenfunction: d 2ψ i (Y ) + μi2W (Y )ψ i (Y ) = 0, 2 dY

dψ i (Y ) dY

Y =0

= 0,

dψ i (Y ) dY

Y =1

=−

0 < Y ΔtDO. Their eighth-order asymptotic expression for the bubble nose film thickness was derived from two prior correlations of Moriyama and Inoue [27]:

⎛ δn νl ⎞ ⎟ = 0.29 ⎜⎜ 3 ⎟ D WD ⎝ ⎠

0.84

[(0.07We

)

0.41 −8

+ 0.1−8

]

−1 8

(16)

MECHANISMS OF BOILING IN MICROCHANNELS

97

with νl the fluid’s kinematic viscosity and We the Weber number (= ρlDW2/σ). In terms of heat transfer, the authors suggested a transient behavior of the heat transfer coefficient, determined by the local flow conditions: (1) single phase convection during the passage of a liquid slug or a dry-zone (vapor slug in Fig. 6), and (2) conduction of heat through the liquid film during the passage of an elongated bubble. The local time-averaged heat transfer coefficient was thus

α( z ) =

Δt L ( z ) α L ( z ) + Δt F ( z ) α F ( z ) + Δt D ( z )α D ( z ) Δt

(17)

with ΔtL the residence time of the liquid slug given by Eq. (11), and ΔtF and ΔtD the residence times of the bubble and dry-zone, respectively, are:

Δt F = ΔtV Δt F = Δt DO

and and

Δt D = 0

for

Δt D = ΔtV − Δt DO

for

ΔtV ≤ Δt DO ΔtV > Δt DO

(18)

The single-phase heat transfer coefficients in Eq. (17) were determined by asymptotic interpolation of standard correlations, i.e. Shah and London (SL) for Re ≤ 2,300 and Gnielinski (G) for Re > 2,300. Thus,

(

4 Nu L , D = Nu SL + Nu G4

)

14

(19)

with

Nu SL = 0.91 3 Pr

ReD L

and

f 23 ( Re − 1, 000) Pr ⎡ ⎛D⎞ ⎤ NuG = 8 1 + ⎢ ⎜ ⎟ ⎥ f ⎝ L ⎠ ⎥⎦ 23 1 + 12.7 ( Pr − 1) ⎢⎣ 8

(20)

These are the average laminar and transition to turbulent Nusselt numbers over the respective single-phase lengths L. In Gnielinski’s correlation the friction factor is taken as f = (1.82 log10 Re − 1.64) −2 . The bubble heat transfer coefficient, αF, was determined by applying simple conduction theory through the liquid film:

98

J.R. THOME AND L. CONSOLINI

1 α F ( z) = Δt F

Δt F

∫ 0

kl 2 kl dt ≅ δ(t , z ) δ n + δt

(21)

with δt the minimum local film thickness (the subscript t stands for the bubble tail) given from Eq. (14) as:

δt ( z) = δ n ( z) − δ t ( z ) = δ min

q ΔtV ρ l hlv

for

for

ΔtV ≤ Δt DO ΔtV > Δt DO

(22)

The final equation that provided closure to the model was for the passage period, Δt, of the liquid–bubble–vapor triplet. The authors correlated Δt with the wall heat flux and the fluid properties represented by the reduced pressure, proposing the following dimensional correlation (q in W/m2 and Δt in s):

⎛ 1 ⎞ Δt = ⎜ pr0.5 q ⎟ ⎝ 3,328 ⎠

−1.74

(23)

where pr is the reduced pressure (pr = psat/pc). The above mechanistic type of model is only strictly for describing the heat transfer process in the elongated bubble flow regime. Significantly, it explicitly explains the influence of heat flux on the flow boiling heat transfer coefficient while empirical correlations do not. Due to lack of an appropriate flow pattern map to classify the existing boiling database as such at the time of its development, the authors used all of the database they put together from seven independent studies for its development, irrespective of the flow regimes involved. It is recommended that a general flow pattern based model be developed in the future to cover all three principal flow regimes, not just one. Furthermore, the model highlights the sensitivity of the slug flow regime heat transfer process to the frequency, the nose film thickness and the onset of dry-out thickness of elongated bubbles. Hence, future experimental studies should address these features of the flow to better understand and model them. For example, the recent mechanistic flow pattern map of Revellin and Thome [28], based on the rate of collision of elongated bubbles to define the flow pattern transitions and predict the bubble frequencies and bubble length distributions (see also [29]), may be a starting point for such a model.

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6. Comparing Prediction Methods

Figure 7 depicts a comparison of four empirical methods and the lone mechanistic method described above for R-134a boiling in a 0.5 mm microchannel by Consolini [30]. As can be seen, the Lazarek and Black [1] and the Tran et al. [13] correlations predict no influence of vapor quality and hence give a fixed value at all values of x, even at very high values of x. The Zhang et al. [25] correlation depicts a slight increase in heat transfer at low vapor quality, nearly no effect of vapor quality at intermediate values and then a slight downward tendency, all trends which are reasonable according to some data sets, but extrapolation of this method to high vapor qualities is clearly not appropriate. The Kandlikar and Balasubramanian [24] correlation shows a tendency to decrease with vapor quality before flattening off at the present simulated conditions. Meanwhile, the Thome et al. [8] three-zone model for elongated bubble flows depicts a monotonic decrease in the heat transfer coefficient when extrapolating it to low vapor qualities characterized by bubbly flow and to high vapor qualities characterized by annular flow. Notable in this simulation is the large discrepancy in the predicted values, which range from about 4,000 to 11,000 W/m2K. Furthermore, it is evident that reliable application of heat transfer prediction methods requires use of a diabatic flow pattern map, such as that in Ref. [28], to determine the critical vapor quality and hence the location where the postdry-out heat transfer regime begins with much lower heat transfer coefficients. Some of the methods presented above have been recently been compared to independent heat transfer databases. For instance, Shiferaw et al. [31] measured local flow boiling data for R-134a in a 2.01 mm stainless steel tube at 8 bar. The three-zone model predicted most of their data within ±20% while their other data at 12 bar were less well predicted, yielding a spread of ±30% while showing a tendency to under predict with increasing pressure. Agostini et al. [21] compared their multi-micro-channel database obtained in collaboration with IBM to selected methods. Utilizing only the data at vapor qualities above 5% to eliminate the inlet effects of the 90° turn in the flow and the orifice at the entrance to each channel, their database used for the comparison consisted of 1,438 data points for R-245fa and R-236fa and accounted for the fin efficiency effects. The three-zone model using the measured surface roughness (0.17 μm for their silicon channels) in place of the original value of 0.3 μm predicted 90% of these data within ±30% (only 31% were predicted within ±30% using the original value, just to indicate the sensitivity of the surface roughness in the model and on the heat transfer process). The Kandlikar and Balasubramanian [24] correlation captured 58% and the Zhang et al. [25] correlation yielded 19% of the data within ±30%.

J.R. THOME AND L. CONSOLINI

100 16000

Lazarek Tran Zhang Kandlikar Thome

heat transfer coefficient (W/m2K)

14000 12000 10000 8000 6000 4000 2000 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

vapor quality

Figure 7. Predicted two-phase heat transfer coefficients. Values for R-134a at 7 bar, with q = 50 kW/m2, G = 500 kg/m2s, in a D = 0.5 mm circular, stainless steel channel (Taken from Ref. [30]).

Consolini and Thome [12] compared their extensive database for R-134a, R-236fa and R-245fa for stable flow conditions for 0.510 and 0.790 mm stainless steel test sections at near ambient saturation temperatures to five of the methods presented earlier. Using the Revellin and Thome [28] diabatic flow pattern map described earlier in this chapter to eliminate the annular flow data from the comparison, they found that 77% of the remaining data were predicted within ±30% by the three-zone model (but still including the bubble flow data). In comparison, the Lazarek and Black [1] correlation captured 88% of the entire database within ±30%, while the Tran et al. [13] correlation captured only 4% within this range, the Kandlikar and Balasubramanian [24] correlation captured 21% and the Zhang et al. [25] correlation yielded 58%. 7. Conclusions

Current experimentation on micro-channel two-phase flows has provided some evidence of the heat transfer mechanisms that govern the micro-scale flow boiling process: (i) at low vapor qualities, when bubbly flow is the dominant flow pattern, thermal transport is primarily associated to nucleate boiling, (ii) at intermediate vapor qualities, with the intermittent passage of elongated bubbles and slugs of liquid, heat is transferred by single phase

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convection in the all liquid and vapor zones, and by conduction/convection through the thin films surrounding the elongated bubbles, and is also highly dependent on the bubble frequency, and (iii) at the high vapor quality characteristic of annular flows, the heat transfer process is expected to be governed by the convective and conductive mechanisms involved in evaporation of the annular film. The presence of nucleate boiling, which many have suggested to be the dominant heat transfer mode, even at high vapor qualities, without physical or theoretical proof, is not substantiated by flow visualizations that report an extensive presence of small bubbles (relative to the channel size) only at the very low vapor qualities. The strong dependency of the boiling heat transfer coefficients on the heat flux is instead mechanistically explainable by the thin film evaporation process and the cyclical heat transfer process occurring in elongated bubble flows, whose elongated bubble frequency and transient heat conduction process are strong functions of heat flux. In addition, the experimental heat transfer coefficients for annular flow pose additional questions, since in this region the values of α do not exhibit the expected increase with x, but rather remain constant or even decrease as evaporation progresses. Future investigations should better address the issues of the heat transfer mechanisms in micro-channel flow boiling, the effect of surface roughness and flow regimes, rather than just continue to add new heat transfer data to the literature. NOMENCLATURE

Latin Bo C Cv D F Fr f G h g k L Nu p Pr q

Boiling number, dimensionless Chisholm parameter, dimensionless Convection number, dimensionless diameter, m two-phase factor, dimensionless Froude number, dimensionless friction factor, dimensionless mass velocity, kg/m2s specific enthalpy, J/kg gravitational acceleration, m/s2 thermal conductivity, W/m/K length, m Nusselt number, dimensionless pressure, Pa Prandtl number, dimensionless heat flux, W/m2

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102

R Re S T t W We X x z

radius, m Reynolds number, dimensionless boiling suppression factor, dimensionless temperature, °C time, s mean axial velocity direction, m/s Weber number, dimensionless Martinelli parameter, dimensionless vapor quality, dimensionless axial coordinate, m

Greek α δ μ ν ρ σ

heat transfer coefficient, W/m2/K liquid film thickness, m dynamic viscosity, Pa s kinematic viscosity, m2/s density, kg/m3 surface tension, N/m

Subscripts c cv D DO F G L l lam lo lv min n nb npb r SL sat sf t tt

critical convective vaporization dry-zone dry-out elongated bubble/evaporating film Gnielinski liquid slug liquid laminar liquid-only liquid–vapor minimum bubble nose nucleate boiling nucleate pool boiling reduced Shah and London saturation surface-fluid bubble tail turbulent–turbulent

MECHANISMS OF BOILING IN MICROCHANNELS

V v

103

elongated bubble + dry zone vapor

References 1. Lazarek, G. M., and Black, S. H., Evaporative Heat Transfer, Pressure Drop and Critical Heat Flux in a Small Vertical Tube with R-113, Int. J. Heat and Mass Transfer, 25(7), 945–960 (1982). 2. Agostini, B., and Thome, J. R., Comparison of an Extended Database for Flow Boiling heat transfer Coefficients in Multi-Microchannel Elements with the Three-Zone Model, ECI Heat Transfer and Fluid Flow in Microscale, Sept. 25–30, 2005, Castelvecchio Pascoli, Italy. 3. Tripplett, K. A., Ghiaasiaan, S. M., Abdel-Khalik, S. I., and Sadowski, D. L., Gas-Liquid Two-Phase Flow in Micro-Channels Part I: Two-Phase Flow Patterns, Int. J. Multiphase Flow, 25, 377–394 (1999). 4. Serizawa, A., Feng, Z., and Kawara, Z., Two-Phase Flow in Microchannels, Experimental Thermal and Fluid Science, 26, 703–714 (2002). 5. Revellin, R., Dupont, V., Thome, J.R., and Zun, I., Characterization of diabatic two-phase flows in micro-channels: flow parameter results for R-134a in a 0.5mm channel, Int. J. Multiphase Flow, 32, 755–774 (2006). 6. Cornwell, K., and Kew, P. A., Boiling in Small Parallel Channels, in Energy Efficiency in Process Technology, Elsevier Applied Science, 624–638, London, 1993. 7. Jacobi, A. M., and Thome, J. R., Heat Transfer Model for Evaporation of Elongated Bubble Flows in Microchannels, Journal of Heat Transfer, 124, 1131–1136 (2002). 8. Thome, J. R., Dupont, V., and Jacobi, A. M., Heat Transfer Model for Evaporation in Microchannels. Part I: presentation of the model, Int. J. Heat and Mass Transfer, 47, 3375–3385 (2004). 9. Kew, P. A., and Cornwell, K., Correlations for the Prediction of Boiling Heat Transfer in Small-Diameter Channels, Applied Thermal Engineering, 17, 705– 715 (1997). 10. Kandlikar, S. G., Heat Transfer Mechanisms During Flow Boiling in Microchannels, Journal of Heat Transfer, 126, 8–16 (2004). 11. Bergles, A. E., and Kandlikar, S. G., On the Nature of Critical Heat Flux in Microchannels, Journal of Heat Transfer, 127, 101–107 (2005). 12. Consolini, L., and Thome J. R., Micro-Channel Flow Boiling Heat Transfer of R-134a, R-236fa, and R-245fa, J. Microfluidics and Nanofluidics, doi: 10.1007/ s10404-008-0348-7 (2008). 13. Tran, T. N., Wambsganss, M. W., and France, D. M., Small Circular- and Rectangular-Channel Boiling with Two Refrigerants, Int. J. Multiphase Flow, 22(3), 485–498 (1996).

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14. Bao, Z. Y., Fletcher, D. F., and Haynes, B. S., Flow Boiling Heat Transfer of Freon R11 and HCFC123 in Narrow Passages, Int. J. Heat and Mass Transfer, 43, 3347–3358 (2000). 15. Lihong, W., Min, C., and Groll, M., Experimental Study of Flow Boiling Heat Transfer in Mini-Tube, ICMM2005, 2005. 16. Lin, S., Kew, P. A., and Cornwell, K., Two-Phase Heat Transfer to a Refrigerant in a 1mm Diameter Tube, Int. J. Refrigeration, 24, 51–56 (2001). 17. Saitoh, S., Daiguji, H., and Hihara, E., Effect of Tube Diameter on Boiling Heat Transfer of R-134a in Horizontal Small-Diameter Tubes, Int. J. Heat and Mass Transfer, 48, 4973–4984 (2005). 18. Martin-Callizo, C., Ali, R., and Palm, B., New Experimental Results on Flow Boiling of R-134a in a Vertical Microchannel, UK Heat Transfer 2007 Proceedings, Edinburgh, 2007. 19. Sumith, B., Kaminaga, F., and Matsumura, K., Saturated Flow Boiling of Water in a Vertical Small Diameter Tube, Experimental Thermal and Fluid Science, 27, 789–801 (2003). 20. Agostini, B., Thome, J. R., Fabbri, M., Calmi, D., Kloter, U., and Michel, B., High Heat Flux Flow Boiling in Silicon Multi-Microchannels: Part I – Heat Transfer Characteristics of R-236fa, Int. J. Heat Mass Transfer, doi:10.1016/ j.ijheatmasstransfer.2008.03.006 (2008). 21. Agostini, B., Thome, J. R., Fabbri, M., Calmi, D., Kloter, U., and Michel, B., High Heat Flux Flow Boiling in Silicon Multi-Microchannels: Part II – Heat Transfer Characteristics of R-245fa, Int. J. Heat Mass Transfer, doi:10.1016/ j.ijheatmasstransfer.2008.03.007 (2008). 22. Thome, J. R., Wolverine Engineering Databook III, at www.wlv.com/products, 2007. 23. Cubaud, T., and Chih-Ming, H., Transport of Bubbles in Square MicroChannels, Physics of Fluids, 16(12), 4575–4585 (2004). 24. Kandlikar, S. G., and Balasubramanian, P., An Extension of the Flow Boiling Correlation to Transition, Laminar, and Deep Laminar Flows in Mini-Channels and Micro-Channels, Heat Transfer Engineering, 25(3), 86–93 (2004). 25. Zhang, W., Hibiki, T., and Mishima, K., Correlation for Flow Boiling Heat Transfer in Mini-Channels, Int. J. Heat and Mass Transfer, 47, 5749–5763 (2004). 26. Forster, H. K., and Zuber, N., Dynamics of vapor bubbles and boiling heat transfer, AIChe J., 1, 531 (1955). 27. Moriyama, K., and Inoue, A., Thickness of the liquid film formed by a growing bubble in a narrow gap between two horizontal plates, J. Heat Transfer, 118, 132–139 (1996). 28. Revellin, R., and Thome, J. R., A New Type of Diabatic Flow Pattern Map for Boiling Heat Transfer in Microchannels, J. of Micromechanics and Microengineering, 17, 788–796 (2006). 29. Revellin, R., Agostini, B., and Thome, J. R. Elongated Bubbles in Microchannels Part II: Experimental Study and modeling of Bubble Collisions, Int. J. Multiphase Flow, doi:10.1016/j.ijmultiphaseflow.2007.07.006 (2008).

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30. Consolini, L., Convective boiling heat transfer in a single micro-channel, Ph.D. dissertation, École Polytechique Fédérale de Lausanne, Switzerland. Available at: http://library.epfl.ch/theses/?nr=4024, 2008. 31. Shiferaw, D., Huo, X., Karayiannis, T. G., and Kenning, D. B. R., Examination of Heat Transfer Correlations and a Model for Flow Boiling of R-134a in Small Diameter Tubes, Int. J. Heat and Mass Transfer (2007), 50, 5177–5193 (2007).

PREDICTION OF CRITICAL HEAT FLUX IN MICROCHANNELS J.R. THOME AND L. CONSOLINI EPFL-STI-IGM-LTCM Ecole Polytechnique Fédérale de Lausanne (EPFL) Lausanne CH-1015, Switzerland, [email protected]

Abstract. An overview of the state-of-the-art of predicting critical heat flux during saturated flow boiling in microchannels is presented. First, a selection of experimental results is described for single channels and for multichannels in parallel, including non-circular channel shapes. Next, the various empirical methods for predicting CHF are presented and discussed. Then, the theoretically based model of Revellin and Thome for microchannels, including prediction of CHF under hot spots, is described and discussed. Finally, some overall comments on the status of CHF modeling and experimentation are provided.

1. Introduction For critical cooling applications using flow boiling in multi-microchannel evaporator plates, a significant research effort is underway. As example of emerging applications, the cooling of microprocessors, power-electronics, microreactors, digital displays, etc. can benefit from the high cooling rate and uniform temperature resulting from forced flow boiling in a multitude of parallel channels to dissipate the heat using the heat of evaporation of the coolant. Among the parameters to be resolved in such a design, the critical heat flux (CHF) in saturated flow boiling conditions represents a very important operational limit. It signifies the maximum heat flux that can be dissipated at the particular operating conditions. Surpassing CHF means that the heated wall becomes completely and irrevocably dry, instigating a very rapid and sharp increase in the wall temperature as the two-phase flow regime passes into the mist flow (post-dryout) heat transfer regime. Figure 1, for example, illustrates the onset of CHF in a single microchannel in a test by Wojtan, Revellin and Thome [1], on R-134a at a saturation temperature of 30°C and a mass velocity of 1,000 kg/m2s (0.509 mm tube, with a heated length of 70 mm). It shows the temperature excursion that occurs during small steps of increasing heat flux. Upon reaching CHF at an imposed heat flux of about 164 kW/m2, the wall temperature takes off and S. Kakaç et al. (eds.), Microfluidics Based Microsystems: Fundamentals and Applications, DOI 10.1007/978-90-481-9029-4_6, © Springer Science + Business Media B.V. 2010

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within about a second surpasses 75°C and proceeds to exceed 120°C (not shown) soon afterwards, at which point the electric heater of the test section is shut off by a control system to keep the heater from reaching the failure temperature of the circuit. For most applications, this temperature excursion would result in irreparable damage to the device being cooled. Thus, the critical heat flux is a particularly important design parameter. Physically speaking, CHF in an annular flow is reached by drying out the liquid film flowing on the channel wall (or destabilizing the film via interfacial waves to create a stable dry spot) and is followed by the complete entrainment of the liquid-phase into the high speed vapor flow. The heat transfer process then occurs through the much less effective vapor-phase heat transfer on the wall that requires a very large temperature to dissipate the imposed heat flux. Regarding macroscale CHF, the Katto and Ohno [2] method is usually considered the most accurate and reliable one. Below, first some experimental results are presented to illustrate typical trends and then several leading empirical CHF prediction methods are described. Next, a recently proposed theoretical microchannel CHF model is presented. The topic of modeling of local CHF under hot spots for computer chip cooling is then addressed.

Figure 1. Heat flux versus wall superheat measurements during a critical heat flux experiment by Wojtan, Revellin and Thome [1].

2. Flow Pattern Effects on CHF Pribyl, Bar-Cohen and Bergles [3] have studied the effect of flow pattern on CHF, based on water data obtained in three independent test facilities with a total number of experimental points of 4109. The tube diameters ranged from 1.0 to 37.0 mm, heated lengths from 31 to 3,000 mm and mass

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velocities from 10 to 18,580 kg/m2s. The database was sorted by regime using Taitel and Dukler [4] flow pattern map to identify annular, intermittent and bubble flows. They found that CHF varied linearly with quality in distinct segments, with a relatively sharp discontinuity and change in slope at low vapor qualities, where the Taitel–Dukler map predicts a regime transition. The most apparent difference in slope was observed between bubbly flow and annular flows. They concluded that a change in flow regime might affect the mechanism of CHF and that within each flow regime a similar but distinct CHF mechanism could be expected to apply. Bergles and Kandlikar [5] reviewed the existing studies on critical heat flux in microchannels. They concluded by saying that few single-tube CHF data were available for microchannels at the time of their review. For the case of parallel multi-microchannels, they noted that all the available CHF data at that time were taken under unstable conditions, where the critical condition was reached as the result of a compressible volume instability upstream or the excursive Ledinegg instability. As a result, the unstable CHF values reported in the literature were expected to be lower than they would be if the channel flow were kept stable by an inlet restriction. 3. Experiments and Correlations for CHF in Microchannels Some early CHF data for saturated CHF (that is, where CHF is surpassed where the local condition is in the saturated liquid–vapor region, not in a subcooled liquid) in small diameter tubes were obtained by Lazarek and Black [6]. They obtained a limited number of measurements for R-113 in a single 3.15 mm bore, stainless steel tube with a heated length of 126 mm. Shah [7] proposed a general CHF correlation for uniformly heated vertical channels created from a database covering 23 fluids (water, cryogens, organics and liquid metals) for tube diameters varying from 0.315 to 37.5 mm and heated length to diameter ratios from 1.2 to 940, taking data from 62 independent sources. His correlation is given as follows:

⎛L qcrit = 0.124 ⎜⎜ h m& hLG ⎝ di

⎞ ⎟⎟ ⎠

−0.89

n

⎛ 10 4 ⎞ ⎜ ⎟ (1 − xinlet ) ⎜Y ⎟ ⎝ Shah ⎠

(1)

In this expression, xinlet is the inlet vapor quality, which can be negative when considering a subcooled inlet condition, i.e. the inlet subcooling enthalpy relative to the latent heat. As CHF normally occurs at the outlet, the heated length Lh is taken as the channel length. The parameter YShah is:

YShah = m&

1.8

⎛ d i0.6 ⎜⎜

c pL

⎞⎛ μ L ⎞ ⎟⎜ ⎟⎟ 0.8 0.4 ⎟⎜ ⎝ k L ρ L g ⎠⎝ μG ⎠

0.6

(2)

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This parameter is evaluated as follows. When YShah ≤ 104, n = 0. When YShah ≥ 104, n is calculated using one of the two expressions:

YShah

⎛d ≤ 10 , n = ⎜⎜ i ⎝ Lh 6

YShah > 10 6 , n =

⎞ ⎟⎟ ⎠

0.54

(3)

0.12 (1 − xinlet )0.5

(4)

For parallel multi-microchannels, Bowers and Mudawar [8] obtained perhaps the first CHF data. Their tests were for R-113 in two test sections, one with 0.510 mm channels and the other with 2.54 mm channels, both circular, with a heated length of 10 mm made of copper and nickel. Qu and Mudawar [9] then obtained CHF data for water in a multi-microchannel heat sink with 21 parallel rectangular channels of 0.215 mm width by 0.821 mm height. They found that as CHF was approached, flow instabilities induced vapor backflow into the heat sink’s upstream plenum as shown in Fig. 2, resulting in mixing vapor with the incoming subcooled liquid. The backflow negated the usual advantage of inlet subcooling, resulting in a CHF virtually independent of inlet subcooling. Using these data together with the previously mentioned CHF data of Bowers and Mudawar [8], they proposed a Katto–Ohno style empirical correlation with CHF occurring in saturated flow, with a new leading constant and exponents, as follows:

⎛ρ qcrit = 33.43 ⎜⎜ G m& hLG ⎝ ρL

⎞ ⎟⎟ ⎠

1.11

Lh ⎞ ⎟⎟ ⎝ di ⎠

⎛ WeL−0.21 ⎜⎜

−0.36

(5)

The liquid Weber number, based on the uniformly heated length Lh, is defined as:

We L =

m& 2 Lh

ρ Lσ

(6)

This correlation predicted their experimental database for water and R-113 with a very small mean absolute error of 4%.

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Figure 2. Qu and Mudawar [9] diagram of flow instabilities observed near CHF.

Zhang et al. [10] analyzed the existing CHF correlations available for water versus a very large international experimental database for small diameter channels (0.33 ≤ di ≤ 6.22 mm). They proposed the following correlation for CHF of saturated water in small channels:

⎡ ⎛L q crit = 0.0352 ⎢We d i + 0.0119 ⎜⎜ h m& hLG ⎢⎣ ⎝ di 0.170 ⎡ ⎤ ⎛ ρG ⎞ ⎜ ⎟ ⋅ ⎢ 2.05 ⎜ − xinlet ⎥ ⎟ ⎢⎣ ⎥⎦ ⎝ ρL ⎠

⎞ ⎟⎟ ⎠

2.31

⎛ ρG ⎜⎜ ⎝ ρL

⎞ ⎟⎟ ⎠

0.361

⎤ ⎥ ⎥⎦

−0.295

⎛ Lh ⎜⎜ ⎝ di

⎞ ⎟⎟ ⎠

−0.311

(7)

The liquid Weber number, based on the channel diameter rather than its length, is defined as:

We d i =

m& 2 d i

ρ Lσ

(8)

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Qi et al. [11, 12] have measured cryogenic CHF data for saturated liquid nitrogen for 0.531, 0.834, 1.042 and 1.931 mm circular microchannels. The tests were done for mass velocities from about 400 to 2,800 kg/m2s at saturation pressures of about 6.8 bar. They found that the macroscale correlation of Katto and Ohno [2] and that of Zhang et al. [10] for water and extrapolated to liquid nitrogen, tended to severely under predict their data by 65–80%. Therefore, they proposed a new correlation based on the Weber number and the Confinement number as follows for CHF of liquid nitrogen:

⎛ρ qcrit = (0.214 + 0.140 Co )⎜⎜ G m& hLG ⎝ ρL

⎞ ⎟⎟ ⎠

0.133

⎛ ⎞ 1 ⎟⎟ (9) Wed−i0.333 ⎜⎜ ⎝ 1 + (0.03 Lh / d i ) ⎠

This method fit their nitrogen data with a mean average error of about 7.4%. Wojtan, Revellin and Thome [1] ran CHF tests in 0.509 and 0.790 mm internal diameter stainless steel microchannel tubes as a function of refrigerant mass velocity, heated length, saturation temperature and inlet liquid subcooling for R-134a and R-245fa. The heated lengths varied from 20 to 70 mm. The results showed a strong dependence of CHF on mass velocity, heated length and microchannel diameter but no measurable influence of small levels of liquid subcooling (2–15 K). An example of their results is shown in Fig. 3. To put these values in perspective, the departure from nucleate boiling using the expression of Lienhard and Dhir [13] yields a value of qDNB = 384 kW/m2, which is similar to the maximum value in the graph. All their CHF results corresponded to annular flow conditions at the exit of the microchannel based on flow pattern results obtained separately in the same test sections. Their experimental results were compared to the CHF single-channel correlation of Katto and Ohno [2] and the multichannel CHF correlation of Qu and Mudawar [9]. The correlation of Katto and Ohno predicted their microchannel data better with a mean absolute error of 32.8% but with only 41.2% of the data falling within a ±15% error band. The correlation of Qu and Mudawar [9] significantly over predicted their data. Based on their own experimental data, a new microscale version of the Katto–Ohno correlation for the prediction of CHF during saturated boiling in microchannels was proposed by Wojtan, Revellin and Thome [1] as:

⎛ρ qcrit = 0.437 ⎜⎜ G m& hLG ⎝ ρL

⎞ ⎟⎟ ⎠

0.073

⎛ We L−0.24 ⎜⎜

Lh ⎝ di

⎞ ⎟⎟ ⎠

−0.72

(10)

PREDICTION OF CHF IN MICROCHANNELS 500

113

0.790 mm 0.509 mm

450 400

CHF [kW/m2]

350 300 250 200 150 100 50 0 0

200

400

600 800 1000 1200 Mass velocity [kg/m2s]

1400

1600

1800

Figure 3. Wojtan, Revellin and Thome [1] CHF data for R-134a at a saturation temperature of 35°C, a heated length of 70 mm and inlet subcooling of 8 K.

WeL is determined using the expression above based on channel length. The experimental points are predicted with the mean absolute error of 7.6% with 82.4% of data falling within a ±15.0% error band. The database covered: two fluids (R-134a and R-245fa), two diameters (0.509 and 0.790 mm), numerous mass velocities (400–1,600 kg/m2s), four heated lengths (20–70 mm), two saturation temperatures (30°C and 35°C) and small subcoolings (2–15 K). Regarding the dimensionless ratios, they ranged as follows: 293–21044 for WeL, 0.009–0.041 for ρG/ρL, and 25–141 for Lh/di. More recently, additional multi-microchannel CHF data have become available. For example, Agostini et al. [14] measured CHF for R-236fa in a silicon test section with a special inlet header to provide stable flow and good flow distribution (the joining of the inlet liquid distributor to the microchannels created a rectangular orifice at the inlet of each channel). Boiling was in a silicon multi-microchannel element with a heated length and width of 20 mm, with 67 channels of 0.223 mm width, 0.680 mm high and 0.080 mm thick fins. Figure 4 depicts some of their test results. Small inlet subcoolings (0.8–18 K) had essentially no effect on the results, primarily because the inlet orifices had a beneficial flashing effect of triggering flow boiling without passing through the onset of nucleate boiling. The wetted wall heat fluxes accounting for the fin efficiency are plotted (not including the top glass plate used for viewing of the process), which ranged from about 219 to 522 kW/m2. These values correspond to cooling rates 1,120– 2,500 kW/m2 in terms of the footprint of the test section (i.e. at these conditions, 112–250 W/cm2 could be dissipated from a microprocessor chip

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for example). The CHF correlation of Wojtan, Revellin and Thome [1] described above and the Revellin and Thome [15] theoretical CHF model (to be described below) were both found to predict all their 26 CHF data points within ±20%. For a uniformly heated circular channel, the critical vapor quality can be obtained from a simple energy balance as follows:

⎛ q xcrit = ⎜⎜ crit ⎝ m& hLG

⎞⎛ 4 Lh ⎟⎟⎜⎜ ⎠⎝ d i

⎞ ⎛ hsub ⎞ ⎟⎟ − ⎜⎜ ⎟⎟ h ⎠ ⎝ LG ⎠

(11)

In this expression, qcrit is calculated with the correlation of choice, while hLG is the latent heat of vaporization and hsub in the enthalpy change necessary to bring the incoming subcooled liquid to saturation. Thus, from a design point of view, once the critical heat flux is known, the maximum exit vapor quality to avoid CHF can be calculated. It should be pointed out that xcrit is not often the same value as xdi, which is the onset of dryout, since the latter can occur from a hydrodynamic effect (vapor shear) at low heat flux. 600 550 500

CHF [kW/m2]

450 400 350 300 250

∆Tsub = −0.8K ∆Tsub = −5K

200

∆Tsub = −11K

150 100 200

∆Tsub = −15K

300

400

500 600 700 Mass velocity [kg/m2s]

800

900

1000

Figure 4. Agostini et al. [14] CHF data for R-236fa at an inlet saturation temperature of 26°C.

4. Mechanistic Model for CHF in Microchannels Revellin and Thome [15] proposed a mechanistic type of method for predicting CHF in microchannels, based on the premise that CHF is triggered in annular flow at the location where the height (trough) of the interfacial waves equals that of the annular film’s mean thickness. To implement their model, they first solve the one-dimensional conservation equations for

PREDICTION OF CHF IN MICROCHANNELS

115

mass, momentum and energy by assuming annular flow from the inlet of the channel at x = 0. This yields the variation of the annular liquid film thickness δ ignoring any interfacial wave formation along the channel. Then, based on the slip ratio and a Kelvin–Helmoltz critical wavelength criterion (assuming the film thickness to be proportional to the critical wavelength of the interfacial waves), the wave height Δδ is predicted with the following expression:

⎛ d ⎞⎛ u Δδ = 0.15 ⎜ i ⎟ ⎜⎜ G ⎝ 2 ⎠ ⎝ uL

⎞ ⎟⎟ ⎠

−

3 7

⎛ g (ρ L − ρ G )(d i 2 )2 ⎞ ⎟ ⎜ ⎟ ⎜ σ ⎠ ⎝

−

1 7

(12)

Then, when δ equals Δδ at the outlet of the microchannel, CHF is reached. The leading constant and two exponents were determined empirically using a database including three fluids (R-134a, R-245fa and R-113) and three circular channel diameters (0.509, 0.790 and 3.15 mm) taken from the CHF data of Wojtan, Revellin and Thome [1] and Lazarek and Black [6]. Figure 5 shows the profiles from the channel centerline to the wall for an example simulation. 250

Radius [mm]

200

150

100

50 Wave height Film thickness 0

0

5

10 Heated length [mm]

15

20

Figure 5. Revellin and Thome [15] CHF model showing the annular film thickness variation along the channel plotted versus the wave height with respect to the channel centerline. The simulation is for R-134a at a saturation temperature of 30°C in a 0.5 mm channel of 20 mm heated length without inlet subcooling for a mass velocity of 500 kg/m2s, yielding a CHF of 396 kW/m2.

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Their model also satisfactorily predicted the R-113 data of Bowers and Mudawar [8] for circular multi-microchannels with diameters of 0.510 and 2.54 mm of 10 mm length. Furthermore, taking the channel width as the characteristic dimension to use as the diameter in their 1-d model, they were also able to predict the rectangular multi-microchannel data of Qu and Mudawar [9] for water. All together, 90% of the database was predicted within ±20%. This model also accurately predicted the R-236fa multimicrochannel data of Agostini et al. [14], utilizing the hydraulic diameter of the heated perimeter. Furthermore, in a yet to be published comparison, this model also predicts microchannel CHF data of liquid nitrogen and also CO2 data from three independent studies. 5. Modeling of CHF at Hot Spots in Microprocessor Cooling Elements Microprocessors in computers can have very high, local heat dissipation rates that are ten times or more the chip’s average heat flux, thus leading to the creation of so-called “hot spots”. Similar situations can also occur in cooling of power electronics and other devices. Thus, it is interesting to know if a local hot spot heat flux will trigger the onset of CHF when applying a multi-microchannel evaporator cooling element. Implementing the mechanistic CHF model of Revellin and Thome [15] described above, but now for a non-uniform heat flux boundary condition along the channel, Revellin et al. [16] simulated the effects of hot spots on triggering of CHF. Figure 6 shows the effect of a small hot spot (0.4 mm long around the perimeter of the channel) on the variation of the annular liquid film thickness with respect to the channel centerline and the liquid film wave height, and its triggering of CHF at their point of intersection. At the conditions shown, CHF at the hot spot occurs at 3,000 kW/m2 for the otherwise uniform heat flux of 218 kW/m2. Hence, in this case, a local heat flux 13.8 times the mean value can be sustained. The value of CHF without a hot spot (that is, with the hot spot heat flux set equal to that of the rest of the channel) for these same conditions is 396 kW/m2 as noted above, and hence the hot spot value is still over seven times that. For cooling of microprocessors and power electronics, this means that very high local hot spot heat fluxes can be sustained as long as they are not located near the exit of the flow channel. In their paper, Revellin et al. [16] also simulated the effects of the location, size and number of hot spots on CHF for various channel sizes, lengths and mass velocities.

PREDICTION OF CHF IN MICROCHANNELS

117

250

Radius [mm]

200

150

100

50 Wave height Film thickness 0

0

5

10 Heated length [mm]

15

20

Figure 6. Revellin et al. [16] simulation of a hot spot of 0.4 mm length located half way along a heated channel of 20 mm length for R-134a at a saturation temperature of 30°C in a 0.5 mm channel without inlet subcooling for a mass velocity of 500 kg/m2s.

6. Additional Comments For those interested in further reading on recent work on CHF in microchannels, refer to: Revellin and Thome [17] for a parametric study using their mechanistic CHF model, Park and Thome [18] for test results with three refrigerants (R-134a, R-236fa and R-245fa) in two copper multimicrochannel test sections, Revellin et al. [19] for CHF in constructal treeshaped microchannel networks, and Revellin et al. [20] on some special CHF effects observed for CO2. For multi-microchannel elements with “fins” separating the channels, the fin efficiency effect should be taken into account in calculating the effective heated perimeter. Furthermore, it is best to use the hydraulic diameter based on the heated perimeter as the “diameter” to implement these methods while the actual mass velocity (that is mass flow rate through the actual cross-sectional area) is also the best to use (thus not the mass velocity calculated using the heated perimeter hydraulic diameter). This choice has been confirmed by Park and Thome [18] to be the best for all the leading methods against their database for three refrigerants and two multimicrochannel test sections with rectangular shapes.

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7. Summary An overview of the state-of-the-art of predicting critical heat flux during saturated flow boiling in microchannels has been presented. Based on our own experience in comparison to published data for small channels, it appears that the best method for predicting CHF for water as the working fluid is obtained using the method of Zhang et al. [10]. For non-aqueous fluids, the two most accurate methods are those of Wojtan, Revellin and Thome [1] and Revellin and Thome [15]. NOMENCLATURE Latin CHF Co c d g h k L m& q u We x

critical heat flux, W/m2 Confinement number specific heat, J/kg/K diameter, m gravity acceleration, m/s2 specific enthalpy, J/kg thermal conductivity, W/m/K length, m mass velocity, kg/m2/s heat flux, W/m2 mean axial velocity, m/s Weber number vapor quality

Greek

δ μ ρ σ

film thickness, m dynamic viscosity, Pa s density, kg/m3 surface tension, N/m

Subscripts

crit di L G

critical Weber number based on diameter liquid phase, or Weber number based on length vapor phase

PREDICTION OF CHF IN MICROCHANNELS

h i sub

119

heated internal subcooled enthalpy difference

References 1. Wojtan, L., Revellin, R. and Thome, J.R., Investigation of Critical Heat Flux in Single, Uniformly Heated Microchannels, Experimental Thermal and Fluid Science, 30, 765–774, (2007). 2. Katto, Y. and Ohno, H., An Improved Version of the Generalized Correlation of Critical Heat Flux for the Forced Convective Boiling in Uniformly Heated Vertical Channels, Int. J. Heat Mass Transfer, 27, 1641–1648, (1984). 3. Pribyl, D.J., Bar-Cohen, A. and Bergles, A.E., An Investigation of Critical Heat Flux and Two-Phase Flow Regimes for Upward Steam and Water Flow, Proc. of the 5th International Conference in Boiling Heat Transfer, May 4–8, 2003, Jamaica. 4. Taitel, Y. and Dukler, A.E., A model for predicting flow regime transitions in horizontal and near horizontal gas-liquid flow, AIChE J., 22, 47–55, (1976). 5. Bergles, A.E. and Kandlikar, S.G., On the Nature of Critical Heat Flux in Microchannels, J. Heat Transfer, 127, 101–107, (2005). 6. Lazarek, G.M. and Black, S.H., Evaporating Heat Transfer, Pressure Drop and Critical Heat Flux in a Small Vertical Tube with R-113, Int. J. Heat Mass Transfer, 25, 945–960, (1982). 7. Shah, M.M., Improved General Correlation of Critical Heat Flux during Upflow in Uniformly Heated Vertical Tubes, Int. J. Heat Fluid Flow, 8, 326– 335, (1987). 8. Bowers, M.B. and Mudawar, I., High Flux Boiling in Low Flow Rate, Low Pressure Drop Mini-Channel and Micro-Channel Heat Sinks, Int. J. Heat Mass Transfer, 37, 321–332, (1994). 9. Qu, I. and Mudawar, W., Measurement and Correlation of Critical Heat Flux in Two-Phase Micro-Channel Heat Sinks, Int. J. of Heat and Mass Transfer, 47, 2045–2059, (2004). 10. Zhang, W., Hibiki, T., Mishima, K. and Mi, Y., Correlation for Critical Heat Flux for Flow Boiling of Water in Mini-Channels, Int. J. Heat Mass Transfer, 49, 1058–1072, (2006). 11. Qi, S.L., Zhang, P., Wang, R.Z. and Xu, L.X., Flow Boiling of Liquid Nitrogen in Micro-Tubes: Part I – The Onset of Nucleate Boiling, Two-Phase Flow Instability and Two-Phase Pressure Drop, Int. J. Heat Mass Transfer, 50, 4999–5016, (2007). 12. Qi, S.L., Zhang, P., Wang, R.Z. and Xu, L.X., Flow Boiling of Liquid Nitrogen in Micro-Tubes: Part II – Heat Transfer Characteristics and Critical Heat Flux, Int. J. Heat Mass Transfer, 50, 5017–5030, (2007). 13. Lienhard, J.H. and Dhir, V.K., Extended Hydrodynamic Theory of the Peak and Minimum Pool Boiling Heat Fluxes, NASA CR-2270, July, 1973.

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14. Agostini, B., Revellin, R., Thome, J.R., Fabbri, M., Michel, B., Kloter, U. and Calmi, D., High Heat Flux Flow Boiling in Silicon Multi-Microchannels: Part III – Saturated Critical Heat Flux of R236fa and Two-Phase Pressure Drop, Int. J. Heat Mass Transfer, 41, 5426–5442, (2008). 15. Revellin, R. and Thome, J.R., A Theoretical Model for the Prediction of the Critical Heat Flux in Heated Microchannels, Int. J. Heat Mass Transfer, 51, 1216–1225, (2008). 16. Revellin, R., Moreno Quiben, J., Bonjour, J. and Thome, J.R., Effect of Local Hot Spots on the Maximum Heat Transfer during Flow Boiling in a Microchannel, IEEE Trans. on Components and Packaging Technologies, 31, 407– 416, (2008). 17. Revellin, R. and Thome, J.R., Critical Heat Flux during Flow Boiling in Microchannels: A Parametric Study, Heat Transfer Engineering, 30, 556–563, (2009). 18. Park, J.E. and Thome, J.R., Critical Heat Flux in Multi-Microchannel Copper Elements with Low Pressure Refrigerants, Int. J. Heat Mass Transfer, 52, in press, (2009). 19. Revellin, R., Thome, J.R., Bejan, A. and Bonjour, J., Constructal Tree-Shaped Microchannel Networks for Maximizing the Saturated Critical Heat Flux, Int. J. of Thermal Sciences, 48, 342–352, (2009). 20. Revellin, R., Haberschill, P., Bonjour, J. and Thome, J.R., Conditions of Liquid Film Dryout during Saturated Flow Boiling in Microchannels, Chem. Engng. Sci., 63, 5795–5801, (2009).

TRANSPORT PHENOMENA IN TWO-PHASE THERMAL SPREADERS H. SMIRNOV1 AND B. KOSOY2* 1

Odessa Academy of Food Technologies, Odessa, Ukraine Odessa State Academy of Refrigeration, Odessa, Ukraine, [email protected] 2

1. Introduction According to the second law of thermodynamics, the entire world is moving towards maximum entropy: “heat cannot of itself pass from a colder to a hotter body”. By definition, “heat transfer is a basic science that deals with the rate of transfer of thermal energy” [1]. There are three basic mechanisms of heat transfer: conduction, convection, and radiation. Conduction is based on energy transfer between two adjacent particles of a substrate with different energy levels, whereas in convection, the heat transfers between a solid and an adjacent moving fluid. The mechanism of heat transfer through the emission of electromagnetic waves (or photons) from a matter is called radiation. Enhanced heat transfer in the industrial applications, such as electronics cooling, is often required. One of the most common methods of heat transfer enhancement is the use of enhanced surfaces, e.g. fins. Moreover, for a constant size and heat exchange rate, a lower temperature gradient shows a more efficient heat transfer. Enhanced heat transfer techniques can be classified as active and passive. Passive techniques do not require any external power and employ surface and fluid treatments to enhance heat transfer. Surface treatment techniques consist of surface coating or surface extension. Surface coating techniques use metallic or non-metallic coating. As an example of nonmetallic coating, Teflon promotes dropwise condensation, while hydrophilic coatings promote the condensate drainage in evaporator. Fine-scale porous coatings enhance heat transfer by enhancing nucleate boiling [2]. Surface extension techniques use offset strip fins, segmented fins, integral strip-finned tubes. These techniques decrease the thermal resistance by increasing the heat transfer coefficient or the surface area. Fluid treatment techniques typically

______

* Boris Kosoy, Odessa State Academy of Refrigeration, 1/3 Dvoryanskaya St, Odessa, 65082, Ukraine e-mail: [email protected]

S. Kakaç et al. (eds.), Microfluidics Based Microsystems: Fundamentals and Applications, DOI 10.1007/978-90-481-9029-4_7, © Springer Science + Business Media B.V. 2010

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contain a number of geometrical arrangements to create a secondary flow. Some examples of fluid treatment techniques include the use of twisted-tape inserts, helical vane inserts and static mixers. Surface tension is typically employed to drive the working fluid in heat pipes. A wick structure in the heat pipe helps the capillary pressure to transport liquid films from the condenser to the evaporator. Active techniques require external power, such as electronic or acoustic fields and vibration sources. In the electrostatic field technique, both direct current and alternative current can be applied to a dielectric fluid. That causes a better bulk mixing of the fluid in the vicinity of the heat transfer surface [2]. Vibration techniques are classified as surface vibration and fluid vibration techniques. Surface vibration impinges small droplets onto a heated surface to promote spray cooling. Both low and high frequencies are used in surface vibration, especially for single-phase heat transfer. However, fluid vibration is a more practical vibration enhancement, due to the mass of most heat exchangers. Surface vibration covers the frequency range from 1 Hz to ultrasound. Besides, modern technology is characterized by the tendency to package larger power conversion or transfer devices in smaller volumes. Ranging from the largest to the smallest, examples of such devices abound in microelectronics, nuclear technology, and aerospace. The heat transfer objectives can usually be stated as either (i) removing large rates of energy generation through small surface areas with moderate surface temperatures rises or (ii) reducing the size of a boiler for a given rating. Both objectives involve higher heat fluxes. This desire to accommodate or promote high heat fluxes has been a major driving force for the study of boiling heat transfer, in general, and the development of methods to enhance boiling heat transfer, in particular. Liquid cooling with boiling has been extensively studied in the past, starting with the pioneering work of Bergles and his group [3, 4] and continuing with Incropera [5], Bar-Cohen [6] and other researchers. The main issues investigated are the critical heat flux (CHF) levels that can be attained, temperature overshoot and incipient excursion, bubble growth and departure as well as the effect of surface enhancement. Microfluidics, fluid mechanics at the micro scale, has received more attention in the past years due to ever-increasing applications. The adaptability of microfluidic devices has been a key factor in their wide range of applications. Thermal microfluidic chips employ the micro scale fluid flow for thermal applications. They have been considered for special applications such as electronics cooling and bio microelectromechanical systems. In microelectronics, thermal microfluidic chips provide attractive solutions for the thermal management in highly compacted integrated circuits. Increasing the compaction of electronic components requires tremendous amount of heat dissipation, i.e. in the order of 100 W/cm2. Traditional techniques of

TRANSPORT PHENOMENA IN TWO-PHASE THERMAL SPREADERS 123

heat removal, such as using cooling fans, cannot meet the thermal requirements of the new electronic chips. For cooling fans, further heat can be removed from a chip by increasing the fan’s RPM. However, the frequencies of the noises generated by these fans pass the threshold of human hearing, and it disturbs the users. Microfluidic chips demonstrated very promising performances for heat removal applications. One very important benefit of using microfluidic chips for electronic cooling is the ability of manufacturing integrated microelectronic/microfluidic chips. Both active and passive techniques are used for different types of thermal microfluidic chips. Micro heat pipe, micro capillary pumped loop, micro loop heat pipe, micro gravitational heat pipe, and micro heat pips heat spreader are some examples of thermal microfluidic chips used in the various applications. During the past two decades, the significant growth of microfluidic systems demonstrated promising capabilities for a wide range of applications. From drug delivery and biosensors in BioMEMS, to heat removal in microelectronic systems, microfluidic devices have proven their high efficiency and versatility. Microscale energy transport is an emerging science with a large number of potential applications [7]. More than 25 years ago, Tuckerman and Pease [8] presented the use of microchannels for electronics cooling. They investigated the thermal removal from planar integrated circuits, and used water as the working fluid in microchannels etched in a silicon substrate. The result was a heat transfer rate of 105 W/m2K that was almost two orders of magnitude higher than state-of-the-art commercial technologies for cooling Integrated Circuits [9]. Since then, experimental and theoretical investigations were conducted to address thermal behavior of microfluidic chips. Research was carried out on single-phase flow microfluidic systems that are employing either gas or liquid [9, 10]. However, it was shown that the latent heat in a vaporization process can highly improve the efficiency of thermal microfluidic chips; hence, extensive research was carried out on two-phase flow thermal microfluidic devices [9–11]. According to the literature, typical passive techniques were used in various microfluidic chips, such as micro heat pipes, micro heat spreaders, micro loop heat pipes, etc. Different investigations on fluid flow and heat transfer in microfluidic devices were compared analytically [12]. Figure 1 presents the basic types of thermal spreaders’ designs. Number of researchers reports the liquid forced convection inside narrow channels is a most valuable form of heat removal from heat sinks [13–16]. However, the respective key issues are the maximum attainable heat flux by using liquid forced convection, and its value in comparison with the preeminent alternatives of boiling critical heat fluxes. We believe that maximum heat flux could be accomplished by using the “inverted meniscus” principle of evaporation coupled with excluding of vapor

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hydraulic losses and minimizing liquid hydraulic losses. Such an approach was discussed in the papers [17–20]. Present paper is devoted to the current state of the art of the “reverse meniscus” concept.

Figure 1. Design of thermal spreaders: A – horizontal two-phase thermosyphon with internal PIN-structure; B – horizontal two-phase heat pipe with internal PIN-structure; C – horizontal liquid TS with internal PIN-structure; D – horizontal liquid TS with internal PIN-structure and spray cooling.

2. Theoretical Analysis of the “Reverse Meniscus” Model As it is known, the principle of vapor and liquid transport lines separation together with using capillary porous structure primarily as a locking wall that provide pumping of working fluid, was first realized in Loop Heat Pipes (LHP) [21]. Modern designs of LHP and CPL evaporators allow transferring of thermal power ~1 kW or even higher, heat flux density up to 100 W/cm2, heat transfer coefficients in the range of 5 × 104…105 W/m2K, vapor and liquid lines length more than 10 m, etc. Development of reliable models of the LHP and CPL evaporators requires special accounting for the following peculiarities: – – – –

Low heat and mass transfer intensity at small heat flux density Noticeably non-monotonous variation of thermal resistance for some evaporators designs and existence of a wide zone of constant thermal resistance for other ones Experimental data on heat transfer coefficients inside the LHP and CPL evaporators Correlation between the heat transfer intensity inside evaporators and saturation temperature

TRANSPORT PHENOMENA IN TWO-PHASE THERMAL SPREADERS 125

–

Influence of the evaporator’s location, its place with respect to the condenser, transport lines geometry and lengths on the heat and mass transfer inside evaporator, etc.

Physical principles and experimental data presented by LHP and CPL researchers proved a capability to apply such technological designs, where the system of vapor removal channels is located right close to the evaporator wall, providing effective vapor generation process. It is a so-called “reverse meniscus” thermal regime. The behavior of the liquid–vapor boundary surface meniscus in the LHP evaporator microporous capillary structure has a critical significance for the start-up and reliable operation of LHP devices. Heat transfer through thin liquid film (microfilm) formed in the root of vapor bubbles determines a scale and peculiarities of the vaporization process. The thinner this film, the higher intensity of heat transfer. However at the break or complete dryout of a film, the heat transfer intensity goes down sharply. Thus, the problem of securing of “micro-film evaporation” consists in providing such conditions when time of survival of this form of vaporization exceeds the characteristic duration of the process. For this purpose, a liquid supply must be provided in the places of micro-film formation. For example, imposition of a porous structure on the vaporization surface provides a necessary liquid input due to the action of capillary forces. The smaller size of the channels through which the medium moves, the higher heat transfer intensity. Consequently, secure heat transfer requires providing a liquid movement near the wall in microchannels. Besides, using of the surface finning reduces the entire thermal resistance. Therefore, creation of systems with the micro-finned surfaces (PIN-structures) contributes to the significant heat transfer augmentation. Technology of the “reverse meniscus” consists in imposition of microporous layer to the PIN-structure that provides high intensity of heat transfer. Using of bidisperse wick structure is also instrumental in intensification of heat transfer. Typical schematics of the LHP evaporators and corresponding heat transfer regimes are shown in Figs. 2 and 3. Hence, the following thermo-hydraulic modes occur inside circumferential channels: 1. Channels and porous structure are filled with a thermal fluid and heat transfers from the wall of LHP evaporator to the surface of compensation chamber and to the edge of the vapor generating surface of the evaporator primarily due to effective heat conduction (Fig. 3, mode 1). This thermal regime occurs when the initial boiling is impossible even inside the near-wall circumferential channels, i.e. temperature drop is less than 4σTs/(rρ″Rch) =ΔTmin, where Rch is an inscribing radius of corresponding near-wall channel.

H. SMIRNOV AND B. KOSOY

126 B

1

1

2 5 3

1

5 3

B 5

B-B-1 1

3 1

B-B-2

3

4 B-B-3

3 B-B-4

A-A Figure 2. Design schematics of the LHP evaporators. A-A is a cross-section of the cylindrical LHP evaporator; B-B-1…B-B-4 are typical circumferential vapor generation channels: 1 – evaporator wall; 2 – axial vapor removal channels; 3 – main porous structure; 4 – compensation chamber; 5 – circumferential vapor generation channels.

2. Wall temperature drop increase causes small vapor bubbles coming out inside the channel and expansion of initial boiling. The boiling regularities are similar to case of boiling inside narrow slits of the identical size. Thus, such thermal mode is similar to boiling in narrow slits and it continues until wall superheat will attain a temperature drop sufficient for the vapor appearance inside the porous structure, i.e. 4σTs/(rρ″Ref)=ΔTmin2. 3. Porous structure counting the contact surface between the porous insert and evaporator wall is saturated with a liquid. Vaporization occurs only on those porous structure elements, which are liquid-free due to heat transfer through the contact surface to the vapor–liquid interface (Fig. 3, mode 2). Curvature of the vapor–liquid interface is reliant on the vapor–liquid pressure drop determined for each steady state mode as the entire hydraulic resistance of LHP or CPL. The value of curvature remains constant within single elementary cell of circumferential channel (Fig. 2, mode 2). 4. Further rise in heat load maintains increasing of the abovementioned entire hydraulic resistance, and if it exceeds 2σ/Rmax; a local deformation of the interface happens at some decreasing of thermal resistance in the evaporation zone. When heat load keeps on increasing and the entire hydraulic resistance exceeds 2σ/Ref, (Rmin < Ref < Rmax) then edging between the wall and the liquid in the porous structure will be destroyed and two-phase boundary layer will appear between the evaporator wall and vapor–liquid interface (Fig. 3, mode 3). This mode exists until the whole porous structure around the circumferential channels is occupied by the two-phase layer. Then vapor phase filtration through the porous

TRANSPORT PHENOMENA IN TWO-PHASE THERMAL SPREADERS 127

structure occurs in the radial direction and the balance between the capillary pressure and the entire hydraulic resistance is irreversibly broken. vapor liquid liquid 1

q ≥ q0 ΣΔpi ≤ 2σ/Reff

2

0 ≤ q ≤ q0

vapor

vapor

3

δ′′

h

Two-phase border

h

δ′′

liquid Two-phase border

ΣΔpi≥ 2σ/Ref, δ′′< h

liquid 4

δ′′> h, ΣΔpi > 2σ/Ref Tw↑

Figure 3. Typical heat transfer modes inside the LHP evaporator.

5. The next thermal mode occurs when the major part of the porous structure remains in superheat state, vapor occasionally enters the compensation chamber, and capillary pressure becomes steady-state. Present mathematical model is not valid for these operating conditions (Fig. 3, mode 4). When thermal mode matches the temperature drop in range of ΔTmin ≤ ΔT ≤ ΔTmax, where ΔTmin ≅

2σ Ts 4σ Ts ; ΔTmax ≅ ; R0 is a pore radius; r ρ ′′R0 r ρ ′′Def

and Def is a channel effective diameter, boiling heat transfer intensity inside narrow slits is prescribed as α ≈ Cq m s − n p k , where 0 < m < 2; 0 < n < 1; and 0 < k < 1. The exact values of C, m, n, and k should be determined experimentally. In case of intensive vaporization, recommendations presented in the papers [22, 23] and approximation performed by Krukov [24] allow determining dependency of specific mass flow rate jz on coordinate z. Therefore, if

j z = 0.6 2 RдTs (ρ s − ρ0 )

ρ0 , ρs

(1)

H. SMIRNOV AND B. KOSOY

128

then

j z = 0.84ε

dPs ΔT0 ( z ) , RдTs dT 1

(2)

where ΔT0(z)=Ts − T0=(ΔT(z) − ΔT*)/(1 + 2σ/rρ″R); and ΔT* = 2σTs/rρ″R. Specific superheat of the evaporator wall υ could be determined by solving the heat conduction equation: ϑ = ϑ0 +

⎡ B0 ⎤ 2σTs 2σTs q0 ( a + b ) , = exp ⎢ − z ⎥+ rρ ′′R λeff b ⎥⎦ rρ ′′R λeff bB0 ⎢⎣

where B0 = 0.84rε

dPs dTs

1 RдTs

; at z = 0, ϑ =

q0 ( a + b )

λeff bB0

+

2σTs rρ ′′R

(3)

(4)

Superheat of evaporator wall is required for providing certain heat flux through the porous structure saturated with liquid. The total superheat of evaporator wall can be determined by treating the heat transferred to edge surface between the evaporator wall and porous structure through a sequence of thermal resistances. Assigning the entire specific thermal resistance of the edge as Rk0 yields the following correlation for the overall average superheat of the evaporator wall in the mode 2:

ΔT0 =

q0 (a + b) 2σTs q0 (a + b) 3 q0 a 3 + b3 + ab2 + + Rk 0 + b 32 λM δ M a+b λeff bB0 rρ ′′R

(5)

Comparison between the Eqs. (3) and (5) gives

jz =

⎡ B0 q0 ( a + b ) B0 ⎤ exp ⎢ − z ⎥ λeff b ⎥⎦ r λeff bB0 ⎢⎣

(6)

One-dimensional filtration equation is −dp/dz = (ν′/Kf)jz, consequently, −

dp ν ′ = dz rK f

⎡ B0 ⎤ ⎥ q0 (a + b) exp ⎢− z λeff b λeff b ⎥⎦ ⎢⎣ B0

(7)

TRANSPORT PHENOMENA IN TWO-PHASE THERMAL SPREADERS 129

Then, the pressure drop in capillary structure is ⎡ ν ′q (a + b) B0 ⎤ ′ Δpm = 0 exp ⎢− z ⎥ + c1 , and if z = 0 → Δpm = ν q0(a + b)/rKf (8) λ rK f b ⎥ eff ⎦ ⎣⎢ In the thermal mode 2, a value Δpm can be considered as auxiliary hydraulic resistance due to concentration of heat and mass fluxes in the zone of vapor generation according to the “reverse meniscus” principle. When specific design of the LHP allows assumption that all hydraulic resistances (excluding Δpm) are much smaller than capillary potential developed by porous structure 2σ/Ref; it is feasible a correlation for the maximum heat flux (q0)max attained in dependence from certain type of the working fluid, saturation pressure and core design parameters of the nearwall capillary structure: (q0)max < 2σrKf /Refν′(a + b)

(9)

As seen from the Eq. (9), accomplishment of the value (q0)max requires both increasing the near-wall zone permeability Kf , and decreasing the radius of pores involved in the vaporization process. It is known that bidisperse pore structures provide maximum heat flux densities at the highest efficiency [25]. Decrease of circumferential channel dimensions (a and b) also causes increasing of (q0)max, however, it also escalating the entire hydraulic resistance inside the LHP. In certain conditions, it plays the major role in heat flow Q and heat flux q0 limitations before the value (q0)max is attained. Thus, besides the Eqs. (4), (5) and (8), the known steady-state thermohydrodynamic correlations of the LHP should be also implemented to the model. The necessity of such mutual consideration appears obvious in case of determining transition conditions from the thermal mode 2 to the thermal mode 3, and in the analysis of heat transfer regularities of the thermal mode 3. Assuming that vapor channel length Lvch is independent on the heat supply, the following equation yields a dependency between the curvature radius and surface area of the vapor–liquid interface: Q ⎧⎪ Πn (a + h)2 (a + b) 1 Ri+1 ⎫⎪ 2σ ≥ + 0.16ν ′∑ ln ⎬+ ⎨4ν ′′ 2 3 K fi Ri ⎪⎭ R rLvch ⎪⎩ n0 (ah) 2 −3 −2 ⎛ Q ⎞ 1 ⎡8.1 ⋅ 10 Lvch 3.2 ⋅ 10 Lvch ⎤ ν ′Q(a + b) +⎜ ⎟ + ⎢ ⎥+ 2 5 Dk5 ⎝ r ⎠ ρ ′′ ⎣ n0 d0 ⎦ Πn LvchrK f

The substitution of following terms in the Eq. (10)

(10)

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130

4ν ′′Π vch ( a + h ) 2 ( a + b ) ν ′ i=n 1 Ri+1 = A ; 0.16 1 ∑ ln = A2 ; n 02 r ( ah ) 3 L vch rLvch i=1 K fi Ri

ν ′(a + b) 1 ⎡ 8.1⋅10−3 Lvch 3.2 ⋅10−2 Lk ⎤ = A4 (11) + = A ; ⎢ ⎥ 3 Π L rK r 2 ρ ′′ ⎣ n02 d05 Dk5 vch vch f ⎦ gives the next correlation ( 2σ / R ≥ { A1 + A2 + A3Q} × Q + A4Q

(12)

Simultaneous consideration of the Eqs. (12) and (5), and introducing the specific thermal resistance of the LHP evaporation section as ΔT0 / q 0 = Rvch in the thermal mode 2, yields

Rvch =

ΔT0 Π L T a +b Πvch Lvch = + vch vch s × Q r ρ ′′ λeff bB0

a +b 3 1 a3 + b3 + ab2 ×{[ A1 + A2 + A4 ] + A3Q} + Rk 0 + b a +b 32 λmδ m

(13)

As seen from the Eq. (13), in the thermal mode 2 the specific thermal resistance (heat transfer coefficient) is practically autonomous of heat supply value. It is also justified by existing experimental data. Thus, the Eq. (13) provides proper description of interrelations of the following parameters: − − −

Decreasing dimensions a and b causes reduction of Rvch, i.e. increasing heat transfer coefficients Increasing the heat transfer parameters of evaporator wall, δm and λm, maintains decrease of Rvch When the LHP is operating in the gravity field, the extra term, ρ′gL0 sinϕ should be added to the right-hand side of the Eq. (12). The angle ϕ accounts for the LHP evaporator location in relation to the condenser. If ρ′gL0 sinϕ > 0, the value Rvch is increased, while the negative values of this term uphold reliable operation of the LHP at low heat supply until the Eq. (12) is valid.

Transition from the thermal mode 2 to the thermal mode 3 is defined by the Eq. (12). Thus, if Eq. (12) is not true at increasing heat supply and R → Rmin in the edge between the evaporator wall and porous structure saturated with liquid, it creates conditions encouraging vapor–liquid interface displacement from the evaporator wall and generation of vapor layer between

TRANSPORT PHENOMENA IN TWO-PHASE THERMAL SPREADERS 131

the evaporator wall and vapor–liquid interface inside the porous structure. As shown by Smirnov [26], a real geometric shape of the interface is quite complex. Appearance of the vapor layer causes vaporization over the whole surface of the vapor–liquid interface separating the porous structure saturated with the liquid from the evaporator wall. It means both possibility to neglect with the first term of the right-hand side of the Eq. (13), and increasing value of Rk0 in the third term; i.e. vaporization of liquid in the edge zone requires introducing an extra thermal resistance term δ/λef corresponded to the heat transfer from the evaporator wall to the vapor–liquid interface through the porous structure occupied by the vapor layer with thickness, δ. Depending on hydraulic resistances ratio, the rate of increasing of the vapor layer thickness changes with respect to the increase in the heat supply, but as a rule dδ/dQ > 0. Available experimental data justify increasing specific thermal resistance when heat supply rises in the thermal mode 3. Thus, the following correlation is valid for the thermal mode 3:

Rn = +

{

}

Π vch LvchTs A1 + A2′ + A3Q + A5 + r ρ ′′

a+b 3 1 a3 + b3 + ab2 δ Rk′ 0 + + b a+b λef 32 λmδ m

(14)

Vapor layer thickness δ could be determined by solving corresponding hydrodynamic equation with boundary condition based on the Eq. (12). When R = Rmin, the transition between the thermal modes 2 and 3 (Q = Q0) could be determined. Irreversible failure of the LHP operation occurs during further displacement of the vapor–liquid interface in the case when Q = Qmax and thickness δ becomes equal to h, i.e. increase of vapor filtration hydraulic resistance is not balanced by the decrease of hydraulic resistance of liquid filtration inside the porous structure anymore. The value Qmax corresponding to equality of δ = h determines the maximum heat supply allowing reliable operating of the LHP. 3. Strategy of Thermal Spreader’s Optimization The geometry of thermal spreader could be optimized to match one of the following criteria: − −

Minimum entire thermal resistance Minimum weight

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132

− −

Minimum heat losses Maximum efficiency

Optimization of the heat spreader involves determining the combination of internal geometric parameters with respect to following constraints: heat removal surface geometry (rectangular (length a and width b are given), cylindrical (radius R and length L are given), spherical (radius R and angle Θ are given), semi-spherical, semi-cylindrical, etc.; feasible thermal regimes (temperature constraint on the heat input surface T0, partial or transient thermal regimes T1, T2, and corresponding heat input scales Q0, Q1, Q2, location change connected with the thermal regimes); temperatures of the heat removal surfaces TA1, TA2; fixed heat removal conditions (radiation, contact heat transfer, convection, etc.). The principal view of the goal function is J = g1 ×

N M1 M M M + g 2 × 2 + ... + g n × n = ∑ g i i , M 01 M 02 M 0 n i =1 M 0i

(15)

where M1, M2, …, Mn and M01, M02, …, M0n are values of variables with different dimensions and physical nature, and they values under some reference state, correspondingly; g1, g2, …, gn are weight factors of these variables. Assuming M1 = R1, M2 = V1 or H1, where R1, V1, and H1 are entire thermal resistance in the main heat spreader’s volume, and its real volume or its height (thickness), the key issue of the method appears as determination of the values R1, and H1. Suppose that cooled chip is located in such a way that the heat carrier returns to the heating zone under the gravity action, i.e. the heat is transferred from the horizontal plate with known power Qi at given temperature level Ti. Heat is removed at given temperature Tj or the heat removal mode is known, i.e. Qi = f(Tj). Then, optimization algorithm appears as following: Step 1. Determine the most extended thermal regime having the temperature T1b. Preliminary select the heat carrier with respect to the condition: T1b − δ t ≥ T S , where δt is a temperature drop on the internal surface of the heat input zone, TS is a saturation temperature. Validate the condition: TS  T0, (T0 a triple point temperature). Step 2. Estimate the temperature drop for the simple design of heating surface (without any enhancements) by calculating a heat flux as qJmax = QJmax/F, where QJmax is a given value of the heat input, and F=a ⋅ b, (a and b are given dimensions of the heat output surface).

TRANSPORT PHENOMENA IN TWO-PHASE THERMAL SPREADERS 133

For selected heat carrier by iterations assume δt, and determine TS. Calculate the critical heat flux by the Kutateladze formula

qCR ≅ const × r × 4 g × σ ( ρ ' − ρ " )

(16)

Validate the condition qCR ≤ qJmax. In case when this condition is false, proceed with the subsequent iteration. Step 3. Select a surface material with respect to its compatibility with the heat carrier, and nature of the finned surface (rectangular, PIN-structure, cylindrical, grooves, porous coating, etc.) Determine the local temperature drop on the lateral part of the finned surface as

⎡q ⎢ J max ⎢ μ1r δ T = C0 × r × (Pr1 )1.7 × ⎣

⎡ ⎤ σ ⎢ ⎥ ⎣ g ( ρ ′ − ρ ′′ ) ⎦ C1

0.5 0.33

⎤ ⎥ ⎥ ⎦

,

(17)

where: r, Pr1, σ, μ, C1, ρ′, ρ″ are the latent heat of evaporation; liquid Prandtl Number; surface tension; liquid dynamic viscosity, specific heat capacity; liquid and vapor densities, correspondingly. C0 is an empirical constant accounting the effect of heat carrier – surface arrangements on the boiling heat transfer augmentation. Local heat transfer coefficient at boiling on the fin lateral surface is

α = qJ max / δ T

(18)

Determine the effectiveness of finned surface as

E f = tanh(mh) / mh; m = (αU f ) /(λ f S f ) ,

(19)

where Uf, λf, and Sf are perimeter, specific thermal conductivity of fins and its cross section area, correspondingly. The entire internal thermal resistance of the heat input zone is

Rb =

1 , α × E f × U f × h + α × F0

(20)

where h and F0 are the fins’ height and the edge surface area without fins. Consequently, the simplest form of the goal function appears as

H. SMIRNOV AND B. KOSOY

134

J = g f × ( Rb / Rb 0 ) + g h × ( h / h0 ) ,

(21)

where gf and gh are the weight factors corresponding to the entire thermal resistance of the finned surface and the consequent occupied. Step 4. Determine the optimal geometric parameters for the condensation zone with respect to the following assumptions of the model: − − −

Calculations for the plane condensation surface has no sense. Primary heat transfer occurs at the lateral surfaces of fins. Part of condensate is collected at the top inside fin’s gap under the action of surface forces; consequently, the entire calculated condensation heat transfer area should be reduced.

Thus, corresponding equation for calculation of condensation heat transfer coefficient is

⎧ ⎫ μ1 × (h − hC ) α C = const × ⎨ ⎬ 3 ⎩ ρ ′ × ( ρ ′ − ρ ′′) × λ1 × r × g ⎭

−1/ 3

× (q ) −1/ 3 , (22)

where (h − hc) is a reduction of the heat transfer surface due to condensate gathering at the fins’ edge under the action of surface tension forces; q is an average heat flux from the fins’ lateral surfaces; and const is a constant parameter determined by solving conventional problem of the condensation heat transfer at the vertical surface. In such a case, the effectiveness of the finned surface is

E fC = tanh{m( h − hC )} /{m( h − hC )}; (23)

m = (α CU C ) /(λ S C )

Here SC = (h − hC ) × U C × N C , where Nc is a fins’ density (their number related to the given surface area). Hence, the entire internal thermal resistance of the condensation zone appears as RC =

1

α C × E fC × SC

+

hC

λ × ( NC × U C × δ C )

×(

δ0 + 1) , δC

where δ0 and δC are fin’s gap and thickness, correspondingly.

(24)

TRANSPORT PHENOMENA IN TWO-PHASE THERMAL SPREADERS 135

In order to validate the present approach, the experimental sample of two-phase thermal spreader was designed and manufactured for cooling of high thermal power chip placed in the horizontal position. With respect to the thermal regime constraint, ammonia was selected as the heat carrier and stainless steel was used as the core material. The following optimal geometric parameters of the experimental sample were determined: − −

Evaporation zone – h = 5 mm; s = 1 mm; δb = 1 mm. Condensation zone – h = 10 mm; s = 2.5 mm; δC = 6 mm. Figure 4 presents design of the experimental sample of thermal spreader. Temperatures were measured in heat input and heat output zones. 32 f 88

f4

2

32

f 80

Y 6

x

5

1

63

10

2,5

30

74

1 63

Figure 4. The real two-phase thermal spreader with finned surfaces in the heat input and heat output zones.

Corresponding temperature sensors’ locations are shown in Figs. 5 and 6.

Figure 5. Locations of experimental temperature sensors in the heat input zone (T2, T3, and T4).

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136

Figure 6. Locations of experimental temperature sensors in the heat output zone.

Representative experimental data shown in the Figure 7.

Figure 7. The effect of heat input on the entire temperature drop in the two-phase thermal spreader.

4. Conclusions

The present approach cannot be considered as the completed theory or the perfect model given accurate values of the corresponding thermal and flow resistances. A number of improvements can be made to theoretical descriptions used at different stages of heat and mass transfer process modeling as well as more accurate two-dimensional or three-dimensional models of heat and mass transfer could be applied. However, the current concept represents a source for further researches committed with such issues as: − −

Determination of optimal geometrical and technological parameters (a, b, h, d0, etc.) by treating the minimum thermal resistance ΔT0/Q under the given heat input Calculation of value Qmax in constraint of ΔT0/Q (aopt, bopt, Lvch, etc.)

TRANSPORT PHENOMENA IN TWO-PHASE THERMAL SPREADERS 137

− −

Determination of the LHP optimal parameters at given value of Q0 with respect to minimization of the weight and maximization of the reliability factor, etc. Study of the physical nature of various heat and flow instabilities

Using the current concept, especially in modeling the LHP dynamics, requires paying special attention to conditions of transition between thermal modes, uncertainty of hydraulic parameters due to the flow mode changing; position of the vapor–liquid interface and its stability, as well as inconsistency of factors determining a structure’s geometry. Further studies in the field of geometric optimization for two-phase thermal spreaders can be classified into two categories: modeling investigations, and validation studies. The future modeling issues worth addressing include: − −

Modeling of more complex geometries (e.g. polygonal, curved sided, or combined cross-sections, as well as interconnected geometries Geometric optimization of three-dimensional networks, using twophase flow simulations maintaining the proper operation and accurately captured the detailed phenomena

References 1. Cengel, Y.A., Heat Transfer: a practical approach. (Second ed., New York: McGraw-Hill, 2003). 2. Webb, R.L. and N.-H. Kim, Principles of enhanced heat transfer (Second ed., New York: Taylor & Francis, 2005). 3. Park, K.A., and Bergles, A.E., Boiling Heat Transfer Characteristics of Simulated Microelectronic Chips with Detachable Heat Sinks, Eighth International Heat Transfer Conference, Vol. 4, Hemisphere Publishing Corporation, Washington, DC, pp. 2099–2104, 1986. 4. Bergles, A.E. and Bar-Cohen, A., Direct Liquid Cooling of Microelectronic Components, Advances in Thermal Modeling of Electronic Components and Systems, Eds., Bar-Cohen, A. and Kraus, A.D., Vol. 2, pp. 233–250, ASME Press, New York, 1990. 5. Incropera, F.P., Liquid Immersion Cooling of Electronic Components, Heat Transfer in Electronic and Microelectronic Equipment, Ed. A. E. Bergles, pp. 407–444, Hemisphere Publishing Corporation, 1990. 6. Bar-Cohen, A., Thermal Management of Electronic Components with Dielectric Liquids, International Journal of JSME 36(1), 1–25 (1993). 7. Tien, C.-L., A. Majumdar, and F.M. Gerner, Microscale energy transport. Series in chemical and mechanical engineering (Washington, DC: Taylor & Francis, 1998).

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8. Tuckerman, D.B. and R.F.W. Pease, High-performance heat sinking for VLSI. IEEE Electron Device Letters, 1981. ED-2(5): p. 126. 9. Zohar, Y., Heat convection in micro ducts. Microsystems, ed. S. Senturia (Norwell, MA: Kluwer Academic Publishers. 2003). 10. Kandlikar, S.G., et al., Heat transfer and fluid flow in minichannels and microchannels., (Oxford: Elsevier, 2006). 11. Zhang, L., T.W. Kenny, and K.E. Goodson, Silicon microchannel heat sinks. Microtechnology and MEMS, ed. H. Baltes, H. Fujita, and D. Liepmann, (New York: Springer-Verlag, Berlin-Heidelberg, 2004). 12. Sobhan, C.B. and S.V. Garimella, A comparative analysis of studies on heat transfer and fluid flow in microchannels. Microscale Thermophysical Engineering, 5(4), 293–311 (2001). 13. Leslie, S.G., Cooling options and challenges of high power semiconductors modules, Electronics Cooling, 12(4), 20–27 (2006). 14. Copeland, D., Fundamental Performance of Heatsinks, ASME Journal of Electronic Packaging, 125(2), 221–225 (2003). 15. Copeland, D., Review of Low Profile Cold Plate Technology for High Density Servers, Electronics Cooling, 11(2), (2005). 16. Clemens J.M. Lasance and R.E. Simons, Advances In High – Performance Cooling For Electronics, Electronic Cooling, http://electronics-cooling.com/ articles/ 2005/2005_nov_article2.php 17. North, M.T., Shaubach R.M., Rosenfeld, J.H., Liquid Film Evaporation From Bidisperse Capillary Wicks in Heat Pipe Evaporators, Proceedings of 9th IHPC, May 1995, Albuquerque NM. 18. Rosenfeld, J.H., Anderson, W.G., North, M.T., Improved High Heat Flux Loop Heat Pipes using bidisperse evaporators wicks, Proceedings of 10th IHPC, September 1997, Stuttgart. 19. H.F. Smirnov and K.A. Goncharov, Physical and Mathematical modelling of loop heat pipes evaporators, Proceedings of 11th IHPC, September 1999, Tokyo. 20. Altman, E.I., Mukminova, M.Ja., Smirnov, H.F., Loop Heat Pipe Evaporators’ Theoretical Analysis, Proceedings of 12th IHPC , May 2002, Moscow. 21. Maidanik, Yu.F., Fershtater, Yu.G., Pastukhov, V.G., Loop Heat Pipes: Working out, Investigations, Engineering calculations’ elements, The Scientific reports of USSR Academy of Sciences, Ural Branch, 1989, Sverdlovsk. 22. D.A. Labuntzov and A.P. Krukov, Intensive evaporation processes, Teploenergetika, 4, 8–11 (1977). 23. D.A. Labuntzov and A.P. Krukov, Analysis of intensive evaporation and condensation, International Journal of HMT, 22, 989–1002 (1979). 24. Krukov, A.P., Kinetic analysis of evaporation and condensing processes on the surface, International Seminar of Belarus Academy of Science, 1991, Minsk. 25. Maidanik, Yu.F., Vershinin, S.V., Fershtater, Yu.G., Heat transfer enhancement in a loop heat pipe evaporator, Proceedings of 10th IHPC, September 1997, Stuttgart. 26. Smirnov, H.F., Transport Phenomena in Capillary-Porous Structures and Heat Pipes (CRC Press, 2009).

AN INVESTIGATION ON THERMAL CONDUCTIVITY AND VISCOSITY OF WATER BASED NANOFLUIDS I. TAVMAN AND A. TURGUT Mechanical Engineering Department, Dokuz Eylul University, 35100 Bornova, Izmir, Turkey, [email protected]

Abstract. In this study we report a literature review on the research and development work concerning thermal conductivity of nanofluids as well as their viscosity. Different techniques used for the measurement of thermal conductivity of nanofluids are explained, especially the 3ω method which was used in our measurements. The models used to predict the thermal conductivity of nanofluids are presented. Our experimental results on the effective thermal conductivity by using 3ω method and effective viscosity by vibro-viscometer for SiO2–water, TiO2–water and Al2O3–water nanofluids at different particle concentrations and temperatures are presented. Measured results showed that the effective thermal conductivity of nanofluids increase as the concentration of the particles increase but not anomalously as indicated in the some publications and this enhancement is very close to Hamilton– Crosser model, also this increase is independent of the temperature. The effective viscosities of these nanofluids increased by the increasing particle concentration and decrease by the increase in temperature, and cannot be predicted by Einstein model.

1. Introduction Nanofluids are solid nanoparticles or nanofibers in suspension in a base fluid. To be qualified as nanofluid it is generally agreed that at least one size of the solid particle be less than 100 nm. Various industries such as transportation, electronics, food, medical industries require efficient heat transfer fluids to either evacuate or transfer heat by means of a flowing fluid. Especially with the miniaturization in electronic equipments, the need for heat evacuation has become more important in order to ensure proper working conditions for these elements. Thus, new strategies, such as the use of new, more conductive fluids are needed. Most of the fluids used for this purpose are generally poor heat conductors compared to solids (Fig. 1).

S. Kakaç et al. (eds.), Microfluidics Based Microsystems: Fundamentals and Applications, DOI 10.1007/978-90-481-9029-4_8, © Springer Science + Business Media B.V. 2010

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It is well known that fluids may become more conductive by the addition of conductive solid particles. However such mixtures have a lot of practical limitations, primarily arising from the sedimentation of particles and the associated blockage issues. These limitations can be overcome by using suspensions of nanometer-sized particles (nanoparticles) in liquids, known as nanofluids. After the pioneering work by Choi of the Argonne National Laboratory, USA in 1995 [1] and his publication [2] reporting an anomalous increase in thermal conductivity of the base fluid with the addition of low volume fractions of conducting nanoparticles, there has been a great interest for nanofluids research both experimentally and theoretically. More than 970 nanofluid-related research publications have appeared in literature since then and the number per year appears to be increasing as it can seen from Fig. 2. In 2008 alone, 282 research papers were published in Science Citation Index journals. However, the transition to industrial practice requires that nanofluid technology become further developed, and that some key barriers, like the stability and sedimentation problems be overcome. 1000

Heat transfer fluids

Metal Oxide

Metal Cu

Thermal Conductivity (W/mK)

Al

100

Al2O3 CuO TiO2

10

1

Water Ethylene Glycol Oil

0.1

Figure 1. Thermal conductivity of typical materials (solids and liquids) at 300 K.

A review of the literature showed that the nanoparticles used in the production of nanofluids were: aluminum oxide (Al2O3), titanium dioxide (TiO2), nitride ceramics (AlN, SiN), carbide ceramics (SiC, TiC), copper (Cu), copper oxide (CuO), gold (Au), silver (Ag), silica (SiO2) nanoparticles and carbon nanotubes (CNT). The base fluids used were water, oil, acetone, decene and ethylene glycol. Modern technology allows the fabrication of materials at the nanometer scale, they are usually available in the market under different particle sizes and purity conditions. They exhibit

THERMAL CONDUCTIVITY AND VISCOSITY OF NANOFLUIDS 141

unique physical and chemical properties compared to those of larger (micron scale and larger) particles of the same material. Nanoparticles can be produced from several processes such as gas condensation, mechanical attrition or chemical precipitation techniques [3]. Papers in the title containing either “nanofluid” or “nanofluids” searched by the ISI web of science-with conference proceedings on October 2009

Number of paper published per year

300

282

250

230

200

170

150

121 91

100

40

50

21 4

1 0

99

6

3 00

01

02

03

04 year

05

06

07

08

09

Figure 2. Publications on nanofluids since 1999.

Nanofluids are generally produced by two different techniques: a onestep technique and a two-step technique. The one-step technique makes and disperses the nanoparticles directly into a base fluid simultaneously. The two-step technique starts with nanoparticles which can usually be purchased and proceeds to disperse them into a base fluid. Most of the nanofluids containing oxide nanoparticles and carbon nanotubes reported in the open literature are produced by the two-step process. The major advantage of the two-step technique is the possibility to use commercially available nanoparticles, this method provides an economical way to produce nanofluids. But, the major drawback is the tendency of the particles to agglomerate due to attractive van der Waals forces between nanoparticles; then, the agglomerations of particles tend to quickly settle out of liquids. This problem is overcome by using ultrasonic vibration, to break down the agglomerations and homogenize the mixture. Figure 3 shows Al2O3–water nanofluids, (a) shows homogenization with ultrasonic vibration, (b) shows the same nanofluids without any homogenization process, we can easily see the settled nanoparticles.

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Figure 3. Al2O3–water nanofluids (a) treated with ultrasonic vibration, (b) untreated – settlement of nanoparticles.

The first publications on thermal conductivity of nanofluids were with base fluids water or ethylene-glycol (EG) and with nanoparticles such as aluminum-oxide (Al2O3) [4–7], copper-oxide (CuO) [4, 5, 7], titaniumdioxide (TiO2) [8], copper (Cu) [9, 10]. They all measured great enhancement in thermal conductivity for low particles addition, typical enhancement was in the 15–40% range over the base fluid for 0.5–4% nanoparticles volume concentrations in various liquids. The increase was from 5% to 60% for nanoparticles additions ranging from 0.1% to 5% by volume. These unusual results have attracted great interest both experimentally and theoretically from many research groups because of their potential benefits and applications for cooling in many industrials from electronics to transportation. Recent papers provide detailed reviews on al aspects of nanofluids, including preparation, measurement and modeling of thermal conductivity and viscosity [11–13, 24]. Very few studies [7, 14–19] have been performed to investigate the temperature effect on the effective thermal conductivity of nanofluids. In a recent study by Turgut et al. [16] on relative thermal conductivity of TiO2–water nanofluids, no temperature effect has been found like in the study by Masuda et al. [18] and Zhang et al. [19]. However, Wang et al. [17] measured an increase in relative thermal conductivity for the same nanofluid. Hence, to confirm the effects of temperature on the effective thermal conductivity of nanofluids, more experimental studies are essential. The experimental data reported in the literature is very scattered, for the same base fluid and the same particles there are many different results. Some researchers [16–19] measured only a moderate increase of effective thermal conductivity with the addition of nanoparticles. Their experimental results can be explained by classical Maxwell [20], Hamilton and Crosser [21] models for mixtures. A recent publication by Keblinski et al. [22] reveals this controversy about the scatter of experimental data and compares the experimental data from different

THERMAL CONDUCTIVITY AND VISCOSITY OF NANOFLUIDS 143

authors for various water based nanofluids. He shows that this results fall within the upper and lower limits of classical two phase mixture theories. There are many publications on predictive models for effective thermal conductivity of nanofluids [5, 11, 23, 25–27], some of these publications make an overview of the existing models, and some drives their own model and compares with experimental data. None of the models is able to explain and predict an effective thermal conductivity value for the nanofluids. Although some review articles [28–30] emphasized the importance of investigating the viscosity of nanofluids, very few studies on effective viscosity were reported. Viscosity is as critical as thermal conductivity in engineering systems that employ fluid flow. Pumping power is proportional to the pressure drop, which in turn is related to fluid viscosity. More viscous fluids require more pumping power. In laminar flow, the pressure drop is directly proportional to the viscosity. Masuda et al. [18] measured the viscosity of TiO2–water nanofluids suspensions, they found that for 27 nm TiO2 particles at a volumetric concentration of 4.3% the viscosity increased by 60% with respect to pure water. In his work on the effective viscosity of Al2O3–water nanofluids, Wang et al. [5] measured an increase of about 86% for 5 vol% of 28 nm nanoparticles content. In their case, a mechanical blending technique was used for dispersion of Al2O3 nanoparticles in distilled water. They also measured an increase of about 40% in viscosity of ethylene glycol at a volumetric loading of 3.5% of Al2O3 nanoparticles. Das et al. [31] and Putra et al. [32] measured the viscosity of water-based nanofluids, for Al2O3 and CuO particles inclusions, as a function of shear rate they both showed Newtonian behavior for a range of volume percentage between 1% and 4%. Das et al. [50] also observed an increase in viscosity with an increase of particle volume fraction, for Al2O3/water-based nanofluids. In all cases the viscosity results were significantly larger than the predictions from the classical theory of suspension rheology such as Einstein’s model [33]. 2. Models for the Effective Thermal Conductivity of Nanofluids Many theoretical and empirical models have been proposed to predict the effective thermal conductivity of two phase mixtures. Comprehensive review articles have discussed the applicability of many of these models that appear to be more promising [34–36]. First, using potential theory, Maxwell [20] obtained a simple relationship for the conductivity of randomly distributed and non-interacting homogeneous spheres in a homogeneous medium. Maxwell model is good for low solid concentrations. Relative thermal conductivity enhancement (ratio of the effective thermal conductivity keff of nanofluid to base fluid kf) is,

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k eff / k f =

k p + 2k f + 2φ (k p − k f )

(1)

k p + 2k f − φ ( k p − k f )

where φ is the particle volume fraction of the suspension, kp is the thermal conductivity of the particle. According to Maxwell model the effective thermal conductivity of suspensions depending on the thermal conductivity of spherical particles, base liquid and the volume fraction of solid particles. Bruggeman [37] proposed a model to analyze the interactions among randomly distributed particles by using the mean field approach.

keff =

k 1 (3φ − 1)kp + (2 − 3φ )kf + f 4 4

[

]

Δ

(2)

where, (3) When Maxwell model fails to provide a good match with experimental results for higher concentration of inclusions, Bruggeman model can sufficiently be used. Hamilton and Crosser [21] modified Maxwell’s model to determine the effective thermal conductivity of non-spherical particles by applying a shape factor n. The formula yields, (4) where n = 3/ψ and ψ is the sphericity, defined by the ratio of the surface area of a sphere, having a volume equal to that of the particle, to the surface area of the particle. Yu and Choi [38] derived a model for the effective thermal conductivity of nanofluid by assuming that there is no agglomeration by nanoparticles in nanofluids. They assumed that the nanolayer surrounding each particle could combine with the particle to form an equivalent particle and obtained the equivalent thermal conductivity kpe of equivalent particles as fallows,

k pe =

[2(1 − γ ) + (1 + β ) (1 + 2γ )γ ] k 3

− (1 − γ ) + (1 + β )3 (1 + 2γ )

p

(5)

THERMAL CONDUCTIVITY AND VISCOSITY OF NANOFLUIDS 145

where γ = klayer/kp, is the ratio of the nanolayer thermal conductivity to particle conductivity, and β = h/r is the ratio of nanolayer thickness to the original particle radius.

k eff / k f =

k pe + 2 k f + 2φ ( k pe − k f )(1 − β ) 3 k pe + 2 k f − φ ( k pe − k f )(1 + β )

3

(6)

Jang and Choi [39] devised a theoretical model that includes four modes of energy transport; the collision between basefluid molecules, the thermal diffusion of nanoparticles in the fluid, the collision between nanoparticles due to Brownian motion, and the thermal interactions of dynamic nanoparticles with base fluid molecules.

k eff / k f = (1 − φ ) +

kp kf

φ + 3C

df dp

φ Re 2d P Pr

(7)

where Redp is the Reynolds number defined by Redp=(CRMdp)/ν, C is a proportional constant, CRM is the random motion velocity of nanoparticles, ν is the dynamic viscosity of the base fluid, Pr is the Prandtl number, df and dp are the diameter of the base fluid molecule and particle. For typical nanofluids, the order of the Reynolds number and the Prandtl numbers are 1 and 10, respectively. Xie et al. [40] derived an expression for calculating enhanced thermal conductivity of nanofluid by considering The effects of nanolayer thickness, nanoparticle size, volume fraction, and thermal conductivity ratio of particle to fluid. The expression is: (8) with Θ=

β lf ⎡⎢(1 + γ )3 − β pl / β fl ⎤⎥ ⎣

(1+ γ )3 + 2β lf β pl

⎦

(9)

where

k −k β lf = l f

k l + 2k f

β pl =

k p − kl k p + 2k l

k −k β fl = f l

k f + 2k l

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and γ = δ/rp is the thickness ratio of nano-layer and nanoparticle. φT is the modified total volume fraction of the original nanoparticle and nano-layer, φT =φ (1+ γ)3. Besides these models there are many others models, but no single model explains the effective thermal conductivity in all cases. Besides the thermal conductivities of the base fluid and nanoparticles and the volume fraction of the particles, there are many other factors influencing the effective thermal conductivity of the nanofluids. Some of these factors are: the size and shape of nanoparticles, the agglomeration of particle, the mode of preparation of nanofluids, the degree of purity of the particles, surface resistance between the particles and the fluid. Some of these factors may not be predicted adequately and may be changing with time. This situation emphasizes the importance of having experimental results for each special nanofluid produced. 3. Experimental 3.1. MATERIALS

Properties of nanoparticles and base fluid used in this study are shown in Table 1. De-ionized water was used as a base fluid. In the nanofluid, nanoparticles tend to cluster and form agglomerates which reduce the effective thermal conductivity. It is known that ultrasonication break the nanoclusters into smaller clusters. Hong et al. [41] investigated the role of sonication time on thermal conductivity of iron (Fe) nanofluids. The thermal conductivity of each nanofluid showed saturation after a gradual increase as the sonication time was increased. The thermal conductivity of 0.2 vol% Fe nanofluid exhibited 18% enhancement with a 30 min sonication and was saturated after 30 min. So, in order to obtain good quality nanofluids, it is essential that the solid–liquid mixture be exposed to ultrasonication. TABLE 1. Properties of nanoparticles and base fluid used in nanofluids preparation.

3

Density (kg/m ) Thermal conductivity (W/mK) Average particle diameter (nm)

SiO 2

TiO 2

Al2O 3

water

2,220

3,800

3,700

1,000

1.38

10

46

0.613

12

21

30

–

A two-step method was used to produce water based nanofluids with, 0.45, 1.85 vol% concentrations of SiO2 nanoparticles; 0.2, 1.0 and 2.0 vol% concentrations of TiO2 nanoparticles and 0.5 and 1.5 vol% concentrations

THERMAL CONDUCTIVITY AND VISCOSITY OF NANOFLUIDS 147

of Al2O3 nanoparticles. In the first stage of preparation of nanofluids, the proper amount of dry nanoparticles necessary to obtain the desired volume percentage was mechanically mixed in de-ionized water. The next step was to homogenize the mixture using ultrasonic vibration, to break down the agglomerations. In order to decide on a sonication time to be used in the preparation of nanofluids, we applied different sonication times for 1% by volume TiO2–water nanofluids and measured their thermal conductivity (Fig. 4). It may be seen that sonication time has practically no effect on thermal conductivity after 30 min, so we decided to use 30 min of sonication time. No surfactant was used in these experiments. Another possibility for preventing clustering of nanoparticles was to eventually use a surfactant. For this purpose sodium dodecylbenzenesulfonate (SDBS) was used as surfactant, it was mixed to pure de-ionized water at different ratio of SDBS/Al2O3, it was observed that the thermal conductivity of SDBS – water mixture decreased with the increasing SDBS ratios which means that the effect of this surfactant was to decrease the thermal conductivity of the base fluid (see Fig. 5). We further used this surfactant in 1% by volume Al2O3–water nanofluids at different ratio of SDBS/Al2O3, as it can be seen from Fig. 5, its effect on thermal conductivity was still negative. In other words, thermal conductivity of Al2O3–water nanofluids was better than with the same nanofluid with surfactant. So, we decided not to use a surfactant in the preparation of nanofluids. 1.035

Relative Thermal Conductivity

1.03 1.025 1.02 1.015 1.01 TiO2 -water 1% volume

1.005 1 0

5

10

15

20 25 30 35 40 45 Sonication Time (minute)

50

55

60

Figure 4. Relative thermal conductivity of (1% vol.) TiO2–water nanofluid as a function of the sonication time.

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Relative Thermal Conductivity

148

1.05

(Al2O3+water)/(water)

1.04

(Al2O3-SDBS+water)/(water)

1.03

(SDBS+water)/(water)

1.02 1.01 1 0.99 0.98 0.97 0.96 0.95

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

(SDBS/Al2O3), mass ratio

Figure 5. Effect of SDBS surfactant on relative thermal conductivity of 1% by volume Al2O3–water nanofluids at different mass ratio of SDBS/Al2O3.

3.2. METHODS FOR MEASURING THERMAL CONDUCTIVITY OF NANOFLUIDS

Experimental studies on the thermophysical properties of liquids are especially very difficult. The main problem lies in the elimination of convectional heat transfer in the liquid and monitoring of the temperature fields and gradients during the measurement. Stationary as well as transient methods for measuring thermal conductivity or diffusivity of liquids are associated with a temperature gradient which in some cases may induce natural convection in the liquid. If there is a natural convection, the thermal conductivity of the liquid is then measured higher than the real thermal conductivity value. For this reason the temperature gradient must be kept as low as possible and the measurement time must be as short as possible. Although many methods are reported in the literature for the determination of thermal conductivity [42, 43] reliable data for these classes of materials are still lacking. With the growing interest for different commercial composite materials used in the casting industry and demands for more efficient coolants with greater heat transfer capabilities in the auto industry, more accurate measurement techniques are needed. The different techniques for measuring the thermal conductivity of liquids can be classified into two main categories: steady-state and transient methods. Both of these methods have some merits and disadvantages. The equipment for steady state method is simple and the governing equations for heat transfer are well known and simple. The main disadvantage is the very long experimental times required for the measurement and the necessity to keep

THERMAL CONDUCTIVITY AND VISCOSITY OF NANOFLUIDS 149

all the conditions stable during this time. For nanofluids, the steady state methods are not very adequate, during the long measurement time particles may settle down or migrate; it is extremely difficult to keep everything stable during the experimental run. That is the reason why there are very few studies on thermal conductivity of nanofluids with steady state methods. Wang et al. [5] measured the effective thermal conductivity of metal oxide nanoparticle suspensions using a steady-state method. Somewhat later, Das and co-workers [7, 44] measured the effective thermal conductivity of metal and metal oxide nanoparticle suspensions using a temperature oscillation method. The transient hot wire (THW) method has been well developed and widely used for measurements of the thermal conductivities and, in some cases, the thermal diffusivities of fluids with a high degree of accuracy [6, 42]. More than 80% of the thermal conductivity measurements on nanofluids were performed by transient hot wire method [6, 8, 18, 19, 45–47]. Another method for measuring thermal diffusivity is the flash method developed by Parker et al. [48] and successfully used for the thermal diffusivity measurement of solid materials [49]. A high intensity short duration heat pulse is absorbed in the front surface of a thermally insulated sample of a few millimeters thick. The sample is coated with absorbing black paint if the sample is transparent to the heat pulse. The resulting temperature of the rear surface is measured by a thermocouple or infrared detector, as a function of time and is recorded either by an oscilloscope or a computer having a data acquisition system. The thermal diffusivity is calculated from this time–temperature curve and the thickness of the sample. This method is commercialized now, and there are ready made apparatus with sample holders for fluids. There is only one publication on nanofluids with this method, Shaikh et al. [50] measured thermal conductivity of carbon nanoparticle doped PAO oil. Finally, recent works on thermal conductivity measurements using the 3ω method have reported [16, 17]. This method is very accurate and fast will be explained fully in the next section. We used this method which has also the advantage of requiring small amounts of liquids for the measurement. 3.2.1. 3ω Method for Measuring Thermal Conductivity of Fluids This technique based on a hot wire thermal probe with AC excitation and 3ω lock-in detection. Since the principle and procedures of the technique have been described in details previously [51] only a brief description is given here. We consider a thermal probe (ThP) consisting of a metallic wire of length 2l and radius r immersed in a liquid sample, acting simultaneously as a heater and as a thermometer. The sample and probe thermophysical properties are the volume specific heat ρc and the thermal conductivity k, with the respective subscripts (s) and (p). The wire is excited by ac current

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150

at frequency f/2 and we assume that it is thermally thin in the radial direction so that the temperature θ ( f ) is uniform over its cross section. Since the electrical resistance of the wire is modulated by the temperature increase, the voltage across the wire contains a third harmonic V3ω proportional to θ ( f ). It is convenient to use a normalized (reduced) 3ω signal, F( f ) [52]. For r/μs  1, the temperature increase θ ( f ) generated by a modulated line heat source P in an infinite and homogeneous medium can be approximated by [53, 54]:

F( f ) ∝θ ( f ) = −

P/l 2π k s

σ r⎞ P/l ⎛ ⎜ γ + ln s ⎟ = − 2 ⎠ 2π k s ⎝

⎛ 1.26 r π ⎞ ⎜⎜ ln + i ⎟⎟ μs 4⎠ ⎝

(10)

where γ = 0.5772 is the Euler constant. The complex quantity σs is given by σs = (1 + i)/μs = (i2πf/αs)1/2 with μs the thermal diffusion length at frequency f and αs = ks/ρscs the thermal diffusivity. In this work we are concerned with the measurement of thermal properties of water-based nanofluids, relative to pure water (subscript w). From Eq. (10) one has:

k s Im(Fw ) = k w Im(Fs )

cot ϕ s − cot ϕ w =

and

sin(ϕ w − ϕ s ) 2 α = − ln s π αw sin ϕ s sin ϕ w

(11)

For small diffusivity difference the phase yields:

αs π (ϕ s − ϕ w ) = 1+ αw 2 sin 2 ϕ w

(12)

In principle, Eq. (11) give frequency-independent results of, but in practice there is an optimum frequency range such that r/μs < 1 in which ks and αs have stable and low noise values as a function of frequency. The first harmonic in the voltage signal is dominant and must be cancelled by a Wheatstone bridge arrangement. The selection of the third harmonic from the differential signal across the bridge is performed by a Stanford SR850 lock-in amplifier tuned to this frequency (Fig. 6 [55]). The thermal probe (ThP) is made of 40 μm in diameter and 2l = 19.0 mm long

THERMAL CONDUCTIVITY AND VISCOSITY OF NANOFLUIDS 151

Ni wire (Fig. 7). The temperature amplitude θ in water was 1.25 K. The minimum sample volume for Eq. (10) to apply is that of a liquid cylinder centered on the wire and having a radius equal to about 3μs. At 2f = 1 Hz, this amounts to 25 μl. The method was validated with pure fluids (water, methanol, ethanol and ethylene glycol), yielding accurate k-ratios within ±2% (Eq. 11) and absolute α value for water within ±1.5% (Eq. 12).

Figure 6. Schematic diagram of 3ω experimental set-up.

Figure 7. Experimental set-up for 3ω method consisting of thermal probe (ThP), Wheatstone bridge and lock-in amplifier.

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3.3. VIBRATION VISCOMETER FOR MEASURING VISCOSITY OF NANOFLUIDS

The experimental setup for measuring the effective viscosity of nanofluids, consists of a Sine-wave Vibro Viscometer SV-10 and Haake temperaturecontrolled bath with 0.1°C. The SV-10 viscometer (A&D, Japan), has two thin sensor plates that are driven with electromagnetic force at the same frequency by vibrating at constant sine-wave vibration in reverse phase like a tuning-fork. The electromagnetic drive controls the vibration of the sensor plates to maintain constant amplitude. The driving electric current, which is an exciting force, will be detected as the magnitude of viscidity produced between the sensor plates and the sample fluid (Fig. 8 [56]). The coefficient of viscosity is obtained by the correlation between the driving electric current and the magnitude of viscidity. Since the viscosity is very much dependent upon the temperature of the fluid, it is very important to measure the temperature of the fluid correctly. By this viscometer we can detect accurate temperature immediately because the fluid and the detection unit (sensor plates) with small surface area/thermal capacity reach the thermal equilibrium in only a few seconds (Fig. 9). Its measurement range of viscosity is 0.3–10,000 mPas.

Figure 8. Schematic diagram of the vibro viscometer [56].

THERMAL CONDUCTIVITY AND VISCOSITY OF NANOFLUIDS 153

Figure 9. Vibrator (sensor plates) and sample cup.

4. Results and Discussion 4.1. THERMAL CONDUCTIVITY OF NANOFLUIDS

Relative Thermal Conductivity

In Fig. 3 our experimental results for SiO2, Al2O3 and TiO2 samples at room temperature were compared with classical effective thermal conductivity model, known as Hamilton–Crosser model (Fig. 10) [21]. 1.08

water based nanofluids

1.07

TiO2 experimental

1.06

Al2O3 experimental SiO2 experimental

1.05

H-C model TiO2

1.04

H-C model Al2O3

1.03

H-C model SiO2

1.02 1.01 1 0

0.5

1

1.5

2

Particle Volume Fraction (%)

Figure 10. Relative thermal conductivity versus particle volume fraction of TiO2, Al2O3 and SiO2 nanofluids.

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Our experimental results for water based SiO2, Al2O3 and TiO2 nanofluids are lower than the H-C model. Moreover, comparison of the TiO2 nanofluids with the Al2O3 nanofluids showed that the highly thermal conductive material is not always the excellent application for enhancing the thermal transport property of nanofluids. Thermal conductivity of TiO2–water nanofluid has higher enhancement than the Al2O3–water nanofluid, even TiO2 bulk thermal conductivity value is lower than the Al2O3. Similar result was presented by Hong et al. [41] for Fe nanofluids compared with the Cu nanofluids. 4.2. VISCOSITY OF NANOFLUIDS

There are some theoretical formulas in the literature which predict the viscosity of particle suspension in a fluid. Most of the existing formulas were derived from the Einstein’s pioneering work [33]. His formula was based on the assumption of a linearly viscous fluid that contains dilute suspended spherical particles. Then by calculating the energy dissipated by the fluid flow around a single particle and by associating that energy with the work done for moving this particle relatively to the surrounding fluid, he obtained:

μ eff = μ l (1 + 2.5φ )

(13)

where φ is the volume fraction of particles, μl and μeff are the viscosity of the base fluid and effective viscosity of the mixture. This formula is valid for non-interacting particle suspension in a base fluid that is for the volume concentrations is less than 5%. Krieger and Dougherty [57] formulated a semi-empirical equation for relative viscosity expressed as

μ eff

⎛ φ = μ l ⎜⎜ ⎜φ ⎝ m

⎞ ⎟ ⎟ ⎟ ⎠

− [η ]φ m

(14)

where φm is the maximum packing fraction and [η] is the intrinsic viscosity ([η] = 2.5 for hard spheres). For randomly mono-dispersed spheres, the maximum close packing fraction is approximately 0.64. Another model was proposed by Nielsen [58] for low concentration of particles. Nielsen’s equation is as follows:

φ / (1 − φm ) μ eff = μ l (1 + 1.5φ )e

(15)

THERMAL CONDUCTIVITY AND VISCOSITY OF NANOFLUIDS 155

where φ and φm are the volume fraction of particles and the maximum packing fraction, respectively. The measurements of effective viscosity of SiO2–water, TiO2–water and Al2O3–water nanofluids at different particle volume concentrations were performed using Vibro Viscometer SV-10. To be use of the accuracy of the measurement the viscosity of water was measured before and after each experiment. The results of the measurements performed at room temperature are shown in Figs. 11–14. For SiO2–water nanofluids of 12 nm particle size, the experimental results are compared with the above cited 3 models in Fig. 11. It may be seen that measured viscosity values are well above the prediction of the models, the difference becoming larger as the volume concentration is increasing. In Fig. 12, these same results are compared with the existing literature values for the same nanofluids by Wang et al. [59] for 7 and 40 nm particle sizes and Kang et al. [60]. Our experimental results are of the same as those by Wang et al. [59] for the particle size of 7 nm, but larger than the other results. 5 SiO2-water

4.5 This study

Relative Viscosity

4

Einstein model [33]) K-D model [57]

3.5

Nielsen model [58]

3 2.5 2 1.5 1 0

1

2 3 Particle Volume Fraction (%)

4

Figure 11. Relative viscosity of SiO2–water nanofluids as a function of nanoparticle volume fraction compared with the models.

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5

SiO2 - water

4.5

This study 12nm Wang et al. (7nm),[59]

Relative Viscosity

4

Wang et al. (40nm),[59] 3.5

Kang et al. (15 nm),[60]

3 2.5 2 1.5 1 0

1

2 3 Particle Volume Fraction (%)

4

Figure 12. Experimental results of relative viscosity of SiO2 nanofluids, compared to selected literature data.

In Fig. 13, we compared our experimental results on TiO2–water with the results of Masuda et al. [18], He et al. [46] and Murshed et al. [61] and also to Einstein model. All results are well above the prediction of the Einstein model. 1.7

TiO2-water

1.6 Turgut et al., [16] Masuda et al., [18] He et al., [46] Murshed et al., [61] Einstein model [33]

Relative Viscosity

1.5 1.4 1.3 1.2 1.1 1 0

0.5

1

1.5

2

Particle Volume Fraction (%)

Figure 13. Relative viscosity of TiO2–water nanofluids as a function of nanoparticle volume fraction.

THERMAL CONDUCTIVITY AND VISCOSITY OF NANOFLUIDS 157 2

water based nanofluids

water 0.2% TiO2 1% TiO2 2% TiO2 0.45% SiO2 1.85% SiO2 0.50% Al2O3 1.50% Al2O3

.

1.6

Viscosity, mPa.s

1.8

1.4 1.2 1 0.8 0.6 0.4 20

25

30

35

40

45

50

Temperature, 8C

Figure 14. Comparison of effective viscosity of water based nanofluids with as a function of temperature.

Figure 14 shows the effective viscosity of all three nanofluids with different volume concentrations of particles, measured at temperatures between 20°C and 50°C. The viscosity of nanofluids increased dramatically with an increase in particle concentration and decreased with temperature, following the trend of the viscosity for pure water, for low particle concentrations. 5. Conclusions The thermal conductivities of SiO2–water, TiO2–water and Al2O3–water nanofluids were measured using a 3ω method for different particle concentrations and temperatures. The experimental results showed that the thermal conductivity enhancements were relatively in good agreement with the Hamilton–Crosser model, and they were moderated increases, not as high and sometimes qualified as anomalous increases as claimed by some researchers [4, 5, 7–10]. In fact the review of experimental studies clearly showed a lack of consistency in the reported results of various research groups. The effects of several important factors such as particle size and shapes, clustering of particles, temperature of the fluid, and dissociation of surfactant on the effective thermal conductivity of nanofluids were not investigated adequately. It is very important that more investigations should be performed, in order to confirm the effects of these factors on the thermal conductivity for wide range of nanofluids. From our results, we also noticed that, although thermal conductivity of TiO2 was much higher than Al2O3,

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the thermal conductivities of Al2O3–water nanofluids were significantly higher then TiO2–water nanofluids, which means that the thermal conductivity of the nanoparticles was not the only factor that determines the thermal conductivity of the nanofluids. We also found that the relative thermal conductivity of the nanofluid was not dependant on temperature. The effective viscosities of SiO2–water, TiO2–water and Al2O3–water nanofluids were measured. The results show that for low volume additions of nanoparticles the measured effective viscosity values follow quite well the viscosity values of pure water with a decrease in viscosity with increasing temperature and may be predicted by the Einstein law of viscosity. But, for higher additions of nanoparticles, the Einstein law of viscosity and other viscosity models failed to explain the large increase in viscosity values. Because of the large increase in effective viscosity, large pumping powers are required to circulate the nanofluid used in cooling systems. In order to have a good idea on the applicability of these nanofluids in real engineering systems, effective viscosity must be measured together with the thermal conductivity of the nanofluids. Acknowledgments This work has been supported by TUBITAK (Project no: 107M160), Research Foundation of Dokuz Eylul University (project no: 2009.KB.FEN.018) and Agence Universitaire de la Francophonie (Project no: AUF-PCSI 6316 PS821).

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THERMAL CONDUCTIVITY AND VISCOSITY OF NANOFLUIDS 161 41. K.S. Hong, T.K. Hong and H.S. Yang, Thermal conductivity of Fe nanofluids depending on cluster size of nanoparticles, Applied Physics Letters, 88, 031901 (2006). 42. K.S. Hong, T.K. Hong and H.S. Yang, Thermal Conductivity of Fe Nanofluids Depending on Cluster Size of Nanoparticles, Applied Physics Letters, 88, 031901 (2006). 43. Y. Nagasaka and A. Nagashima, Absolute measurement of the thermal conductivity of electrically conducting liquids by the transient hot wire method, J Phys E: Sci Instrum., 14, 1435–1440 (1981). 44. J.S. Powell, An instrument for the measurement of thermal conductivity of liquids at high temperatures, Meas. Sci. Technol., 2, 111–117 (1991). 45. H.E. Patel, S.K. Das and T. Sundararajan, Thermal conductivities of naked and monolayer protected metal nanoparticle based nanofluids: Manifestation of anomalous enhancement and chemical effects, Appl. Phys. Lett., 83, 2931– 2933 (2003). 46. D.H. Yoo, K.S. Hong and H.S. Yang, Study of thermal conductivity of nanofluids for the application of heat transfer fluids, Thermochim. Acta, 455, 66–69 (2007). 47. Y. He, Y. Jin, H. Chen, Y. Ding, D. Cang and H. Lu, Heat transfer and flow behaviour of aqueous suspensions of TiO2 nanoparticles (nanofluids) flowing upward through a vertical pipe, Int. J. Heat Mass Transfer, 50, 2272–2281 (2007). 48. M.J. Assael, C.F. Chen, I. Metaxa and W.A. Wakeham, Thermal conductivity of suspensions of carbon nanotubes in water, Int. J. Thermophys., 25(4), 971– 985 (2004). 49. W.J. Parker, R.J. Jenkins, C.P. Butler and G.L. Abbott, Flash method of determining thermal diffusivity, heat capacity, and thermal conductivity, J. Appl Phys, 32, 1679–1684 (1961). 50. I. Tavman, Flash method of measuring thermal diffusivity and conductivity, Nato Asi Series, Series E: Applied Sciences, 196, 923–936 (1990). 51. S. Shaikh, K. Lafdi and R. Ponnappan, Thermal conductivity improvement in carbon nanoparticle doped PAO oil: An experimental study, J. Appl. Phys., 101, 064302 (2007). 52. A. Turgut, C. Sauter, M. Chirtoc, J.F. Henry, S. Tavman, I. Tavman and J. Pelzl, AC hot wire measurement of thermophysical properties of nanofluids with 3 omega method, Europ. Phys. J. Special Topics, 153, 349–352 (2008). 53. M. Chirtoc. and J.F. Henry, 3ω hot wire method for micro-heat transfer measurements: From anemometry to scanning thermal microscopy (SThM), Europ. Phys. J., Special Topics, 153, 343–348 (2008). 54. H.W. Carslaw and J.C. Jaeger, Conduction of Heat in Solids, Oxford University Press, London, UK (1959). 55. D.G. Cahill, Thermal conductivity measurement from 30 to 750 K: the 3 omega method, Rev. Sci. Instrum., 61, 802–808 (1990). 56. M. Chirtoc, X. Filip, J.F. Henry, J.S. Antoniow, I. Chirtoc, D. Dietzel, R. Meckenstock and J. Pelzl, Thermal probe self-calibration in ac scanning thermal microscopy, Superlattices and Microstructures, 35, 305–314 (2004).

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FORMATION OF DROPLETS AND BUBBLES IN MICROFLUIDIC SYSTEMS P. GARSTECKI

Department of Soft Condensed Matter, Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland, [email protected]

Abstract. The lecture will review the recent advances in the techniques for formation of bubbles of gas and droplets of liquid in two-phase microfluidic systems. Systems comprising ducts that have widths of the order of 100 μm produce suspensions of bubbles and droplets characterized by very narrow size distributions. These systems provide control over all the important parameters of the foams or emulsions, from the volumes of the individual bubbles and droplets, through the volume fraction that they occupy, the frequency of their formation, and the distribution of sizes, including monodisperse, multimodal and non-Gaussian distributions. The lecture will review the fundamental forces at play, and the mechanism of formation of bubbles and droplets that is responsible for the observed monodispersity.

1. Introduction 1.1. MICROFLUIDICS

Microfluidics is a concept that describes the science and technology of design, fabrication and operation of systems of microchannels that conduct liquids and gases. Typically, the channels have widths of tens to hundreds of micrometers and the speed of flow of the fluids is such that the viscous forces dominate over inertial ones. The resulting – linear – equations of flow and its laminar character provide for extensive control: the speed of flow obeys the simple Hagen–Poiseuille equation that relates the speed linearly to the pressure drop through the particular channel and to its inverse hydraulic resistance, which in term is a function of the dimensions of the channel and the viscosity of the fluid. This property, when combined with typically large values of the Peclet number [1] that reflect the fact that diffusional transport is typically slow in comparison to the flow, it is possible to control the profiles of concentration [2] of chemicals and S. Kakaç et al. (eds.), Microfluidics Based Microsystems: Fundamentals and Applications, DOI 10.1007/978-90-481-9029-4_9, © Springer Science + Business Media B.V. 2010

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profiles of temperature [3] in the channels, all with minute consumption of the fluids and energy. These characteristics prompted for visions of use of the microfluidic chips in analytical chemistry and diagnostics. In the 1990s, the existing technologies of chemical analysis – chromatography and electrophoresis – which already took advantage of guiding fluids in channels of small crosssections inspired the vision of constructing more integrated devices (in the format of chips) for sensitive assays with high resolution and operating on small samples of fluids [4]. The vision of integration is one of the keys to the interest in microfluidics in general. Already first demonstrations of electrophoresis on chip [5] suggested that complicated protocols for chemical analyses will be feasible – as already demonstrated by a number of groups [6]. A crucial contribution to the explosion of research activity in the field of microfluidics was the development of approachable procedures for microfabrication [4]. Fast prototyping via lithography and replication of the masters in polydimethylosiloxane – a technique often related to as softlithography [7] – made it possible to go from the idea to the fabricated chip within a day, with facile reproduction of the existing masters for multiple experiments [7]. Now, about 20 years from the first demonstrations [5] the field has generated thousands of academic demonstrations of analytical techniques performed on-chip, including e.g. highly integrated systems [8] and commercial applications. 1.2. DROPLET MICROFLUIDICS

A new wave of interest and prospects for applications came in the beginning of this century with the demonstration from Thorsen et al. [9] of formation of monodisperse aqueous droplets in an organic carrier fluid performed on a microfluidic chip. Although the use of fluidic ducts of micron-scale crosssections for generation of monodisperse droplets [10] have been known, this demonstration was critical for establishing the new field. The observation that one can control the flow of immiscible fluids with similar fidelity as that practiced with simple fluids [11] was highly non-trivial: introduction of the interfacial forces results in complicated interactions with their magnitude depending on the curvature and surface area of the interface. In spite of this, and as will be described in this lecture, multiphase flows do subject themselves to extensive control. In particular, and of highest interest, are the processes of formation of droplets, bubbles, and more complicated objects, such as multiple droplets, particles and capsules. These phenomena and their understanding form the basis of a number of potential applications – both in the field of synthesis of new materials and formulations for the

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pharmaceutical, cosmetic and food industries, and in construction of systems for analytical and synthetic chemistry.

Figure 1. Number of scientific articles citing the word ‘microfluidics’ plotted as a function of the year of publication [ISI Web of Knowledge]. The dashed line gives an exponential growth of the number of publications in the years 1994 to ~2002.

The field of microfluidics has gone through the phase of rapid expansion and is now maturing (Fig. 1). The exponential explosion of interest in the field has slowly saturated and the field is transiting into the phase of more application oriented research. This is possible because the fundamental concepts and understanding – although still being areas of active investigation – have been already laid. Our lectures during the NATO Advanced Study Institute on Microsystems for Security in Cesme (2009) concentrated on the fundaments of understanding of (i) formation of droplets, and (ii) transport of droplets in complicated networks of channels. Here we discuss the first of these two subjects, describing the most important forces at play, the mechanism of formation of bubbles and droplets in common microfluidic geometries, and the show examples of the use of this technology. We note that this lecture does not strive to provide an in-depth review of the field, but rather an approachable introduction that contains the basic understanding of the most common techniques. 2. Interfacial Tension and Conventional Methods of Emulsification Immiscible fluids, when brought in contact, develop a well defined interface between them. The existence of this interface contributes a cost to the free energy of the system. This contribution Eγ, which is often related to as interfacial energy, is proportional to the surface area A of the interface. The

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coefficient of proportionality is the coefficient of interfacial tension γ with the units of force per length [N/m]. One can easily translate the equation Eγ′ = Aγ

(1)

that relates the energy with the surface area of the interface, into the language of forces.

Figure 2. The Laplace pressure – pressure exerted by curved interfaces – is proportional to the sum of the principal curvatures. This is why a deformed droplet restores its perfectly spherical shape. The red arrows signify the direction and magnitude of the restoring interfacial force.

If we consider a small a change of the shape of the interface, parameterized by a small displacement dr, the force will read: F = dEγ′/dr = γ dA/dr.

(2)

It is more convenient to express the force per unit area, which is the pressure exerted by an interface. For a sphere with A = 4πr2, we have: pγ = (1/A)(dEγ /dr) = γ(1/Α)(dA/dr) = 2γ(1/r).

(3)

The pressure inside a droplet being in equilibrium with its surrounding, immiscible fluid is larger than the pressure p outside exactly by the value of pγ. Importantly, for an arbitrary surface, the two principal radii of curvature may be pointing in opposite directions and then the Laplace pressure will be given by the difference of their magnitudes and oriented into the direction of the smaller radii of curvature – into the direction in which the interface is more concave (Fig. 2). This is why a cylindrical morphology of an immiscible fluid is unstable. Any infinitesimal undulation of the axial profile of the cylinder can be

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Figure 3. The Rayleigh–Plateau instability. A cylindrical morphology of an immiscible fluid is unstable: even the smallest undulation of the radius of the cylinder amplifies because the radial curvature at the point at which the radius is smaller than the average radius is larger than at the point in which the radius is larger than average. The resulting Laplace pressure drives the fluid out from the collapsing neck and the cylinder breaks up into droplets. The photograph on the right illustrates a jet of water breaking up into droplets in air.

decomposed – via a series expansion – into sinusoidal perturbations, and all of these perturbations characterized by a length larger than a certain critical value spontaneously amplify (Fig. 3) and the cylinder breaks into droplets. The speed of this spontaneous break-up can be estimated from dimensional analysis. When the viscous terms dominate the dynamics, the surface of the cylinder will be imploding with a speed that can be approximated as u = γ/μ, where μ is the viscosity of the fluid. The Rayleigh–Plateau instability underlies most of the common techniques of emulsification and atomization: it is enough to deform the immiscible fluid into elongated morphologies, and this deformation triggers the onset of the Rayleigh Plateau instability. There are several ways of deforming the immiscible fluids. For example, in a fountain the liquid (water) is ejected from a nozzle at a large speed. The inertia of water is much larger than the interfacial forces that act to minimize the interfacial area of the out-flowing water and an elongated jet can be readily formed. This jet subsequently undergoes the instability and breaks into small droplets. Similarly, a jet can be pulled from a reservoir of liquid by gravity (e.g. in a dripping faucet). In industry, the most common way of emulsification is shearing: a high magnitude shear stress is applied to a blend of two immiscible fluids, or a suspension of large droplets, and these droplets are elongated in the shear field into unstable, elongated shapes that subsequently break into smaller

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droplets. The interplay between the viscous shear forces and the interfacial forces is reflected by the value of the non-dimensional capillary number: Ca = μu/γ.

(4)

The mean size of the droplets formed by shearing can be approximated by equating an estimated shear stress τ in the system, given by the characteristic speed divided by the characteristic length L over which the liquid is sheared (e.g. the radius of the container): τ ~ μu/L, with an estimated interfacial restoring pressure pγ ~ γ/r. The radius r of the tightest curvature that can be created with shear τ can be then estimated from τ = pγ , which yields: r ≈ L(γ /μu) = LCa– 1.

(5)

Since the average diameter of the droplets formed via the Rayleigh–Plateau instability of a liquid cylinder is proportional (and similar) to the diameter of the unstable cylinder, r ∝ Ca– 1 also gives an estimate of the radii of the droplets formed by shearing. Importantly, in practically all common techniques of formation of drops and bubbles, the liquids are deformed geometrically with the use of a force of choice, and then they spontaneously break into smaller bits by the action of the interfacial tension. As we will discuss it below, emulsification in microfluidic devices constitutes a very different route to emulsification. 3. Microfluidic Emulsification One of the features that are particular to microfluidics – as opposed to other experiments on viscous flows or flows dominated by interfacial effects – is the physical confinement of the flow by the walls of the microchannels. As we describe below, this feature plays an important role in the processes of formation of bubbles and droplets. Although there are numerous variants and detailed technical solutions, the two most commonly used geometries for formation of bubbles and droplets on microfluidic chips are very simple: a T-junction and a flow-focusing geometry. The T-junction was introduced by Thorsen et al. [9] and comprises a main channel carrying the continuous fluid and a side channel that delivers the fluid-to-be-dispersed (Fig. 4). The flow-focusing geometry was first demonstrated in the work by A. GananCalvo on axisymmetric systems operating at higher Reynolds, capillary and Weber numbers. As shown early in 2003 by S. Anna and collaborators [12], this concept proved to be applicable also to the planar geometries of standard microfluidic chips.

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Figure 4. The T-junction [9] (Adapted from Ref. [13]). An axisymmetric flow-focusing geometry [10] (Adapted from Ref. [14]). A planar flow-focusing device [12] (Adapted from Ref. [15]).

3.1. FORMATION OF BUBBLES AND DROPLETS IN A PLANAR FLOW-FOCUSING GEOMETRY

Qualitatively, the operation of the microfluidic flow-focusing system can be described in the following way. Two immiscible phases (e.g. Nitrogen and water, or water and oil) are delivered via their inlet channels to the flowfocusing junction. In this junction, one central inlet channel, that delivers the fluid-to-be-dispersed (e.g. Nitrogen to be dispersed into bubbles) ends upstream of a small constriction (an orifice). From the sides of the central channel, two additional ones terminate upstream of the orifice. These side channels deliver the continuous fluid (e.g. aqueous solution of surfactant). It is important that these continuous phase wets the walls of the microfluidic device preferentially. Otherwise – if the fluid-to-be-dispersed – wets the walls, the resulting flows are erratic [16] and it becomes virtually impossible to form bubbles (droplets) in a reproducible and controllable process. The fluids are delivered to the chip with constant input conditions – either a fixed rate of flow or a fixed pressure applied to the inlet. Regardless of the choice of the boundary conditions [17] (fixed rate of flow or fixed pressure) a pressure gradient develops along the central axis of the flow focusing device and this pressure drop drives the two immiscible fluids through the constriction: the tip of the inner phase enters the orifice and starts to inflate a bubble (or fill a droplet) growing upstream of the orifice. At the same time, in the orifice, a neck develops on the inner stream and it begins to thin, breaks, releases a bubble (droplet) and retracts upstream to its original position. The range of pressures (rates of flow) applied to the inlets for which such a simple, periodic dynamics is observed depends on the particular system, and e.g. coupling between the dynamics of flow in the orifice and the flow in the outlet channel [18–20] yet it is typical for microfluidic system, that this simple mode of operation can be obtained and

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sustained in a stable operation. Also, typically the bubbles and droplets produced in this mode of operation are tightly monodisperse with the standard deviation of their diameter well below of 5% of the mean value.

Figure 5. The simple periodic mode of a flow-focusing device illustrated on five micrographs taken during the period of formation of a single bubble in this microfluidic flow-focusing device [15].

In our experiments [15] on using the microfluidic flow-focusing geometry for formation of monodisperse bubbles of Nitrogen in a continuous liquid of aqueous solutions of surfactant and glycerin we found that the volume of the bubbles (V ) depended on the pressure ( p) applied to the stream of gas, the rate of flow (Q) of the continuous liquid and its viscosity ( μ) (Fig. 5): V ∝ p/Qμ

(6)

In addition we noticed that the frequency ( f ) of formation of the bubbles was proportional to the product of Q and p: f ∝ pQ.

(7)

Interestingly, the volume of the bubbles depends on the ratio of p and Q, while the frequency of their formation on the product of the two values. This interdependence of V and f on p and Q is equivalent to a transformation of variables: (p, Q) → (V, f )

(8)

which allows for a simultaneous and independent tuning of the volume of individual bubbles and volume fraction of the gaseous phase in the resulting foam. As such, the microfluidic flow-focusing device is a perfect foammaker, as all the important parameters of a monodisperse foam can be controlled independently and in parallel.

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W liquid Wm

gas liquid

Zm

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500 µm 100 µm

t = 0 µs

230 µs

320 µs

400 µs

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Figure 6. Experiments on time-resolved tracking of the shape of the gas–liquid interface during the process of formation of a single bubble in a microfluidic flow-focusing device. From a video recording of the process of break-up, we extract the projection of the interface on the x–y plane (plane of the microfluidic device). We then extract the minimum width of the neck as a function of time (Adapted from Ref. [21]).

Quite surprisingly, alternation of the interfacial tension (γ) did not introduce significant changes in V. This observation is curious because (i) the proportionality between the volume of the bubble and a term (Qμ)−1 suggests a dependence on the capillary number, similar to that observed in classical shearing, (ii) the values of the capillary number for the experiment lay in the range of 10–3 to 10–1, suggesting that interfacial tension should dominate over the shear stresses or at least play an important role in the process of formation of bubbles. In order to understand the process of break-up with recorded high-speed videos (Fig. 6) of the profile of the gaseous tip during the process of formation of a bubble, for a wide range of values of p, Q, μ and γ. Analysis of these videos allowed us to determine the width (w) of the collapsing neck as a function of time and the speed of collapse ucollapse = dw/dt. We observed that this speed depends only on the value of the rate of flow of the continuous phase and is linearly proportional to Q. Second important observation is that the values of the speed of collapse that we recorded in our experiments were significantly smaller than the value of the capillary speed (γ/μ) which for our experiments should range between 10 and 100 m/s, while ucollapse lay in the range of 10–3 to 1 m/s.

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Figure 7. Left chart shows the evolution of the width of the collapsing neck (w) as a function of time within the process of formation of a single bubble. The graph on the right shows the speeds of collapse (the slopes of the linear decay of w) as a function of the rate of flow of the continuous fluid for a range of parameters (p, μ, γ) (Adapted from Ref. [21]).

These observations suggest that the collapse of the gaseous thread – and the break-up of the stream of gas into bubbles – cannot be driven by interfacial stresses, as is the case in conventional emulsification techniques. The process of break-up can be qualitatively understood when one notices that the shape of the gaseous thread in the orifice is actually stable against the action of interfacial stresses (that is against a Rayleigh–Plateau type of an instability). This supposition was confirmed via numerical simulation of a catenoid-shaped membrane spun on two rectangular rims: one corresponding to the end of the inlet channel for gas, and the second to the terminus of the orifice. In addition, these simulations allowed for determination of the width of the neck of this membrane as a function of the volume (Vthread) enclosed inside the membrane, or – alternatively – of the remaining volume of the orifice and the inlet channels for the continuous fluid, outside of the membrane. The dependence of w on Vthread (Fig. 8) looks qualitatively similar to the dependencies of w on time recorded in our experiments (Fig. 7). The experimental traces of w(t) can be translated into w(V0 − Vthread) by multiplying time (t) by the rate of inflow of the continuous phase (Q). This construct allows for a quantitative comparison of the kinetics of break-up (collapse of the neck of the gaseous thread) recorded experimentally with the quasistatic evolution of the interface that traverses shapes that minimize their interfacial area for a given boundary condition (Vthread). This comparison yields an almost perfect agreement (Fig. 8) between experiment and the quasistatic evolution, for a wide range of the pressures, rates of flow, viscosities and interfacial tensions.

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Figure 8. Quasistatic break-up. The chart on the left shows the width of the neck of simulated catenoid-like interfaces as a function of the volume that is enclosed inside them. The plot on the right shows a quantitative comparison of the simulated – quasistatic – process with the experimental data for a range of parameters (Q, p, μ, γ) (Adapted from Ref. [21]).

The above observations can be explained as follows. Once the tip of the gaseous phase enters the orifice, it fills almost the entire cross-section of this microchannel. This is because the value of the capillary number is low: the interfacial forces dominate the shear stress, the tip assumes a compact, and area-minimizing shape, and restricts the flow of the continuous liquid to thin films between the interface and the walls of the orifice. As the flow in thin films is subject to an increased viscous dissipation (and resistance) the liquid inflowing from the inlet channels cannot pass through the orifice. Instead, the pressure upstream of the orifice rises and the liquid squeezes the neck of the stream of gas. As the rate of inflow of the continuous liquid is externally fixed to a constant value, this squeezing proceeds at a rate that is strictly proportional to Q and independent of all the other parameters (pressure, viscosity of the liquid, the value of interfacial tension). This model has been confirmed in detailed experiments by Marmottant et al. [22]. The quasistatic model of formation of bubbles explains the observed monodispersity of the bubbles: because the speed of collapse is much smaller than the capillary speeds and the speed of sound in the liquid, any perturbations in flow, pressure, or shape of the interface are equilibrated on timescales much shorter than the interval needed for formation of a single bubble.

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Figure 9. Formation of droplets in microfluidic flow-focusing devices. The micrographs on the left illustrate the process of formation of aqueous drops in an organic continuous fluid [S. Makulska, P. Garstecki, Institute of Physical Chemistry PAS]. The chart on the right shows the dependence of the volume of liquid droplets formed in a planar flow focusing device on the value of the capillary number (Adapted from Ref. [24]).

The quasistatic model of break-up can be extended also to the liquid– liquid systems. In the case of formation of droplets in microfluidic flowfocusing devices the situation is more complicated, because the viscosities of both of the liquids play a role in the process, and the shear stresses can be transferred between them (Fig. 9). Further, the quasistatic model will work only in the regimes in which the capillary speed is larger than the characteristic time for break up which is related to the time needed for filling the volume of the orifice with the continuous fluid. Nie et al. [23] and Lee et al. [24] reported detailed experiments on formation of droplets in planar microfluidic flow-focusing chips and identified distinct regimes of squeezing (the quasistatic mode), dripping, and jetting. Importantly, in the squeezing mode, the break-up obeys the quasistatic model with only a slight dependence of the diameter of the droplets on the value of the capillary number [24]. 3.2. FORMATION OF BUBBLES AND DROPLETS IN A T-JUNCTION

The T-junction, depicted in Fig. 4, is one of the most common geometries used in microfluidic chips to create discrete segments of immiscible fluids. The design of the apparatus is extremely simple – a main, straight channel, that carries the continuous fluid is joined from the side, usually at a right angle, by a channel that supplies the fluid-to-be-dispersed. The operation of the T-junction depends on the values of the speeds of flow of the two phases that can be parameterized by the value of the capillary number (Fig. 10). At low values of the capillary number (typically Ca < 10–2) formation of droplets obeys the squeezing model, that we will

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describe shortly below, at intermediate values of Ca the device operates in the dripping mode in which the viscous effects become noticeable, and finally, at highest rates of flow, the system develops a long jet from which droplets are sheared off.

Figure 10. Regimes of formation of droplets in microfluidic T-junction: squeezing at low values of the capillary numbers, dripping (with slight dependence of the volume of the droplets on the value of the Ca) for intermediate values of the capillary number, and jetting at high values of Ca (Adapted from Ref. [25]).

In the first demonstration of formation of monodisperse droplets in a microfluidic T-junction [9], on the basis of the experimental results on scaling of the droplet size with the rate of flow of the continuous fluid, it was hypothesized that the droplets are sheared off from the junction by the flow of the continuous fluid, similarly to the classical models of sheardriven emulsification. However, the fact that the break-up occurs in a confined geometry of the microchannels, and that the droplet growing off the inlet of the fluid-to-be-dispersed usually occupies a significant fraction of the cross-section of the main channel, suggest that the pressure drop along a growing droplet may be an important factor in the process. Garstecki et al. conducted careful experiments [13] in which they varied (i) the geometry of the device, (ii) the rates of flow of the two fluids, (iii) the viscosity of the continuous fluid and (iv) the value of the interfacial tension. These experimental results verified that at low values of the Capillary number – which are typical to those typical for flows in microsystems – indeed the mechanism of break-up is similar to that observed in the flowfocusing system. Namely, as the tip of the dispersed phase enters the main channel, and fills its cross-section, the hydraulic resistance to flow in the thin films between the interface and the walls of the obstructed microchannel creates an additional pressure drop along the growing droplet. This pressure drop has a primary influence on the dynamics of break-up: namely, once the main channel is obstructed by the growing droplet, the upstream interface of

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the droplet is pushed downstream by the continuous fluid at its – externally fixed – rate of flow. Once this interface is pushed against the downstream wall of the channel that delivers the fluid-to-be-dispersed to the junction, the neck connecting the stream of this fluid with the droplet breaks and the droplet is released. ~W

Vc

μc

μd

Vd

ε ~W/2 ~W W

Figure 11. Forces acting on the droplet growing in a T-junction. As the droplet fills the cross-section of the main channel, it is separated from the wall of the main channel by thin films of the continuous fluid, with the thickness of the film separating it from the wall that is opposite to the inlet for the dispersed phase marked as ε. The blue arrow symbolizes the interfacial forces that stabilize the droplet against breaking off from the junction. The green arrow indicates the shear stress that acts to break the droplet off, and scales as ε−n with n < 2. Finally, the black arrow denotes the pressure drop along the droplet, that scales as ε−m with m > 2 (The left panel adapted from DeMenech et al. [25]).

Within this simple model the volume of the droplet is determined only by the rates of flow of the two immiscible fluids and not by their material parameters (viscosities and interfacial tension between them). For the simplest geometry of the T-junction with the widths (w) of the main and side channels equal to their common height, the volume of the droplet is approximately equal to the initial volume of the droplet that blocks the channel (~w3) plus the volume of the to-be-dispersed fluid that flows into the droplet while it is squeezed. This last volume is equal to the rate of flow of the inner (droplet) phase (Qin) multiplied by the time that it takes to squeeze the collapsing neck of the inner phase by the outer fluid: tsqueeze ~ w3/Qout. Combining these two terms and normalizing by w3 yields an equation for normalized length of the droplet (Fig. 11): L/w = 1 + αQin/Qout.

(9)

The above equation correctly approximates the volumes of the droplets at low values of the Capillary numbers for a range of geometries of the Tjunctions, with the exact value of the constant α of order one depending on the aspect ratios of the widths and height of the microchannels forming the T-junction device.

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1

slope =−

1/5

p slo e =

10

10m Pas, 0.028 mL/s 10m Pas, 0.28 mL/s 100m Pas, 0.0028 mL/s 100m Pas, 0.028 mL/s 10 0m Pas, 0.028 mL/s

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Vd

L/W

−1

1 1

1

λ=1 λ = 1/8

squeezing 0.1 0.01

0.1

1

Qwater /Qoil

squeezing 10

0.001

0.01 Ca

dripping 0.1

Figure 12. The graph on the left shows the dependence of the volume of the droplets (here length of the droplets) on the value of the ratio of the volumetric rates of flow of the inner and outer immiscible phases. The fact that series recorded for varied speed of flow, viscosity and interfacial tension overlay on each other confirm the validity of the squeezing model of break-up for low values of the capillary number (Adapted from Ref. [13]). The chart on the right shows the variation of the volume of the droplets with an increasing value of the capillary number, illustrating the transition from squeezing to dripping at Ca ~ 10–2 (Adapted from Ref. [25]).

As can be noticed in the right-hand side plot in Fig. 12, in both the squeezing and the dripping regimes, the shearing effects do play a role. In the squeezing regime these effects are secondary and the squeezing model approximates the volume of the droplets well. In the dripping regime, both the shear stress exerted by the continuous fluid on the growing droplet and the pressure drop along the growing droplet are important and both in simulations [25] and experiment [26] the scaling of the volume of the droplet exhibits a significant dependence on the value of the Capillary number. We refer the interested reader to the recent publications [25, 26] that detail the concepts, observations and understanding of formation of bubbles and droplets in microfluidic T-junctions. 3.3. SUMMARY

The mechanisms of formation of discrete segments of fluids in microfluidic flow-focusing and T-junction devices, that we outlined above point to (i) strong effects of confinement by the walls of the microchannels, (ii) importance of the evolution of the pressure field during the process of formation of a droplet (bubble), (iii) quasistatic character of the collapse of the streams of the fluid-tobe-dispersed, and (iv) separation of time scales between the slow evolution of the interface during break-up and fast equilibration of the shape of the interface via capillary waves and of the pressure field in the fluids via acoustic waves. These features form the basis of the observed – almost perfect – monodispersity of the droplets and bubbles formed in microfluidic systems at low values of the capillary number.

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3.4. EXTENSION OF THE TECHNIQUES OF FORMATION OF DROLETS

The control that can be exerted over the flow of immiscible fluids in microfluidic devices to formation of monodisperse droplets and bubbles can be extended to formation of more complicated objects and architectures of the droplets, such as multiple emulsions [27–32], Janus particles [33, 34] and other morphologies of liquid droplets, solidified particles and capsules [35– 39]. Figure 13 presents micrographs of the droplets, particles and capsules produced in exemplary techniques.

Figure 13. (a–c) Examples of multiple emulsions formed in microfluidic systems. (a) Adapted from Okushima et al. [29]. (b) Adapted from Seo et al. [30]. (c) Adapted from Utada et al. [31]. (d) ‘Composite emulsion’ formed by droplets of different composition and different volume formed in situ in a microfluidic device comprising three flow-focusing geometries integrated into one outlet channel (Adapted from Hashimoto et al. [40]). (e) Examples of anisotropic particles formed by either polymerization (spheres and disks, rods) of droplets of monomer or thermal setting of droplets of metal (ellipsoids) in situ in a microfluidic device (Adapted from Xu et al. [35]). (f) A micrograph of a nylon capsule polymerized in situ in a microfluidic device, with an aqueous core containing magnetic particles [39].

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4. Conclusions Microfluidic systems offer techniques for- and extensive control over-the processes of formation of bubbles, droplets, compound droplets, particles and capsules. Understanding of these processes form the basis for applications in on-chip systems for analytical an synthetic chemistry and in preparatory technologies.

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14. P. Garstecki, A.M. Ganan-Calvo, and G.M. Whitesides, Formation of bubbles and droplets in microfluidic systems, Bulletin of the Polish Academy of Sciences, 53, 361–372, (2005). 15. P. Garstecki, I. Gitlin, W. DiLuzio, G.M. Whitesides, E. Kumacheva, and H.A. Stone, Formation of monodisperse bubbles in a microfluidic flowfocusing device, Applied Physics Letters, 85, 2649–2651, (2004). 16. R. Dreyfus, P. Tabeling, and H. Willaime, Ordered and disordered patterns in two-phase flows in microchannels, Physical Review Letters, 90, (2003). 17. T. Ward, M. Faivre, M. Abkarian, and H.A. Stone, Microfluidic flow focusing: Drop size and scaling in pressure versus flow-rate-driven pumping, Electrophoresis, 26, 3716–3724, (2005). 18. J.P. Raven and P. Marmottant, Periodic microfluidic bubbling oscillator: Insight into the stability of two-phase microflows, Physical Review Letters, 97, (2006). 19. J.P. Raven and P. Marmottant, Microfluidic Crystals: Dynamic Interplay between Rearrangement Waves and Flow, Physical Review Letters, 102, (2009). 20. M.T. Sullivan and H.A. Stone, The role of feedback in microfluidic flowfocusing devices, Philosophical Transactions of the Royal Society a-Mathematical Physical and Engineering Sciences, 366, 2131–2143, (2008). 21. P. Garstecki, H.A. Stone, and G.M. Whitesides, Mechanism for flow-rate controlled breakup in confined geometries: A route to monodisperse emulsions, Physical Review Letters, 94, (2005). 22. B. Dollet, W. van Hoeve, J.P. Raven, P. Marmottant, and M. Versluis, Role of the channel geometry on the bubble pinch-off in flow-focusing devices, Physical Review Letters, 100, (2008). 23. Z.H. Nie, M.S. Seo, S.Q. Xu, P.C. Lewis, M. Mok, E. Kumacheva, G.M. Whitesides, P. Garstecki, and H.A. Stone, Emulsification in a microfluidic flow-focusing device: effect of the viscosities of the liquids, Microfluidics and Nanofluidics, 5, 585–594, (2008). 24. W. Lee, L.M. Walker, and S.L. Anna, Role of geometry and fluid properties in droplet and thread formation processes in planar flow focusing, Physics of Fluids, 21, (2009). 25. M. De Menech, P. Garstecki, F. Jousse, and H.A. Stone, Transition from squeezing to dripping in a microfluidic T-shaped junction, Journal of Fluid Mechanics, 595, 141–161, (2008). 26. G.F. Christopher, N.N. Noharuddin, J.A. Taylor, and S.L. Anna, Experimental observations of the squeezing-to-dripping transition in T-shaped microfluidic junctions, Physical Review E, 78, (2008). 27. T. Nisisako, Microstructured devices for preparing controlled multiple emulsions, Chemical Engineering & Technology, 31, 1091–1098, (2008). 28. T. Nisisako, S. Okushima, and T. Torii, Controlled formulation of monodisperse double emulsions in a multiple-phase microfluidic system, Soft Matter, 1, 23–27, (2005). 29. S. Okushima, T. Nisisako, T. Torii, and T. Higuchi, Controlled production of monodisperse double emulsions by two-step droplet breakup in microfluidic devices, Langmuir, 20, 9905–9908, (2004). 30. M. Seo, C. Paquet, Z.H. Nie, S.Q. Xu, and E. Kumacheva, Microfluidic consecutive flow-focusing droplet generators, Soft Matter, 3, 986–992, (2007).

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31. R.K. Shah, H.C. Shum, A.C. Rowat, D. Lee, J.J. Agresti, A.S. Utada, L.Y. Chu, J.W. Kim, A. Fernandez-Nieves, C.J. Martinez, and D.A. Weitz, Designer emulsions using microfluidics, Materials Today, 11, 18–27, (2008). 32. A.S. Utada, E. Lorenceau, D.R. Link, P.D. Kaplan, H.A. Stone, and D.A. Weitz, Monodisperse double emulsions generated from a microcapillary device, Science, 308, 537–541, (2005). 33. T. Nisisako and T. Torii, Formation of biphasic Janus droplets in a microfabricated channel for the synthesis of shape-controlled polymer microparticles, Advanced Materials, 19, 1489–+, (2007). 34. T. Nisisako, T. Torii, T. Takahashi, and Y. Takizawa, Synthesis of monodisperse bicolored janus particles with electrical anisotropy using a microfluidic coflow system, Advanced Materials, 18, 1152–+, (2006). 35. S.Q. Xu, Z.H. Nie, M. Seo, P. Lewis, E. Kumacheva, H.A. Stone, P. Garstecki, D.B. Weibel, I. Gitlin, and G.M. Whitesides, Generation of monodisperse particles by using microfluidics: Control over size, shape, and composition, Angewandte Chemie-International Edition, 44, 724–728, (2005). 36. D. Dendukuri, S.S. Gu, D.C. Pregibon, T.A. Hatton, and P.S. Doyle, Stop-flow lithography in a microfluidic device, Lab on a Chip, 7, 818–828, (2007). 37. D.K. Hwang, D. Dendukuri, and P.S. Doyle, Microfluidic-based synthesis of non-spherical magnetic hydrogel microparticles, Lab on a Chip, 8, 1640–1647, (2008). 38. R.F. Shepherd, P. Panda, Z. Bao, K.H. Sandhage, T.A. Hatton, J.A. Lewis, and P.S. Doyle, Stop-Flow Lithography of Colloidal, Glass, and Silicon Microcomponents, Advanced Materials, 20, 4734–+, (2008). 39. S. Takeuchi, P. Garstecki, D.B. Weibel, and G.M. Whitesides, An axisymmetric flow-focusing microfluidic device, Advanced Materials, 17, 1067–+, (2005). 40. M. Hashimoto, P. Garstecki, and G.M. Whitesides, Synthesis of composite emulsions and complex foams with the use of microfluidic flow-focusing devices, Small, 3, 1792–1802, (2007).

TRANSPORT OF DROPLETS IN MICROFLUIDIC SYSTEMS P. GARSTECKI

Department of Soft Condensed Matter, Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland, [email protected]

Abstract. Microfluidics provides for a convenient playground for experiments on dynamic systems. Two phase microfluidic systems present a new class of behaviors that are both complex and stable. The dynamics of flow of droplets through micro-networks are one of such examples: they are complicated because there are long-range interactions between the droplets that modify the pressure distribution in the channels, at the same time the resulting complicated dynamics are robust against experimental disturbances. Flow of droplets through microfluidic networks provide a route to nontrivial and reversible operations on streams of bubbles, logic operations on droplets. This lecture will introduce the rudimentary physics of Stokes flow in a simple pipe, the recent experiments and simulations on the flow of droplets and bubbles through microfluidic networks, and the vision of complex and automated microfluidic chips that perform combinatorial operations on miniaturized chemical reaction beakers – droplets.

1. Introduction 1.1. DROPLET MICROFLUIDICS

Droplet microfluidics is a science and technology of controlled formation of droplets and bubbles in microfluidic channels. The first demonstration of formation of monodisperse aqueous droplets on chip – in a microfluidic T-junction [1] – was reported in 2001. Since then, a number of studies extended the range of techniques, from the T-junction [2–5], to flowfocusing [6–10] and other geometries [11], and the capabilities in the range of diameters of droplets and their architectures [12–16]. These techniques opened attractive vistas to applications in preparatory techniques [17–19], and – what is the focus of this lecture – analytical techniques based on performing reactions inside micro-droplets.

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1.2. FORMATION OF DROPS AT CONSTANT FORCING

The usual way of feeding the microfluidic systems with fluids is to apply either a constant rate of inflow into the chip, or a constant pressure at the inlet [20]. Formation of droplets or bubbles in systems with such, fixed, boundary conditions for flow is realtively well understood. Two microfluidic geometries are most commonly used: a microfluidic T-junction [1] or a microfluidic flow-focusing geometry [6]. After the introduction of the T-junction by Thorsen et al. [1] the details of the mechanism of operation of this system were studied experimentally by Garstecki et al. [3], Colin et al. [5], numerically by De Menech [21]. Recently, a thorough experimental study by Christopher et al. [4] characterized the relevant regimes of formation of droplets in detail and provided accurate analytical models for the scaling of the droplet volume. The flow focusing geometry was first introduced in an axi-symmetric system by Ganan-Calvo [22]. Later, the same concept was succesfully used in a – typical to current microfluidic techniques – planar chip by Anna et al. [6]. The mechanism of formation of bubbles in this planar system was characterized by Garstecki et al. [8] and Marmottant [9]. Later, Kumacheva et al. [23] and Anna et al. [10] extended this characterization to liquid– liquid systems and formation of droplets in continuous liquids at different viscosities of the two immiscible liquids, interfacial tension and geometries of the devices. 1.3. CHEMISTRY IN DROPLETS

The development of techniques and understanding of the processes of formation of monodisperse microdroplets constituted the fundaments for the vision of performing chemical and biochemical reactions inside these nanoand micro-liter liquid segments. Orignially, the interest in the use of microdroplets as reaction chambers stemmed from the opportunity to minimize the volume of liquid samples and – at the same time – obtain multiple measurements from identical, or continuously varied [24] compositions. The feature that the droplets can be practically formed at frequencies of hundreds or thousands droplets per second provides for reliable statistics. Within few years of the first demonstrations [25] it became realized, that performing reactions within droplets offer additional, highly attractive features [26]. These include, for example, the avoidance of dispersion of time of residence in the channels, that is inherent to pressure driven flow-through reaction chambers. This quality stems from the fact that the reaction mixture is enclosed, and constantly stirred [27], within the droplet. Second, the droplet systems provide for convenient and rapid mixing [27] that is otherwise one of the hallmark problems in single fluid microfluidcs. Further, the microfluidic

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droplet systems – via the simple correspondance between the time and position of the droplet flowing in a microchannel – offer for convenient temporal resolution and for control of the kinetic conditions of reactions [28]. 1.4. VISION OF INTEGRATED SYSTEMS

The numerous demonstrations of chemical and biochemical reactions performed in droplets on microfluidic chips [26] has inspired a more challenging vision of the development of automated microfluidic chips having the functionality of a macro-scale, conventional, chemical or biochemical laboratory. Within this vision, the systems should be able to perform reactions within the micro-droplets (i) fast, (ii) on small samples of reagents, and (iii) with reliable statistics of the results. At the same time, these systems need to be capable of performing complicated protocols (with varied temperature, exposition to light, titrations, controlled additions at desired times, separations, etc.) on droplets with on-demand formulated chemical compositions – reaction mixtures of arbitrary concentrations of a large number of reagents. To date, and for reasons that we explain below, the current capabilities fall short of this outstanding vision because they lack the versatility e.g. the commercial well-plate technology. 1.5. OPEN CHALLANGES

Extending the current capabilities of microfluidic droplet based systems for applications in chemistry certainly requires construction of the systems of complicated networks of microchannels, controlled introduction of droplets into these networks, controlled guiding of these droplets, sorting, merging, splitting etc. These requirements open questions and challenges in (i) understanding of the dynamics of transport of droplets through networks of microchannels, and (ii) construction of tools for computer controlled formation and guiding of droplets. As we discuss in more detail below, the flow of droplets through networks of microchannels provides for fascinating but also complex set of phenomena. These complicacies arise from the fact that a droplet (or bubble) traveling in a microchannel increases the hydraulic resistance to flow in that channel, and this – in turn – affects the distribution of pressure in the system, which has an effect on the trajectories of the subsequent droplets. Recent experiments [11, 29] have demonstrated that these properties of flow of droplets in networks can be used to demonstrate intricate processing of signals encoded in sequences of droplets (or intervals between droplets). For example, Fuerstman et al. [30] demonstrated ciphering and deciphering of signals in an all-fluidic microsystem. Prakash and Gershenfeld [31] showed logic operations performed by droplets traveling in appropriately designed microfluidic

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networks. These results, with the observation that the – even very intricate or complex – dynamics of multiphase flows in microchannels is robust to random disturbances or noise [30, 32] suggest that it should be possible to design and operate automated chips performing non trivial operations (e.g. merging, splitting, distributing in the network) on the micro reaction vessels (droplets). Performing thousands of different reactions on a single chip will certainly require computer controlled execution of the pre-encoded protocols. This execution necessitates the development of computer controlled modules for sorting (guiding) droplets and – above all – for introducing droplets of predesigned volumes at scheduled times of emission – a technique often called ‘droplet on demand’. In the last part of this lecture we will review also this subject. 1.6. THE PLAN OF THE LECTURE

We first introduce the basic concepts in physics of flow of simple and multiphase fluid in networks of microchannels. We then go on to demonstrate the phenomenology of the flow of droplets through the simplest network – a single loop of channels – and then provide examples of experiments on more complicated systems. The third part of the lecture introduces the subject of modeling of the dynamics of flow of units of resistance through networks of conductors, and show the results of these efforts and their correspondence to microfluidic flows. Finally, we provide an introduction to the subject of automation of flows of droplets in microchannels and demonstrate an example of the droplet-on-demand system constructed in our laboratory. 2. Flow of Simple and Multiphase Fluids Through Networks 2.1. SIMPLE FLUID IN A NETWORK OF MICROCHANNELS

One of the more beautiful techniques in fluid mechanics is the dimensional analysis, that provides – via simple calculations – a reliable judgment of the relative importance of the various forces that can drive or retard the flow of fluids. In short the procedure rests on construction of non-dimensional groups of parameters that constitute the so-called non-dimensional numbers. The most important non-dimensional number in fluid mechanics is the Reynolds number that judges the relative importance of the inertial and viscous effects. At low values of the Reynolds number – a situation that is common to microsystems – the Navier Stokes equation can be well approximated by the Stokes equation, that, in the absence of body forces, reads:

μΔ Δ u − ∇p = 0

(1)

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where μ is the viscosity of the fluid, u is the velocity field of the fluid, and p is the pressure field. The Stokes equation relates the speed of flow with the pressure gradient, and the relation between the two quantities is that of a simple proportionality. The resulting flow is highly regular (e.g. laminar, without turbulence), which is one of the fundaments of the control over flow of fluids at microscale. As will become important in one of the examples of droplet flow through networks of channels, the Stokes equation has also the interesting property that it is invariant with respect to the simultaneous change of the sign (orientation) of the velocity field and the gradient of pressure. A manifestation of this property is that if we allow a fluid to flow ‘forward’ for a given interval of time by application of a ‘positive’ difference of pressure between the inlet and outlet of the system, and then suddenly will change the sign of the pressure drop to the negative of the original value, the fluid will trace back its original trajectory, regardless of how complicated it were. Conveniently, when one considers the flow of simple fluids through channels, the Stokes equation – that describes the velocity field as a function of the pressure field – can be integrated to yield a very simple relation (Hagen–Poiseuille Law) between the difference (Δp) of pressures at inlet and outlet of the tube (channel) and the volumetric rate of flow (Q) of the simple fluid: Q = Δp/R,

(2)

where R is the hydraulic resistance of the given channel and depends on the viscosity of the liquid. For channels of uniform, circular cross-sections, the resistance is equal to: R = 8μL/πr4

(3)

where L is the length of the capillary and r is its inner radius. For rectangular and other cross-sections the equation for R is more complicated, yet it can be analytically derived [33]. The Hagen–Poiseuille law is mathematically analogous to the Ohm’s Law. In addition, the conservation of mass (or flow for incompressible fluid) of fluid is analogous to the law of conservation of charge and current in electrical systems. This analogy allows for the use of Kirchoffs equations for calculation of the distribution of the volumetric flow of liquid between channels in a microfluidic network: once we know the resistances of all the channels in the network and the pressures at the inlet and outlet, we can calculate the speed of flow in any part of the network (Fig. 1).

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Figure 1. The analogy between the distribution of volumetric rate of flow of a simple fluid flowing through a network of microchannels and the Kirchoffs equations for the flow of current through a network of conductors.

2.2. FLOW OF DROPLETS AND BUBBLES THROUGH CHANNELS

In the absence of any obstacles in the channel, the simple fluid develops a parabolic profile of speed of flow: the fluid flows the fastest in the center of the channel, and rests at the walls of the capillary. When a droplet or bubble is introduced into this flow, the velocity field is modified. Because the droplet (bubble) separates the continuous liquid that is in front of it, from the liquid behind it, the parabolic profile can no longer be sustained, and close to the caps of the droplet addition recirculation of the continuous fluid is created. In addition, there is circulation of the liquid inside the droplet, and there is some flow along the droplet (or bubble) (see Fig. 2). All these effects increase the viscous dissipation in the carrier (continuous) fluid and the liquid inside a droplet. As a result, it demands a higher pressure drop along the capillary to maintain the same average speed of flow as without the bubble or droplet inside of it. Equivalently, for a constant pressure drop along the capillary the speed of flow decreases after the addition of the droplet (or bubble). This can be described by an increased resistance to flow in that capillary, or by an additional charge of resistance carried by the droplet (or bubble).

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Figure 2. The flow of a simple fluid through a microchannel develops a parabolic profile of speed of flow, that minimizes viscous dissipation for a given pressure drop Δp along the capillary. A droplet introduced into the flow modifies the flow field and increases dissipation. For a constant pressure drop this results in reduction of the volumetric rate of flow through that capillary.

The problem of characterization of the exact velocity field in the presence of a droplet in a capillary is difficult. It was first elaborated on by Taylor [34] and Bretherton [35] in 1960s. Taylor found a relation for the thickness (proportional to the capillary number Ca) of the film deposited on a capillary after passage of a semi-infinite bubble, while Bretherton proposed the scaling for the pressure drop along a finite bubble (proportional to the Ca2/3). Contemporary studies confirm the Bretherton scaling and provide numeric results for the exact resistance contributed by the droplets and bubbles [36–39]. Still, as the flow around a bubble (droplet) depends critically on a large number of parameters (volume of the immiscible segment, interfacial tension between the fluids, surface coverage with surfactant, viscosities of the two fluids, the speed of flow) a unified picture (or equations for the resistance introduced by bubbles and droplets in capillaries) is not yet available. 2.3. FLOW OF DROPLETS THROUGH A NETWORK OF CHANNELS

The fact that a droplet (or bubble) introduces additional resistance to flow in the given capillary has pronounced consequences on the dynamics of flow of discrete segments of immiscible fluids through microfluidic networks.

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Figure 3. The flow of simple fluid distributes between the two arms of the loop in inverse proportion to their hydraulic resistances. A droplet flowing in to the junction of the two arms of the loop flows into the arm that is characterized by the larger momentary rate of flow, or equivalently by the lower momentary resistance to flow. Once the droplet enters the channel it raises its hydraulic resistance and hence affects the choices (trajectories) of subsequent droplets.

As illustrated in Fig. 3, the flow of droplets through networks obeys dramatically different rules from the simple laws of distribution of flow of simple fluid between the nodes of the network. The trajectory of any given droplet depends on the positions of other droplets in the network. This coupling – or feedback – is transmitted via the pressure field and thus provides for long-range interactions. This in turn provides for the complexity of the flow. Figure 4 illustrates the experimental results on the flow of droplets through the simplest network – a single loop. At low frequencies of feeding of the droplets into the loop, only one droplet is present in the section of parallel channels at a time. This example clearly shows the nonlinearity (or binary character) of the flow of droplets. The experimental system was designed to be symmetric – i.e. the two arms of the loop have the same nominal length and cross-section. The finite resolution of the microfabrication technique [40] resulted in a small bias in resistances of the two arms. For a simple fluid, this small bias would result in an inversely proportional small bias in the rates of flow through the two arms. For droplets it results in a complete redirecting of all the droplets into one (here lower) arm of the loop. For higher frequencies of feeding a droplet arrives at the entrance to the loop while a previous one is still there. The presence of the previous droplets redirects the next one into the upper arm of the loop. At even higher frequencies more intricate temporal patterns of sequences of trajectories of the droplets can be observed.

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Figure 4. The flow of droplets through a section of two parallel microfluidic channels. (top row) a sequence of micrographs illustrating the trajectories of droplets flowing through the bottom arm of the loop. (bottom row) a sequence illustrating the effect of the presence of one droplet on the trajectory of the next one [29]. The numbers identify the droplets in order of their entry into the loop. The outlines of the channels were added in adobe illustrator.

3. Reversibility of Droplet Trains and Logic Operations on Droplets 3.1. REVERSIBILITY OF DROPLET TRAINS

The flow of droplet through the bifurcating channels can produce both periodic and irregular sequences of trajectories. This complex dynamics of flow roots in the (i) binary character of the choice of a that based on the momentary resistances of the two channels, (ii) a change of the resistance of one of the channels by a finite value of the added resistance of the droplet and (iii) long range character of the interactions between the droplets via the pressure field. All the above effects contribute to the observed complexity of the temporal patterns of the flow of droplets. On the other hand the flow of droplets proceeds at low values of the Reynolds number and is imbedded in a viscous flow that should – in principle – be described by the Stokes equation that is linear and reversible in the sense of symmetry with respect to the inversion of the orientations of the velocity of flow and of the gradient of pressure. The experiment illustrated in Fig. 5. demonstrated the highly unexpected feature of the microfluidic two-phase flow in that it combines the non-linear character of the interactions between the droplets, with the linearity of the underlying equations of flow of the carrier fluid. This combination provides for (i) the ability to construct complicated protocols of flow of droplets through microfluidic networks, and (ii) the feasibility of practical realization of such protocols thanks to their apparent robustness to random disturbances.

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Figure 5. The diagram on the left shows the trajectories of droplets first entering at uniform intervals and leaving the loop in a period 7 mode of seven different intervals, and then, after switching the direction of the pressure gradient, entering the loop at seven different intervals and leaving it at uniform intervals. The Poincare plots on the right show that the disturbances in the positions of the droplets in the channel in which they were stored did not amplify upon the reverse operation of the microfluidic loop (Adapted from Ref. [30]).

3.2. CIPHERING AND DICEPHERING SIGNALS ENCODED IN SEQUENCES OF DROPLETS

The fact that the processing of strings of bubbles can be reversed opens a possibility for a demonstration of a non-trivial operation on the information encoded into the intervals between the bubbles. Further, because the period 2

Figure 6. Left panel illustrates the symmetry of the period-2 sequence of intervals and shows corresponding Poincare maps constructed on the intervals between bubbles before, after the first loop and after the second loop. Right panel illustrates the ciphering/deciphering experiment (Adapted from Ref. [30]).

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sequences (short–long–short–long intervals) are symmetric with respect to forward/backward mirror symmetry, it is not necessary to reverse the flow: in spite it is sufficient to position a copy of the original loop downstream. Figure 6 illustrates the intervals between the bubbles entering the first loop (into these intervals a simple message is encoded), intervals after passing the first loop which amplifies small differences in intervals to an unreadable signal, and intervals after passing the second loop: a sequence that restores the original information. 3.3. LOGIC GATES

Prakash and Gershenfeld [31] demonstrated that appropriate design of the microfluidic network can provide for a range of logic operations on droplets. These operations included a demonstration of a AND–NOT, and AND–OR gate, in which the presence of a droplet coded for bit value 1, and absence of a droplet for a bit value 0. These authors constructed also a synchronizer of droplet flows, a flip-flop counter and a ring oscillator [31]. 4. Modeling of the Flow of Droplets Through Microfluidic Networks As it will be briefly described in this section, the phenomenology of droplet flows in microfluidic networks can be effectively recovered by simple numerical models [39, 41–43] that assume the generic features of the multiphase microfluidic flows. These very basic models offer an insight into the qualitative features of the dynamics. As the understanding and characterization of the flow of droplets and bubbles in capillaries, junctions, corners etc. progresses, it can be expected that the same simple models, with the appropriate numeric input will able to predict the trajectories of droplets flowing in real microfluidic networks. At the end of this section we provide an example of a quantitative match between experiment and numerical simulation. 4.1. CONSTRUCTION OF THE MODEL

Within the simplest numerical model the channels are represented as onedimensional wires and the droplets as non-dimensional points that traverse along the wires. Taking from the analogy between Hagen–Pouiseille Law and the Ohm, and Kirchoff Laws, it can be written, that if the pressure drop in a channel is Δp, the speed of flow (u) is: u =Q/A = Δp/ARtotal = Δp/A(R + nr)

(4)

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where A is a the cross-section of the channel, Rtotal is the total hydrodynamic resistance comprising the resistance of the channel (R) and the resistances introduced by the (n) droplets each carrying the same resistance r. In the simulation only the pressure drop (or flow rate) between inlet and outlet of the system is externally fixed and controlled. All the pressures and speeds of flow in the channels that comprise the network are calculated on the basis of the positions of the droplets, via the Kirchoffs laws. The flow of droplets, and in particular the acts of traversing of the droplets between the different channels in the network introduce step changes in these quantities. These occur when: (i) a new droplet enters the system, (ii) a droplet leaves the system, or (iii) a droplet traverses through an internal node. In the last case, when a droplet arrives at an internal junction, the droplet enters the channel with the largest momentary inflow (calculated before the act of the droplet entering the channel). The numerical scheme that executes the algorithm outlined above can be found in Refs. [41, 43]. 4.2. BIFURCATION DIAGRAMS AND COMBINATORIAL COMPOSITION OF PATTERNS

The numerical models provide a convenient tool for rapid scan of the dynamics of the flow of droplets over wide ranges of parameters of the system. For example, the top panels of Fig. 7 show a diagram of the intervals between droplets leaving the microfluidic loop for a large range of frequencies of feeding of the droplets into the system. One can clearly see bands of regular flows and bands of irregular (or highly complex) flow. Within the regular bands, the dynamics of the system is strictly periodic. From the numerical simulations we can extract the number of droplets in the loop for a particular regular band. A very interesting feature of this flow is that any given number (n) of droplets traversing the loop in a periodic fashion can generate a number (m) of distinct, periodic, sequence of the left/ right choices of subsequent droplets [43]. For example, eight droplets can generate ten distinct temporal patterns. Once the system settles in one of the patterns it repeats it ad infinitum. A small perturbation (an external stimulus) can switch the system to a different pattern [43].

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4.3. MODELLING AS A DESIGN TOOL

Even the simple numerical scripts that are currently used for simulation of droplet flows in microfluidic networks can provide for quantitative match with the experimental measurements (Fig. 8). The development of an ability for a quantitative prediction of the dynamics of physical systems will demand incorporation into the scripts the details characterizing the speed of flow of droplets, the resistance that they carry, the delays at junctions and corners.

Figure 8. A comparison of the positions of droplets in a loop in experiment (bottom micrographs) and in simulation (top renderings) at three different instants of time.

5. Automation The development of truly versatile chips for analytical, synthetic and biological chemistry will require not only the understanding of the flow in networks, but also the development of modules for active control over the flow, merging, splitting and above all, formation of droplets. Below we review the field of active control over formation of droplets and provide an example of a microfluidic droplet-on-demand system. 5.1. ACTIVE CONTROL OVER FLOW AT MICROSCALE

Techniques for formation of droplets on demand must provide – in contrast to the traditional techniques of formation of droplets at constant rate of flow or constant pressure – for the ability to issue the droplet at arbitrary times and with arbitrarily prescribed volume. This goal involves incorporation of a valve. It is necessary to control the flow of the fluid-to-be-dispersed: it needs to be stopped over arbitrarily long intervals and then opened with an external signal. In analogy to the classic division of hydraulic valves, there are two ways to construct a droplet on demand chip. First is to actively force the flow of fluid with external stimuli at predefined instants (that is, the fluid is ‘normally stopped’). The second way is to have the fluid

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normally flowing, and actively stopped. The valving of fluids at microscale can be done with the use of many different types of physical forces: electric (dielectrophoresis [44, 45] or a direct electrostatic force on a charged interface) [46], magnetic, capillary, electrowetting [47], Marangoni (e.g. thermocapillary flow) or mechanical (i.e. with the use of valves). For example, dielectrophoresis can be used in a system of two parallel electrodes [44]. In this system it is possible to control of generation of droplets with pulses of an alternating electric field [45]. Also electrowetting can be used to this end [47–49]. He et al. [46] demonstrated that short pulses of electrostatic potential applied along the axis of formation of water droplets in oil can generate a Taylor cone and formation of droplets via an electro-hydrodymic mechanism [50]. These droplets are typically polydisperse (3–25 μm) and it is difficult to produce individual droplets. Weitz et al. [51] demonstrated control over volumes and frequencies of formation of droplets with the use of electric field. Also thermocapillarity can be utilized to control the flow of the droplet (or bubble) phases: Baroud et al. demonstrated control over formation of droplets and guiding them with a laser beam [52]. The conceptually simplest approach to valving at small scales is to construct micromechanical valves. These approach, however, needs not be simple in terms of fabrication of the devices. Mechanical microvalves have two most popular varieties, both utilizing the deformation of elastic membranes in soft (PDMS) systems [53] proposed by Quake et al., and for rigid chips [54] by Grover et al. 5.2. DROPLET ON DEMAND SYSTEMS

To date, there is only a hand full of reports on microfluidic droplet on demand systems. Prakash and Gershenfeld [31] used such a system based on thermo-capillary effect in their experiments on droplet logic. In these experiments the fluid-to-be-dispersed flew into the droplet generating junction via a narrowing nozzle. This geometry blocked the flow by the action of the Laplace pressure. A micro-heater placed under the junction enabled lowering of the interfacial tension and generation of single bubbles for each 100 ms pulse of current. The Laplace blockade was used also by Attinger et al. [55], who utilized a piezoelectric actuator glued to a PDMS reservoir of the fluid-to-be-dispersed to force its flow through the narrowing junction. The actuation allowed for generation of monodisperse nL droplets at few Hz. Bransky et al. [56] integrated the piezoelectric actuator into the PDMS device and obtained slightly better results. The use of Laplace blockade strongly limits the range of pressures that can be applied to the droplet phase without overcoming the Laplace pressure of the order of ~10 mbar.

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Recently Lin and Su [57] and Wang et al. [58] utilized the pneumatically actuated PDMS valves [53] to control of the volumes of the droplets (~1 nL and above) and of the times of their emission with frequencies approaching 15 Hz. The drawback of these techniques lies in the use of PDMS, which is known [59] to be incompatible with many solvents. We have recently reported [60] a DOD system in a stiff polymeric device based on an integrated microvalve [54]. This system allows for formation of both droplets and bubbles on demand (Fig. 9), in both the flow-focusing and the T-junctions, and can be made compatible with any chemistry by the virtue of its compatibility with both polymeric and glass devices. 6. Conclusions The recent progress in understanding of the flow of droplets through networks of channels, and in automation of droplet flows suggest that construction of fully automated and truly versatile chips for chemical syntheses and analyzes to be performed on chip will be possible within the next few years of research. These techniques, with the advantages of performing chemistry inside droplets, that we reviewed in this lecture have a potential changing the laboratory standards. If this revolution is indeed to happen depends on a number of scientific, technical and marketing factors and remains to be seen.

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THE FRONT-TRACKING METHOD FOR MULTIPHASE FLOWS IN MICROSYSTEMS: FUNDAMENTALS M. MURADOGLU

Department of Mechanical Engineering, Koc University, Istanbul, Turkey, [email protected]

Abstract. The aim of this paper is to formulate and apply the front-tracking method to model multiphase/multifluid flows in confined geometries. The front-tracking method is based on a single-field formulation of the flow equations for the entire computational domain and so treats different phases as a single fluid with variable material properties. The effects of the surface tension are treated as body forces and added to the momentum equations as δ functions at the phase boundaries so that the flow equations can be solved using a conventional finite-difference or a finite-volume method on a fixed Eulerian grid. The interface, or front, is tracked explicitly by connected Lagrangian marker points. Interfacial source terms such as surface tension forces are computed at the interface using the marker points and are then transferred to the Eulerian grid in a conservative manner. Advection of fluid properties such as density and viscosity is achieved by following the motion of the interface. The method has been implemented for two (planar and axisymmetric) and fully three dimensional interfacial flows in simple and complex geometries confined by solid walls. The front-tracking method has many advantages including its conceptual simplicity, small numerical diffusion and flexibility to include multiphysics effects such as thermocapillary, electric field, soluble surfactants and moving contact lines. In this chapter, the fundamentals of the front-tracking method including the formulation and details of the numerical algorithm are presented.

1. Introduction Multiphase/multifluid flows are ubiquitous in microsystems since, as sizes continue to reduce in such devices, surface to volume ratio increases and thus surface forces become dominant over the volume forces. It is therefore of great importance to understand and manipulate multiphase/multifluid flows in micro channels [1, 2]. Direct simulation of multiphase flows is notoriously difficult mainly due to the presence of deforming phase boundaries. Strong interactions S. Kakaç et al. (eds.), Microfluidics Based Microsystems: Fundamentals and Applications, DOI 10.1007/978-90-481-9029-4_11, © Springer Science + Business Media B.V. 2010

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between the phase boundaries and complex channel walls make the problem even more difficult in micro channels. Although efforts to compute the motion of multiphase flows are as old as computational fluid dynamics, progress was rather slow and simulations of finite Reynolds number multiphase flows were limited to very simple problems for a long time [3]. In the past two decades, however, major progress has been achieved and a variety of numerical methods have been developed and successfully applied to a wide range of interfacial flow problems [3–7]. The computational methods developed for interfacial flows can be classified into four major categories. The first class is the front-capturing method that explicitly captures the interface on a regular stationary grid. This is the oldest technique and is still widely used in applications. The marker-and-cell (MAC), the volume-offluid (VOF), the level-set, the constrained interpolation profile (CIP) and diffuse interface methods are the most popular examples of the front-capturing techniques [4–7]. The major problem that the front-capturing methods suffer is the excessive numerical diffusion that makes it difficult to maintain sharp boundary between the phases. The second class of methods employs separate grids in each phase and thus it potentially has the highest accuracy as discussed by Ryskin and Leal [8]. The major difficulty in using this class of methods is to generate grids in both phases and maintain them smooth throughout simulations. Due to this difficulty, the method is applicable only for simple geometries so it is not suitable for microfluidics as microchannels often involve complex geometries [9, 10]. The third class is the fronttracking method developed by Glimm et al. [11]. In this method, the interface is marked by Lagrangan grid but a separate fixed grid that is modified near the interface is also used in each phase. The fourth class is the boundary integral method that is applicable only in the Stokes flow regime [12]. Since the flow is very often in the Stokes flow regime in microchannels, this method can be used in microfluidic applications provided that a care is taken to make sure that flow remains in the creeping flow regime throughout the computational domain. Here, we describe a method that has been particularly successful for a wide range of multifluid and multiphase flow problems. The front-tracking method is based on a single-field formulation of the flow equations for the entire computational domain and so treats different phases as a single fluid with variable material properties [3, 13]. In fact, the front-tracking method discussed here is an application of the immersed boundary method of Peskin [14] to the interfacial flows. The front-tracking method can be properly described as a hybrid method between the front capturing and front-tracking technique [3]. In this method, the interface between the bubble and the ambient fluid is represented by connected Lagrangian marker points moving with the local flow velocity interpolated from the neighboring fixed Eulerian grid points. The front-tracking method has many advantages such

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as its conceptual simplicity, small numerical diffusion and flexibility to include multiphysics effects such as thermocapillary [15], electric field [16], soluble surfactants [17, 18] and moving contact lines [19]. However, its main disadvantage is probably the difficulty to maintain the communication between the Lagrangian marker points and Eulerian body-fitted curvilinear or unstructured grids. Tracking marker points is a trivial task in regular Cartesian grids but is considerably more difficult in curvilinear or unstructured grids. The auxiliary grid method has been recently developed to overcome this difficulty and been successfully applied to multiphase flow problems involving strong interactions between the phase boundaries and complex channel walls [9, 10]. The algorithm reduces particle tracking in curvilinear or unstructured grids to tracking on a uniform Cartesian grid with a look up table while retaining all the advantages of the front-tracking method. In this chapter, the fundamentals of the front-tracking method are described as a computational method that can be used as a design tool in microfluidic systems. 2. Mathematical Formulation The key to the front-tracking method, as well as to several other methods such as volume of fluid (VOF) [5], level-set [6] and diffuse interface methods, is the use of a single set of conservation equations for the entire flow field. To achieve this, differences in the material properties of the different phases should be accounted for and the interfacial phenomenon such as surface tension must be included by adding the appropriate interface terms to the governing equations [3]. Since these terms are concentrated at the boundary between the different fluids and the material properties and the flow field are, in general, discontinuous across the interface, the differential form of the governing equations must be interpreted either as a weak form, satisfied only in an integral sense, or all variables must be interpreted in terms of generalized functions. In the front-tracking method, the latter approach is taken. The fluid motion is assumed to be governed by the Navier–Stokes equations in all phases: r r rr r r r r r ∂ρv + ∇ ⋅ ( ρv v ) = −∇p + ρf + ∇ ⋅ μ(∇v + ∇ T v ) + ∫ σκnδ ( x − x f )ds. (1) ∂t This equation is valid in the entire flow field even if the material properties vary discontinuously across phase boundaries. In Eq. (1), ρ andr μ are r density and viscosity, v is the velocity field, p is pressure, and f is the body force. The effects of the interfacial tension are accounted for by the last term in Eq. (1). In this term, δ is two or three dimensional delta function, σ is surface tension coefficient, κ is the curvature of two-

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dimensional flow or twice of the mean curvature for three r v dimensional x flow, n is a unit outward normal vector to the interface, is the point at r which the equation is evaluated and x f is a point on the interface. Note that the surface tension coefficient is not necessarily constant and can depend on the temperature field and/or the surfactant concentration at the interface [15, 17]. The integral is taken over the entire interface. The flow is assumed to be incompressible:

r ∇ ⋅ v = 0.

(2)

We also assume that the material properties remain the same following a fluid particle, i.e.,

Dρ = 0; Dt r where D / Dt r = ∂ /∂t + v • ∇ is the function I( x,t) is defined such that

Dμ = 0, Dt

(3)

substantial derivative. An indicator it is zero in the continuous fluid and unity in the disperse phase. The material properties are then set in each phase by

r

r

ρ = ρi I ( x , t ) + ρo (1 − I ( x , t ));

r

r

μ = μi I ( x , t ) + μo (1 − I ( x , t )).

(4)

The indicator function is computed based on the location of the interface represented by marker points using the standard techniques [3]. On a regular grid, this process involves solution of a separable Poisson equation that can be solved very efficiently using a fast Poisson solver. In the case of complex geometries, the indicator function is still computed on a regular Cartesian grid using a fast Poisson solver and is then interpolated onto the curvilinear grid [9, 10]. Note that the computation of the indicator function is discussed in Section 3.5. 3.

Numerical Solution

Equations (1–4) are in the same form as the conventional flow equations so that they can be solved by standard numerical methods used for homogeneous flows. Once the interface has been advected and the surface tension computed, virtually any standard algorithm based on fixed grids can be used to integrate Eq. (1) in time. The grids used in the front-tracking method are shown in Fig. 1a for simple geometries and in Fig. 1b for the complex geometries. In simple geometries, the conservation equations are solved on a fixed Eulerian grid while the interface is tracked by a

FRONT-TRACKING METHOD: FUNDAMENTALS a

b

Stationary Eulerian Grid

Auxilary Uniform Cartesian Grid

207

Curvilinear Grid

Lagrangian Grid Front

Front

Fluid I

Fluid I

Fluid II

Front Element

Marker Point

Fluid II

Figure 1. Computations of flow containing more than one phase. The governing equations are solved on a fixed grid but the phase boundary is represented by a moving “front,” consisting of connected marker points. (a) Grid system used in simple rectangular geometries and (b) the grid system used in complex geometries.

Lagrangian grid of lower dimension. The Lagrangian grid consists of linked marker points that move at the local flow velocity interpolated from the Eulerian grid. The interface element between two marker points are called a front element. Tracking the marker points is a trivial task in simple geometries but it is not easy in complex geometries and requires a special treatment. The auxiliary grid method developed by Muradoglu and Kayaap [10] overcomes this difficulty and reduces the tracking of Lagrangian points on curvilinear grids to tracking on a uniform Cartesian grid with a look up table as discussed below. The flow equations (Eqs. (1–4)) are solved using a finite-difference method or a finite-volume method. The finite-difference method is preferred when the flow geometry is simple whereas the finite-volume method is preferred for complex geometries. The finite-difference algorithm is based on the projection method of Chorin [20]. The version of the projection method employed here can be found in Tryggvason et al. [3]. The implementation of the fronttracking method combined with the finite-difference scheme is referred here as FD/FT method. The finite-volume method is based on the pseudo time stepping and is second order accurate both in time and space. The detailed discussion about the finite-volume method employed here can be found in Caughey [21] and Muradoglu and Gokaltun [9]. The implementation of the front-tracking method that uses the finite-volume method as flow solver is referred here as FV/FT method. 3.1. STRUCTURE OF LAGRANGIAN GRID

The Lagrangian grid consists of linked marker points. In two dimensions, the piece of the front element between the marker points is called a front

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element as shown in Fig. 1. There is a linked list that contains information about the neighbors of each marker points as well as the neighbors of each front element. This linked list gives a flexibility to remove or add a front element very easily in order to restructure the Lagrangian grid as will be discussed below. In three dimensions, the marker points form a surface as shown in Fig. 2. Three marker points make a triangular front element. Again a linked list is maintained such that each element knows the marker points that make its corners as well as its immediate neighboring elements. Note that a front element is allowed to share only one edge with its neighbor as sketched in Fig. 2.

Figure 2. Structure of the front in three dimensions. The interface is represented by a triangular grid. Each front element is allowed to share only one edge with its each neighbor (Adapted from Tryggvason et al. [3]).

3.2. RESTRUCTURING THE LAGRANGIAN GRID

Ideally the front elements must be uniform and remain so throughout the simulations. In addition, the size of the front elements must remain comparable to the Eulerian grid size in order to maintain good resolution. However, the interface moves and deforms. This dictates that the Lagrangian grid must be dynamically restructured during the simulations in order to avoid having too small or too large front elements. Restructuring of the Lagrangian grid is crucial in the front-tracking method since front elements that are too large compared to the Eulerian grid size result in lack of resolution while the front elements that are too small result in formation of “wiggles” much smaller than the grid size. In two dimensions, the restructuring is simply

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Figure 3. Restructuring the front in two dimensional case. The element that is larger than a prespecified threshold value is splitted (left) and the element that is smaller than a prespecified threshold value is deleted (right).

Figure 4. Restructuring the front in three dimensional case (Adapted from Tryggvason et al. [3]).

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done by splitting the elements that are larger than a prespecified value and removing the elements that are smaller than a prespecified value as shown in Fig. 3. In both splitting and deleting elements, a cubic Legendre polynomial is fitted to the marker points of the front element that is to be deleted and its immediate neighbors on each side as shown in the sketched (Fig. 3). This simple procedure conserves curvature but not necessarily the volume. Therefore a care must be taken not to do unnecessary restructuring operations. In the three dimensions, in addition to deletion and addition operations, the elements are also reshaped as shown in Fig. 4. Note that neither curvature nor the volume is conserved in any of the restructuring operations in threedimensional cases. Details of the restructuring can be found in the review paper by Tryggvason et al. [3]. 3.3. COMPUTING SURFACE TENSION FORCE

The surface tension force is computed at center of front elements. It is then converted into equivalent body force and distributed onto the neighboring Eulerian grid points in a conservative manner. The distribution procedure is discussed in the next section. The accurate treatment of the surface tension force is probably one of the most important ingredients of any computational method developed for computation of interfacial flows. In the present method, the interface is represented explicitly by the marker points and these discrete points are used to approximate the surface tension. Although there are several alternative ways, the procedure preferred here is based on fitting a cubic Legendre polynomial to the marker points of the front element for which the surface tension is to be computed and its immediate neighbors for two-dimensional computations. In the multiphase flow problems, we often need to find the surface tension force but not the curvature. The force acting on a small front element can be given by

r r r r r ∂σs δf s = ∫ σκnds = ∫ ds = (σs )2 − (σs )1 , (5) ∂ s Δs Δs r r r r where the identity κn = ∂s /∂s has been used. The vectors s1 and s2 in Eq.

(5) denote the unit tangent vectors computed at the end points of the front element as shown in Fig. 5a. In computing the unit tangent vectors, a cubic Lengedre polynomial is fit to the four marker points on each side of the corner. Since this can be done in two different ways, an average is taken to reduce the numerical error as shown in Fig. 5b. This procedure is highly accurate and robust as reviewed by Tryggvason et al. [3].

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Figure 5. Computation of unit tangent vectors in two-dimensional cases. Tangent vectors at the end points of mth element (sketch on the left). Approximation of unit tangent vectors (sketch on the right).

In three-dimensional case, surface tension computation is not as elegant as that in two-dimensional case but it has been still found satisfactory in a wide variety of multiphase flow computations [3]. In 3D, the mean curvature is given by

r

r

δf s = ∫ σκnds = ΔA

r

r r

(

r

ΔA

)

r r

r

∫ (n × ∇ ) × ndA = ∫ t × nds,

(6)

S

r

where the identity κn = n × t × n has been used. In the last step of Eq. (6), the Stokes theorem is employed to convert the surface integral into r a contour integral along the edges of the element (see Fig. 2). In Eq. (6), n is the unit outward normal vector to the surface of the front element and it is computed by fitting a quadratic surfacer to the marker points of the front element and its neighbors. The vector t is the unit tangent vector to the edge of the front element and is simply computed by taking difference between marker points sharing the same edge. The line integral in Eq. (6) is evaluated numerically by dividing each edge into four segments and using a midpoint rule in the same way as done by Tryggvason et al. [6]. The line integrals can be evaluated in two ways using the elements sharing the same edge. This fact is exploited by taking simple average of line integrals computed for each element sharing the same edge in order to reduce the numerical error as well as to ensure the conservation of the surface tension forces [3]. 3.4. COMMUNICATION BETWEEN EULERIAN AND LAGRANGIAN GRIDS

Information must be exchanged between the Eulerian and Lagrangian grids at every time step during a simulation. Therefore it is of crucial importance to maintain efficient and robust communication between these two grids. The surface tension force is computed at the interface and it needs to be

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transferred to the Eulerian grid in a conservative manner, which is called “smoothing operation” and is achieved using a distribution algorithm. The distribution algorithm approximates the δ functions appearing in Eq. (1). Let φf be an interface property expressed in units per unit area, then the corresponding grid value φg should be expressed in units per unit volume. The conservation of the total value of φf requires that

∫φ

Δs

f

r ( s )ds = ∫ φ g ( x )dv.

(7)

Δv

This is achieved at discrete level using a distribution function as

φijk = ∑ φlϖ ijkl l

Δs l , Δx 3

(8)

where φl is the discrete approximation to the interface value of φf, φijk is the approximation to grid value φg, Δx is the Eulerian grid size and Δsl is the area of the front element l. In Eq. (8), ϖ lijk is the weight representing the discrete version of the distribution function. The weights can be selected in different ways but they must satisfy the conservation requirement:

∑ϖ ijk

l ijk

= 1,

(9)

where the summation is carried out over all the grid points used to distribute interface property φ l of the l th front element. In the front-tracking simulations, the distribution function suggested by Peskin [14] is usually used although other distribution functions can also be used. The marker points move at the local flow velocity interpolated from the Eulerian grid. The interpolation scheme is important since interpolation error may result in a violation of mass conservation. Ideally, the interpolation scheme must satisfy the mass conservation at the discrete level in the same way as done in the flow solver [19]. However, the Peskin distribution function or simple bi-linear interpolation is usually used in the fronttracking method [3]. Note that none of these interpolation schemes satisfies the mass conservation at discrete level. This is in fact an important factor for the change in drop volume especially for long simulations. 3.5. UPDATING THE MATERIAL PROPERTIES

The material properties such as density and viscosity vary discontinuously across the interface. However, it is desirable to have smooth transition of the properties between different phases for numerical stability and accuracy. One way to do this is to advent the material properties similar to the VOF or

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level-set methods [4, 5]. Alternatively, the boundary between phases can be moved first and then the material properties can be set based on the new location of the interface. The latter approach is usually preferred in the front-tracking computations. For this purpose, we define an indicator function I that is unity inside droplet and zero otherwise. Since the indicator function represents a unit jump across the interface, the gradient of the indicator function can be written as

r r r ∇I = ∫ n δ ( x − x f )ds,

(10)

and the discrete version of this equation is given by l r ∇ h I ijk = ∑ϖ ijk nl Δsl ,

(11)

l

l is the same weight where Δsl is the area of the front element l and ϖ ijk function as discussed in the previous section. Taking numerical divergence of Eq. (11) yields

∇ 2 I = ∇ h • (∇ h I ijk ),

(12)

which is a separable Poisson equation and can be solved very efficiently using a fast Poisson solver such as MUDPACK package [23]. Solution of Eq. (12) yields smooth transition of the indicator function at the interface. Once the indicator function is determined, then the material properties are simply set as a function of the indicator function:

ρ = ρ i I + (1 − I ) ρ o ;

μ = μ i I + (1 − I ) μ o

(13)

where subscripts “i” and “o” denotes the properties of the drop and ambient fluids, respectively. 3.6. TRACKING ALGORITHM

As mentioned above, the interface between different phases is represented by linked marker points moving at the local flow velocity. Since the flow equations are solved on the fixed Eulerian grid, it is of fundamental importance to maintain the communication between the Lagrangian and Eulerian grids. In simple geometries, this is a trivial task as the flow equations are solved on a regular Cartesian grid. However, the tracking of Lagrangian marker points is a formidable task in complex geometries where the flow equations must be solved on curvilinear or unstructured grids. To overcome this difficulty, Muradoglu and Kayaap [10] developed a very efficient and robust tracking algorithm. This algorithm is summarized as follows: At the beginning of a simulation, a uniform auxiliary Cartesian grid is generated such that it

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covers the entire computational domain as sketched in Fig. 1b. The uniform grid cell size is typically selected as half of the smallest grid size of the curvilinear grid. It is then found which uniform grid nodes reside in each curvilinear grid cell and this information is stored in an array. This operation can be easily done using vector algebra as sketched in Fig. 6. It is emphasized here that this is a preprocessing step and is done only once in each simulation. After this preprocessing step, in each time step, it is first determined where the marker points reside in the uniform grid by a simple division. Referring to Fig. 7, for instance, the marker point P is determined to reside in (I,J) node of the uniform grid and then the nodes of (I,J) cell reside in the curvilinear grid cells of (i,j), (i,j − 1) and (i − 1,j − 1). Therefore we conclude that the marker point P resides in the region consisting of the curvilinear grid cells of (i − 2:i + 1,j − 2:j + 1). Finally the cells (i − 2:i + 1,j − 2) and (i − 2,j − 2:j + 1) are eliminated based on the relative Figure 6. Preprocessing for determination distance of their outer nodes to the of which uniform Cartesian grid nodes point P. A the end of this process, it reside in each curvilinear grid cell. is determined that the marker point P resides in the domain composed by the curvilinear cells of (i − 1:i + 1,j − 1:j + 1). The further details of this j) (i, algorithm can be found in Muradoglu and Kayaap [10]. P The particle-tracking algorithm is (I,J) ) tested for the rigid body rotation of j-1 (ifluid in a circular channel as shown ) j-1 in Fig. 8. The radius of the outer 1(iboundary and the width of the channel are set to Rc = 1 and wc = 0.2, respectively. The velocity field is specified as u = yo – y and v = x – xo Figure 7. The tracking algorithm for curvilinear grids. where x and y are the two-dimensional Cartesian coordinates and xo and yo ate the centroid of the circular channel. A two-dimensional drop with diameter d = 0.15 is initialized at (x,y) = (0.1,1.0) and is set to motion by the fluid. Passive tracer particles are used for visualization. The particles are distributed inside the drop randomly and the particles occupying the first and third quadrant are identified as red and the other particles are blue. A coarse version of the curvilinear grid is shown in Fig. 8a. As can be seen in

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Fig. 8b, the drop makes rigid body motion as expected indicating the accuracy of the tracking algorithm. Accuracy of the tracking algorithm is quantified in Fig. 9. As can be seen in Fig. 9a, b, the tracking algorithm is second order accurate both in time and space.

Figure 8. (a) A coarse curvilinear grid and (b) rigid body motion of the drop. The drop is enlarged three times at the locations shown by the thick arrows.

(a)

100

10−1

(b)

10−1

Location 3 Location 6

10−2

Slope - 2.10

Location 3 Location 6

Slope - 0.98

Error

Error

10−2 10−3

10−3

Slope - 2.11 Slope - 0.95

10−4

10−4 10−5 10−3

10−2

∆t

10−1

100

10−6

10−5

10−4 M −2

10−3

10−2

Figure 9. Error in the position of the drop centroid (a) against the time step and (b) against the inverse of the total number of grid cells.

4. Validation The finite-difference/front-tracking method has been validated for a wide variety of test cases in simple geometries as reviewed by Trgyyvason et al. [3]. Therefore the emphasis is placed here on the accurate computations of interfacial flows in complex geometries as the complex geometries are ubiquitous in microfluidic applications. For this purpose, the FV/FT method that is designed to compute multiphase flows in complex geometries is first validated against the FD/FT method that can simulate flows only in simple

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geometries. Both FV/FT and FD/FT methods are first applied to compute the gravity-driven falling drop in a straight channel. The physical problem and the computational domain are shown in Fig. 10a. The computational domain is 5d in the radial direction and 15d in the axial direction, where d is the initial drop diameter. The drop centroid is initially placed at (rc,zc) = (0,12d) into otherwise quiescent ambient fluid. The details of the test case can be found in Muradoglu and Kayaalp [10]. Figure 10b shows the evolution of droplet for the Eotvos number Eo = 24. The results are obtained using two different implementations of the front-tracking method. This figure indicates that there is a good qualitative agreement between two different implementations. More quantitative comparison of these two different implementations are shown in Fig. 11a, b for the terminal velocity and percentage change in drop volume, respectively. These figures indicate again a good agreement between two implementations. Note that the change in drop volume is a good indicator for the accuracy of the numerical method and ideally the drop volume must remain constant. However, the drop volume changes due to accumulation of numerical errors. Figure 11b indicates that both implementations of the front-tracking method are quite accurate and total change in drop volume is less than a few percent for this challenging test case where drop undergoes large deformations.

Figure 10. (a) The schematic illustration of the physical problem and computational domain and (b) the evolution of drop for Eo = 24.

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Figure 11. (a) Terminal velocity of drop and (b) the percentage change in drop volume for Eo = 12 and Eo = 24.

The curvilinear implementation of the front-tracking method is then applied to study motion, deformation and breakup of viscous droplet passing through a constricted capillary tube. This buoyancydriven flow has been studied by Hemmat and Borhan [24] and computationally by Olgac et al. [25]. The computational domain and a portion of coarse version of the computational grid are shown in Fig. 12. The snapshots of the computed and experimental drop shapes are shown in Fig. 13. As can be seen in this figure, there is a remarkable agreement between the computed and experimental drop shapes indicating the performance of the Figure 12. The schematic illustration front-tracking method. The constant of the physical problem and a portion pressure contours and velocity vectors of coarse grid. are plotted in Fig. 14 in the vicinity of droplet while it passes though the throat and the expansion portions of the channel. This figure clearly shows the power of the front-tracking method to provide detailed information about the flow field inside and outside the droplet.

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Figure 13. Evolution of viscous droplet with breakup. The computed drop shapes (second and fourth rows) are in a good agreement with the experimental pictures taken by Hemmat and Borhan [24].

Figure 14. Velocity vectors (right portion) and pressure contours (left portion) in the vicinity of a buoyancy-driven viscous droplet while it passes through (a) the throat and (b) the expansion region of a constricted capillary tube.

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5. Conclusions The front-tracking method has been developed by Trgyyvason and coworkers and been successfully used for computational modeling of interfacial flows [3]. The method is essentially an implementation of the immersed boundary method of Peskin [14] to multiphase flow problems. The method has a number of advantages including its conceptual simplicity, small numerical diffusion and flexibility to include multiphysics effects such as thermocapillary, electric field, soluble surfactants and moving contact lines. These features of the front-tracking method make it a good candidate to be a viable design tool for microfluidic applications. It has been demonstrated that the explicit tracking of the interface facilitates increased accuracy especially for the cases where the interface undergoes extreme deformations. One of the most important disadvantages of the front-tracking method was the difficulty to maintain efficient communication between the Lagrangian marker points and curvilinear or unstructured Eulerian grid. This difficulty has been overcome by recent development of auxiliary grid method [9, 10]. Acknowledgement This work is supported by Turkish Academy of Sciences through GEBIP program.

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9. M. Muradoglu, S. Gokaltun, Implicit Multigrid Momputations of Buoyant Light Drops Through Sinusoidal Constrictions, J. Appl. Mech., 71 (2004). 10. M. Muradoglu and A. D. Kayaalp. An Auxiliary Grid Method for Computations of Multiphase Flows in Complex Geometries, J. Comput. Phys., 214 (2006). 11 J. Glimm, J.W. Grove, X.L. Li, W. Oh and D.H. Sharp, A Critical Analysis of Rayleigh-Taylor Growth Rates, J. Comput. Phys., 169 (2001). 12. C. Pozrikidis, Interfacial Dynamics for Stokes Fow, J. Comput. Phys., 169 (2001). 13. S.O. Unverdi, G. Tryggvason, A Front-Tracking Method for Viscous Incompressible Multiphase Flows, J. Comput. Phys., 100 (1992). 14. C.S. Peskin, Numerical Analysis of Blood Flow in the Heart, J. Comput. Phys., 25 (1977). 15. S. Nas, M. Muradoglu, G. Tryggvason, Pattern Formation of Drops in Thermocapillary Migration, Int. J. Heat Mass Trans., 49(13–14), 2265–2276 (2006). 16 A. Fernandez, G. Tryggvason, J. Che and S.L. Ceccio, The Effects of Electrostatic Forces on the Distribution of Drops in a Channel Flow: Two-Dimensional Oblate Drops, Phys. Fluids, 17 (9), Art. No: 093302 (2005). 17. M. Muradoglu and G. Tryggvason, A Front-Tracking Method for Computation of Interfacial Flows with Soluble Surfactants, J. Comput. Phys., 227 (4), 2238– 2262 (2008). 18. S. Tasoglu, U. Demirci and M. Muradoglu, The Effect of Soluble Surfactant on the Transient Motion of a Buoyancy-Driven Bubble, Phys. Fluids, 20, 040805 (2008). 19. M. Muradoglu and S. Tasoglu, A Front-Tracking Method for Computational Modeling of Impact and Spreading of Viscous, Droplets on Solid Walls, Comput. Fluids (in press) (2009). 20. A.R. Chorin, Numerical solution of the Navier–Stokes equations, Math. Comput., 22 (1968). 21. D.A. Caughey, Implicit Multigrid Computation of Unsteady Flows Past Cylinders of Square Cross-Section, Comput. Fluids, 30, 939–960 (2001). 22. R. McDermott and S.B. Pope, The Parabolic Edge Reconstruction Method (PERM) for Lagrangian Particle Advection, J. Comput. Phys., 227, 5447–5491 (2008). 23. J. Adams, MUDPACK: Multigrid FORTRAN Software for the Efficient Solution of Linear Elliptic Partial Differential Equations, Appl. Math. Comput., 34 (1989). 24. M. Hemmat and A. Borhan, Buoyancy-Driven Motion of Drops and Bubbles in a Periodically Constricted Capillary, Chem. Eng. Commun., 150 (1996). 25. U. Olgac, A. Doruk Kayaalp and M. Muradoglu, Buoyancy-Driven Motion and Breakup of Viscous Drops in Constricted Capillaries, Int. J. Multiphase Flow, 32(9), 1055–1071 (2006).

THE FRONT-TRACKING METHOD FOR MULTIPHASE FLOWS IN MICROSYSTEMS: APPLICATIONS M. MURADOGLU

Department of Mechanical Engineering, Koc University, Istanbul, Turkey, [email protected]

Abstract. The aim of this paper is to present computational modeling of multiphase/multifluid flows encountered or inspired by lab-on-a-chip applications. In particular, the motion and deformation of drops/bubbles moving through micro channels, the effects of channel curvature on the liquid film thickness between a large bubble and serpentine channel, chaotic mixing in a micodroplet moving through a serpentine channel, effects of channel curvature on the chaotic mixing and axial dispersion in a segmented gas–liquid flow, effects of soluble surfactants and modeling of a single cell epitaxi are discussed. Computational results are compared with the analytical results in limiting cases as well as with the available experimental data. Difficulties in mathematical and computational modeling of multiphase flow problems in Microsystems are emphasized and some remedies for these difficulties are offered.

1. Introduction The front-tracking method [1] has been successfully applied to multiphase flow problems encountered or inspired by lab-on-a-chip applications. Mutiphase/fluid problems are ubiquitous in microfluidic systems since the surface forces become dominant over the volume forces as the channel size gets smaller [2, 3]. Computational fluid dynamics (CFD) is ideally suited for simulation of microfluidic systems since flow is almost always laminar. In fact, flow is even in the Stokes flow regime in many microfluidic applications and lubrication type of approaches are relevant [2]. Therefore virtually any commercial CFD package can be used for the analysis of single phase flows in such systems. However the interaction of flow with deforming interface separating different phases as well as with the channel walls makes the multiphase flows highly complex and nonlinear. In addition, multiphysics effects such as thermocapillary, electric field, soluble surfactants and chemical reactions add further complexity to the problem. Thus the numerical simulation of multiphase flows is still a challenging task even S. Kakaç et al. (eds.), Microfluidics Based Microsystems: Fundamentals and Applications, DOI 10.1007/978-90-481-9029-4_12, © Springer Science + Business Media B.V. 2010

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in the creeping flow regime and offers good research opportunity in this fast developing field. In addition, computational tools can provide detailed insight about the flow physics that is extremely difficult to obtain experimentally since the microsystems is not experimentally friendly environment due to limited optical access, seed particles smaller than wavelength of light, noise caused by Brownian motion of seed particles and large background reflections [2]. There are several computational methods developed for direct simulation of multiphase flows. Each numerical method has its own advantages and disadvantages. In particular, the front-tracking method has been successfully applied to a wide range of multiphase flow problems [1]. Here we discuss sample applications of the front-tracking method to multiphase/fluid problems encountered or inspired by microfluidic systems. The first application concerns with mixing in microsystems. It is well known that mixing is notoriously difficult in microsystems due to laminar nature of the flow and thus requires passive or active chaotic mixing protocols to homogenize the fluid streams over typical residence times in microchannels. It has been shown that viscous droplets moving through a serpentine channel can be used as a mixer and chemical reactor [4, 5]. This method has a number of advantages including elimination of axial dispersion completely. Similarly gas segmentation creates chaotic mixing in liquid slugs moving through curved channels and significantly reduces the axial dispersion [6]. The front-tracking method has been successfully used to simulate flows in these micromixers [6–10]. The simulations shed light on the ways to improve the mixing and to reduce axial dispersion [6]. Another important application of the front-tracking method is to simulate the drop/bubble formation in flow-focusing devices. Production of mono disperse drops/bubbles in microchannels is of fundamental importance for the success of the concept of lab-on-a-chip. It has been shown that flowfocusing can be effectively used for this purpose. Filiz and Muradoglu performed front-tracking simulations in order to understand the physics of the breakup mechanism and effects of the flow parameters on the droplet/ bubble size in the flow-focusing devices [11]. Surface active agents (surfactant) are either present as impurities that are difficult to remove from a system or they are deliberately added to fluid mixtures to manipulate interfacial flows. It has been well known that the presence of surfactant in a fluid mixture can critically alter the motion and deformation of bubbles moving through a continuous liquid phase. Probably, the best-known example is the retardation effect of surfactant on the buoyancy-driven motion of small bubbles. Numerous experimental studies have shown that the terminal velocity of a contaminated spherical bubble is significantly smaller than the classical Hadamard–Rybczynski prediction

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and approaches the terminal velocity of an equivalent solid sphere. The physical mechanism for this behavior was first consistently explained by Frumkin and Levich [12] by noting that the surfactant adsorbed from the bulk fluid is convected toward the back of the bubble and the resulting Marangoni stresses act to reduce the interface mobility. This reduction in surface mobility increases the drag force and, thus, reduces the terminal velocity. In microfluidic applications, surfactants are usually used to manipulate the multiphase flows in microchannels. Modeling of soluble surfactants is a challenging problem due to deforming interface and mass transfer between the bulk fluid and the interface. In addition, the Marangoni stresses caused by non-uniform distribution of the surfactant concentration at the interface further complicates the problem. The front-tracking method has been recently used successfully to accurately model the effects of soluble surfactants on the interfacial flows [13, 14]. A few sample results about effects of the soluble surfactant are presented here together with some numerical details. It is well known that the surface tension generally reduces with increasing temperature and thus Marangoni stresses are induced due to non-uniform surface tension at the interface caused by non-uniform temperature field. This is called thermocapillary effect and can be used to manipulate multiphase flows in microchannels. The front-tracking method can be used effectively to model the thermocapillary effects as shown by Nas and Tryggvason [15] and Nas et al. [16]. Here front-tracking modeling of thermocapillary effects is not discussed since it is very similar to and simpler than modeling the soluble surfactants. Finally impact and spreading of a viscous droplet on a partially wetting solid substrate will be discussed. It is known that no-slip boundary condition exhibits singular behavior at the moving contact line in the case of partially wetting solid surface. This singularity is removed when a slip model is used. However the slip mechanism is still not well understood. One popular approach employed to model the moving contact line is to dynamically set the contact angle using the experimental correlations between the apparent contact angle and the capillary number of the moving contact line. This approach is taken here and successfully applied to simulate impact and spreading of a viscous microdroplet on a partially wetting substrate with various static contact angles. The ultimate goal is to be able to develop a model for single cell epitaxi demonstrated experimentally by Demirci and Munteseno [17] and suggested as an alternative way of creating three dimensional tissues layer by layer using existing ink-jet printing technology. Some details of the numerical method, validation tests for the simple droplets and some preliminary results for the single cell epitaxi are presented.

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2. Mixing and Dispersion Mixing in microchannels is notoriously difficult since flow is usually laminar and molecular diffusion is not sufficient to mix fluid streams on the time scale of the typical residence time. The mixing is especially problematic when fluid stream containing macromolecules such as DNA are to be mixed. Diffusion coefficient of the macromolecules is typically one or two orders of magnitude smaller than that of small molecules [1]. Therefore it is necessary to develop mixing protocols that significantly enhance the mixing in laminar flow environment. Nearly all mixing protocols are based on the concept of chaotic advection [18, 19]. In addition to enhanced mixing, it is also desirable to have a uniform residence time distribution as much as possible. This requires significant reduction or complete elimination of axial dispersion [6]. Taylor demonstrated that nonuniform velocity profile causes axial dispersion that is inversely proportional to the molecular diffusion coefficient [20]. Ismagilov and coworkers have shown that a droplet can be used as micromixer [4, 5]. As droplet moves through a serpentine channel, streamlines periodically cross each other causing chaotic mixing within the droplet. Mixing inside droplet also completely eliminates the axial dispersion [4, 5]. Alternatively, Guenther et al. [6] demonstrated that chaotic mixing also occurs in the bulk fluid when a serpentine channel is segmented by injecting gas bubbles. This gas-segmented micromixer significantly reduces but cannot eliminate the axial dispersion completely due to leakage from the liquid film between the gas bubbles and channel wall. The front-tracking method has been successfully used to model the mixing in microdroplet moving through a serpentine channel, mixing and dispersion in gas-segmented micromixer and the effects of the channel curvature on the liquid film thickness between the gas bubble and channel wall. 2.1. MIXING IN MICRODROPLET

The front-tracking method is used to study the mixing in microdroplet that moves through a serpentine channel. Computations are performed in twodimensional setting in order to facilitate extensive simulations. Although the problem is studied in two-dimensional setting, the flow is time dependent and so time acts as a third dimension making it possible for streamline patterns at one time to cross the streamline patterns at a later time and so produce effective mixing via chaotic trajectories. The channel used in the computation consists of a straight entrance, a sinusoidal mixer and a straight exit section as sketched in Fig. 1. The droplet is placed in the entrance section and passive tracer particles are used to visualize and quantify the mixing. The tracer particles are initially distributed uniformly at random

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within the drop and the particles occupying the lower half of the drop are identified as “white” while the other particles are “black.” These particles are moved with the local flow velocity interpolated from the neighboring computational grid points using the same advection scheme as used for moving the interface marker points. The flow is assumed to be fully developed at the inlet and the pressure is fixed at the outlet. The detailed description of the problem can be found in Ref. [8]. Lm

Li

Le

L dc dd

Figure 1. The sketch of the channel used in the computations.

The evolution of mixing patterns as the droplet moves through the channel is shown in Fig. 2. The capillary number, Reynolds number, viscosity ratio and the bubble size relative to the channel width are set to Ca = 0.025, Re = 6.6, λ = 1 and Λ = 0.76, respectively. This figure clearly shows that chaotic mixing occurs within the droplet. The effects of capillary number are also studied. For this purpose, the computations are performed for the capillary numbers ranging between 0.00625 and 0.2. Figure 3 shows the mixing patterns at the exit of the channel. This figure indicates that the quality of mixing increases as the capillary number increases.

Figure 2. Evolution of mixing patterns as the droplet moves through the channel.

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Ca

0.2

Ca

Ca

0.05

Ca

0.025

0.0125

Ca

0.00625

Figure 3. Effects of the capillary number on the mixing patterns at the exit of the channel.

The mixing entropy and intensity of segregation measures are used to quantify the mixing. For this purpose, the droplet area Sd is divided into small Nδ pixels with area of Sδ =δ2 such that Sd = NδSδ. Then a coarsegrained probability density function is defined as Dn = N(n)b/(N(n)b + N(n)w), where N(n)b and N(n)w are the number of black and white particles in nth pixel. The probability density function PDF is then defined as

D =

1 Nδ

Nδ

∑D n =1

=

n

Nδ , Nb + N w

(1)

where Nb and Nw are total number of black and white particles, respectively. Based on the coarse grained density, the entropy of the mixtures is defined as

s = − D log D = −

1 N

Nδ

∑D n =1

n

log Dn

(2)

The entropy is always positive and has the maximum value of

s o = − D log D ,

(3)

when fluids get fully mixed. The intensity of segregation is defined as

I=

(D −

D

)

2

D (1 − D )

.

(4)

The intensity of segregation has an advantage of varying between zero (compete mixing) and unity (no mixing). Finally the mixing number measure developed by Stone and Stone [21] is also used. Note that the mixing number is independent of grid but it cannot provide any detailed information about the quality of mixing. Figure 4 shows the quantification of mixing for the same case as in Fig. 3. As can be seen in this figure, all the mixing measures are consistent and the quality if mixing increases as the capillary number decreases.

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a

b

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1

100

Intensity 0f segregation

Mixing Number

0.9

10−1 Ca = 0.2 Ca = 0.05 Ca = 0.025 Ca = 0.0125

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1.5

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3.5

0.6

Ca = 0.2 Ca = 0.05

0.5

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x/L

c

d

0.6

Ca Ca Ca Ca Ca

0.58 0.56

= 0.2 = 0.05 = 0.025 = 0.0125 = 0.00625

Ca = 0.025 Ca = 0.0125 Ca = 0.00625

0.5

Entropy

0.5 0.48 0.46

1.5

2 2.5 x /L

3

3.5

4

2

3

3.5

4

Ca = 0.2 Ca = 0.05 Ca = 0.025

0.5

0.52

1

0.7 0.6

0.54 PDF

0.7

0.4

Ca = 0.00625

10−2

0.8

Ca = 0.0125 Ca = 0.00625

0.4 0.3 0.2

0.44 0.1

0.42 0.4 0.5

1

1.5

2

2.5

3

3.5

0

4

0.5

x/L

1

1.5

2.5 x /L

Figure 4. Effect of the capillary number on mixing. (a) Mixing number, (b) intensity of segregation, (c) PDF, (d) entropy.

The effects of the other parameters can be found in Muradoglu and Stone [8]. 2.2. MIXING IN GAS-SEGMENTED CHANNEL

The front-tracking method is then applied to study mixing in liquid slugs moving through a gas-segmented serpentine channel. The problem is again studied in a two-dimensional setting as shown in Fig. 5. Again passive Li

Lm

Le

L

dc Ld

Figure 5. The sketch of the model serpentine channel used to study the mixing within the liquid slug moving through a gas-segmented serpentine channel.

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tracer particles are used to visualize and quantify the mixing. The molecular mixing is ignored. The particle initially occupying the lower portion of the channel are identified as black while those occupying the upper portion are white. The flow rate is specified at the inlet assuming a fully developed channel flow and the pressure is fixed at the exit. The particles crossing the bubble interfaces or the solid wall due to numerical error are reflected back into the computational domain. Here one sample result is shown as an example and the readers are referred to Dogan et al. [9] for a detailed discussion about this problem. Figure 6 shows the evolution of mixing patterns in the liquid slug. This figure clearly shows that a chaotic mixing occurs within the liquid slug as it moves through the channel. A careful examination also shows that there is some leakage through the liquid film between the gas bubbles and the solid wall even in the absence of molecular mixing and this issue will be discussed in Section 2.4.

Figure 6. Snapshots of mixing patterns for a two-bubble system. The top plots are the enlarged versions of the corresponding scatter plots shown in the channel (lower plots).

2.3. LIQUID FILM BETWEEN GAS BUBBLE AND CHANNEL WALL: EFFECTS OF CHANNEL CURVATURE

We next study the effects of the channel curvature on the liquid film thickness between a bubble that is much larger than the channel size and the channel wall. This problem was originally studied by Bretherton [22] for straight channel case and is generally called a Landau–Levich problem. In studying the mixing in gas-segmented serpentine channel, we observed computationally that the film thickness on the inner and outer walls of the curved channel is not the same and the film thickness on the inner channel is thinner than that on the outer wall. This observation motivated to study the effects of the channel curvature on the liquid film thickness. This problem is again studied in a simple two-dimensional setting and a lubrication analysis is also performed in the limit of vanishing capillary number. The computational setup and the lubrication model are sketched in Fig. 7. Here the results are briefly summarized and the interested readers are referred to

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Muradoglu and Stone [10] for complete information about the lubrication analysis and details of computational study. A simple lubrication analysis indicates that the inner film is thinner than that of the outer film, i.e., the film thickness gets thinner with increasing channel wall curvature. The inner and outer film thicknesses are given by Muradoglu and Stone [10]. wRi 2 1 = Ca ; Re effi = w, 2+β 2Ri + w 2 + β

hi∞ = 1.3375 Re effi Cai2 / 3 ;

Cai =

ho∞ = 1.3375 Re effo Ca

wRo 2 + 2β 1+ β = Cao = Ca ; Re effo = w, 2+β 2 Ro − w 2 + β

2/3 o

;

(5)

where Ca = μUb /σ is the capillary number.

Figure 7. (a) Sketch for motion of a large bubble in curved channel. (b) The lubrication model for the inner wall.

Figure 8a shows the film thickness distribution along the circular channel on the inner and outer walls for Ca = 0.1 and 0.01. This figure clearly shows that the inner layer is thinner than the outer layer as predicted by the lubrication theory. The inner and outer film thicknesses are plotted in Fig. 8b as a function of capillary number together with the Bertherton’s solution for the straight channel. This figure shows that the inner film is thinner while the outer film is thicker than the corresponding film thickness in a straight channel. When the film thicknesses are properly scaled, all the results collapse on the same curve as shown in Fig. 9a. This figure shows that there is a very good agreement between the computational results and the lubrication theory for small capillary numbers. In addition, the scaled film thickness collapses on the same curve as that obtained for the straight channel, i.e., the present theory maps the curved channel into an equivalent straight channel.

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Figure 8. (a) Computed film thickness on the inner and outer walls for Ca = 0.1 and 0.01. The inset shows a portion of computational grid. (b) The Film thicknesses as a function of capillary number.

Figure 9. The film thickness scaled by the effective radius versus the effective capillary number.

2.4. AXIAL DISPERSION IN GAS-SEGMENTED CHANNEL FLOW

Finally the front-tracking method is used to study the axial dispersion caused by the leakage through the liquid film between the gas bubble and the channel wall both in a straight and curved channels. Tracer particles are used for the visualization and quantification of the axial dispersion. The molecular diffusion is modeled by random walk of tracer particles. Figure 10 shows the schematic illustration of axial dispersion in two-bubble system and bubble train. The computational setup is similar to those used in the previous sections so it will not be given here. Interested readers are referred

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to Muradoglu et al. [7]. Here only a two-bubble system is considered and computations are performed for various values of Peclet number. The results are plotted in Fig. 11.

Figure 10. Schematic illustration of a two-bubble system (top) and a bubble train (bottom).

Finally the effects of the channel curvature on the axial dispersion are examined. It is found that the channel curvature enhances the axial dispersion in gas-segmented serpentine channel and there is significant leakage from the liquid films between the bubble and the curved channel wall even in the absence of molecular diffusion [23]. A lubricating liquid layer forms and persists on the channel wall in the case of straight channel but this lubricating layer is periodically broken in the serpentine channel leading to enhanced axial dispersion. Here only one sample result is presented to show the effects of the channel curvature. Figure 12 shows the effects of the channel curvature on the axial dispersion. In Fig. 12a, the solute concentration within the liquid slug is plotted as a function of time both for straight and curved channels for a range of Peclet numbers at capillary number Ca = 0.01. As can be seen in this figure, the channel curvature generally enhances the leakage through the liquid films but the enhancement is more pronounced at high Peclet numbers. A simple theory is developed based the difference between film thicknesses on the inner and outer walls as discussed in Section 2.3 as well as in Muradoglu and Stone [10] in order to predict the amount of leakage caused solely by the channel curvature [23]. Figure 12b demonstrates that the theory predicts the axial dispersion successfully both for Ca = 0.01 and Ca = 0.005.

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a

1 Pe → ∞

0.9 0.8

Pe = 105

0.7 Pe = 103

〈C〉 / 〈C〉 i

0.6

Pe = 104

0.5

Pe = 102

0.4 Pe = 10

0.3 0.2 0.1 0

b

Pe = 0 (Theory) 0

5

10 15 Non-dimensional time, t*

20

25

100 t* = 10 t* = 20

(〈C〉 i − 〈C〉) / 〈C〉 i

10−1 Slope = − 0.641

10−2 Slope = − 0.645

10−3

102

104 Peclet Number, Pe

106

Figure 11. (a) Evolution of tracer concentration in the liquid segment as a function of nondimensional time for various Peclet numbers. (b) Variation of the average tracer concentration as a function of the Peclet number at t* = 10.

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Figure 12. Effects of the channel curvature on the axial dispersion. (a) The variation of solute concentration within liquid slug as a function of time for various Peclet numbers in straight and serpentine channels. (b) Computational results and theoretical predictions in the absence of molecular diffusion for Ca = 0.01 and 0.005.

3. Soluble Surfactants Surfactants are either present as impurities that are difficult to remove from the system or are added deliberately to the bulk fluid to manipulate the interfacial flows [24]. Surfactants may also be created at the interface as a result of chemical reaction between the drop fluid and solutes in the bulk fluid [25, 26]. Surfactants usually reduce the surface tension by creating a buffer layer between the bulk fluid and droplet at the interface. Nonuniform distribution of surfactant concentration creates Marangoni stress at the interface and thus can critically alter the interfacial flows. Surfactants are widely used in numerous important scientific and engineering applications. In particular, surfactants can be used to manipulate drops and bubbles in microchannels [2, 25], and to synthesize micron or submicron size monodispersed drops and bubbles for microfluidic applications [27]. It is a challenging task to model the effects of interfacial flows with soluble surfactants since surfactants are advected and diffused both at the interface and in the bulk fluid by the motion of fluid and by molecular mechanism, respectively. Therefore the evolution equations of the surfactant concentrations at the interface and in the bulk fluid must be solved coupled with the flow equations. The surfactant concentration at the interface alters the interfacial tension and thus alters the flow field in a complicated way. This interaction between the surfactant and the flow field is highly nonlinear and poses a computational challenge.

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The front-tracking method has been recently developed and successfully applied to model the effects of soluble surfactants on the motion and deformation of viscous droplets [13, 14]. Here the method is not described in details but some sample results are presented in order to show the power of the front-tracking method to model this challenging flow problem. Complete information about the numerical method can be found in Ref. [14]. The method is tested for the effects of the soluble surfactants on the motion and deformation of buoyancy-driven gas bubbles. The physical problem is assumed to be axisymmetric and is schematically illustrated in Fig. 13. The bubble is initially clean and placed instantaneously at the centerline near the south boundary in otherwise quiescent ambient liquid. It is well known that contaminated spherical bubble moves much slower than that of a clean bubble and its terminal velocity approaches that of a solid sphere rather than the classical Hadamard–Rybczynski prediction [28]. This phenomena was first explained consistently by Levich [12]. The Marangoni stresses created by the non-uniform surfactant concentration Figure 13. Schematic at the interface act opposite to the viscous stresses illustration of the computand tries to immobilize the interface, which results ational setup. in no slip boundary conditions at the interface like a solid sphere. Figure 14a shows the terminal Reynolds number of clean and contaminated bubbles for various droplet sizes relative to the channel diameter. This figure clearly shows the retardation effect of the surfactants. The computed steady Reynolds number is plotted in Fig. 14b as a function of the channel confinement D/d and compared to the available experimental data collected by Clift et al. [28] both for the clean and contaminated cases. It is interesting to observe that the steady terminal Reynolds number of the contaminated bubble is significantly smaller than that of the clean bubble and approaches the steady Reynolds number of a solid sphere. The rigidifying effect of surfactant can also be seen in Fig. 15 where the velocity vectors and streamlines are plotted in the reference frame moving with the bubble centroid. Finally the effects of the elasticity number are demonstrated in Fig. 16 for an ellipsoidal bubble. Complete description of the numerical method and effects of the soluble surfactant on the buoyancy-driven bubble can be found in Refs. [13, 14].

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Figure 14. Reynolds number vs. nondimensional time for D/d = 1.6, 2.5, 5, 7.5, 10, and 15, and (b) steady Reynolds number vs. non-dimensional channel diameter for clean (solid lines) and contaminated (dashed lines) bubbles (Eo = 1 and Mo = 0.1).

Figure 15. Spherical bubble. The streamlines and the velocity vectors at steady-state in a coordinate system moving with the bubble centroid for (a) a clean bubble and (b) a contaminated bubble. Every third grid points are used in the velocity vector plots (Eo = 1 and Mo = 0.1).

Figure 16. Ellipsoidal bubble. (Top row) The contour plots of the constant surfactant concentration in the bulk fluid (left side) and the distribution of the surfactant concentration at the interface (right side).

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4. Modeling Contact Line Impact and spreading of a viscous droplet on solid wall is of fundamental importance in many engineering and natural processes including ink-jet printing, spray coating, DNA microarrays, spray cooling and fuel injection in engines [29]. It also finds applications in emerging technologies such as single cell epitaxi [17]. The three-phase moving contact line is a notoriously difficult problem involving highly complicated physical processes and offers a challenge for computational models. During the collision and till the equilibrium, droplet passes various phases in which inertial, viscous, capillary, and contact line forces are dominant. It is well known that the noslip boundary condition yields stress singularity at the contact line since the fluid velocity is finite at the free-surface but zero on the wall [29]. This singularity is usually removed by relaxing the no-slip boundary condition with a slip model. Although numerous models and solutions to this problem have been proposed, we are still far from reaching a consensus for a definitive answer [29]. Direct numerical simulation of interfacial flows is a formidable task mainly due to the presence of moving and deforming interface. The existence of the contact line makes the problem even more complicated. The front-tracking method has been recently extended to treat the moving contact line [19] and successfully applied to model single cell epitaxi [30]. The model is briefly described here and some sample results are presented. Figure 17 shows the computational setup and treatment of the contact line in the framework of front-tracking algorithm for an axisymmetric droplet collision. The droplet is assumed to connect the substrate when it crosses the threshold distance hth using either a linear or cubic extrapolation function as shown in the inset of Fig. 17b. The contact angle is determined dynamically and imposed explicitly. The experimental correlation collected by Kistler [31] is used to determine the dynamic contact angle in the same way as done by Sikalo et al. [32]. The method is first tested for droplet impact and relaxation to its final equilibrium shape. This is a simple test but provides significant information about the accuracy of the contact line treatment. For this test problem, computations are performed for a range of Eotvos number (Eo) that represents the importance of gravitational force relative to the surface tension force. The computational results are plotted in Fig. 18 where the analytical solutions are also shown for the limiting cases of Eo = 0 (no gravitational effects) and Eo →∞ (gravitational effects are dominant). It is seen that there is excellent agreement between the computational results and the analytical solutions in the limiting cases and there is smooth transition in between. This figure indicates that the front-tracking method predicts the final equilibrium shapes of the droplet for a wide range of Eotvos numbers.

FRONT-TRACKING METHOD: APPLICATIONS

(a)

237

(b)

Figure 17. (a) Schematic illustration of the computational setup. (b) Treatment of the contact line.

After the static test mentioned above, the method is now tested for the impact and spreading of a glycerin droplet on a wax substrate and the computational results are compared with the experimental data of Sikalo et al. [32]. The details of the experimental setup, material properties and computational model can be found in Refs. [33, 51]. The computed and experimental spread factor and contact line are plotted in Figs. 19a and b, respectively. These figures show that the present front-tracking method is a viable tool for simulation of interfacial flows involving moving contact lines. Finally the method is applied to study the impact and spreading of a compound droplet on a flat substrate as a model for the single cell epitaxi [17]. The single cell epitaxi is an emerging technology that utilizes the conventional inkjet printing technology to print biological cells precisely on a substrate in order to create 2D and 3D tissue. The purpose of the present model is to understand the complicated impact dynamics of droplet encapsulated biological cell and determine the optimal conditions for cell viability. In this model, the inner and outer droplets represent the biological cell and the encapsulating droplet, respectively. The biological cell is modeled as a highly viscous Newtonian droplet as a first step in developing a more realistic model in which the biological cell will be treated as a nonNewtonian fluid. Figure 20 shows an example simulation of the compound droplet model. This figure demonstrates the power of the numerical simulation that provides detailed information about the pressure contours and pressure distribution on the inner droplet (biological cell). The deformation and rate of deformation of the inner droplet are also plotted in Fig. 21 for various impact Reynolds numbers.

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Figure 18. The normalized static droplet height versus Eotvos number in the range Eo = 0:01 and Eo = 64. Solid and dashed lines denote the analytical solutions for the limiting cases of Eo ≪ 1 and Eo ≫ 1, respectively. The inset shows the initial conditions for the droplet relaxation test. 2.5

180

Exp. (Sikalo et al.) We = 802 Re = 106 We = 93 Re = 36 We = 51 Re = 27

160 2 Contanct Angle

140

R /R0

1.5 1 Exp. (Sikalo et al.) We = 802 Re = 106 We = 93 Re = 36 We = 51 Re = 27

0.5 0

0

2

6

4

8

120 100 80 60 40 20

10

0

0

2

4

6

tVcol /D

tVcol /D

(a)

(b)

8

10

Figure 19. Glycerin droplet spreading on the wax substrate. Time evolution of (a) the spread factor and (b) the dynamic contact angle.

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Figure 20. Evolution of compound droplet impacting on a flat surface (left half: pressure contours and right half: pressure distribution on the surface of the cell). Time evolves from left to right and from top to bottom.

Figure 21. Deformation and rate of deformation vs. nondimensional time for Re = 15, 20, 30, 40 and 45.

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5. Conclusions The front-tracking method developed by Unverdi and Tryggvason [34] has been successfully applied to interfacial flow problems encountered or inspired by microfluidic systems. It has been shown that the method can be used to study mixing in a micro-droplet moving through a serpentine channel, mixing within liquid slugs in gas-segmented serpentine channel, the effects of channel curvature on the Landau–Levich problem, axial dispersion, soluble surfactants and moving contact lines. The explicit tracking of the interface eliminates excessive numerical dissipation that frontcapturing methods such as VOF and level-set suffer and this feature makes the front-tracking method especially useful in microfluidic applications where it is often required to resolve thin fluid layers. Another important advantage of the front-tracking method is its ability to incorporate multiphysics effects such as thermocapillary, electric field, soluble surfactants, moving contact lines, chemical reactions etc. In this chapter, a few applications involving the multiphysics effects are presented as examples but more such applications can be found in the literature. The front-tracking method is only one example of computational tools that can be used in analysis and design of microfluidic systems. The computational methods for multiphase/fluid flows have been matured enough that they can be safely used as a design tool in microfluidics. In addition, they can be also very useful to discover or understand new flow physics emerging from the miniaturization of flow systems. Acknowledgement This work is supported by Turkish Academy of Sciences through GEBIP program.

References 1. G. Tryggvason, B. Bunner, A. Esmaeeli, D. Juric, N. Al-Rawahi, W. Tauber, J. Han, S. Nas, and Y.-J. Jan. A Front-Tracking Method for the Computations of Multiphase Flow, J. Comput. Phys., 169, 708–759 (2001). 2. H.A. Stone, A.D. Stroock, and A. Ajdari. Engineering Flows in Small Devices: Microfluidics Toward a Lab-on-a-Chip, Annu. Rev. Fluid Mech., 36 (2004). 3. T.M. Squires and S.R. Quake, Microfluidics: Fluid Physics at the Nanoliter Scale, Rev. Modern Phys., 77(3), 977–1026 (2005). 4. M.R. Bringer, C.J. Gerdts, H. Song, J.D. Tice, and R.F. Ismagilov, Microfluidic Systems for Chemical Kinetics That Rely on Chaotic Mixing in Droplets, Philos. Trans. R. Soc. London, Ser. A 362, 1087 (2004).

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5. H. Song, J.D. Tice, and R.F. Ismagilov, A Microfluidic System for Controlling Reaction Networks in Time, Angew. Chem., Int. Ed., 42 (2003). 6. A. Guenther, S.A. Khan, M. Thalmann, F. Trachsel, and K.F. Jensen, Transport and Reaction in Microscale Segmented Gas-Liquid Flow, Lab. Chip. 4 (2004). 7. M. Muradoglu, A. Guenther and Stone, A Computational Study of Axial Dispersion in Segmented Gas-Liquid Flow, Phys. Fluid, 19, 072109 (2007). 8. M. Muradoglu and Stone, Mixing in a Drop Moving Through a Serpentine Channel: A Computational Study, Phys. Fluid, 17, 073305 (2005). 9. H. Dogan, S. Nas, and M. Muradoglu, Mixing of Miscible Liquids in GasSegmented Serpentine Channels, Int. J. Multiphase Flow (in press) (2009). 10. M. Muradoglu and Stone, Motion of Large Bubbles in Curved Channels, J. Fluid Mech. 570 (2007). 11. I. Filiz and M. Muradoglu, A Computational Study of Drop Formation in an Axisymmetric Flow-Focusing Device, Proceedings of ASME, ICNMM2006, 4th International Conference on Nanochannels, Microchannels and Minichannels, June 19–21, Limerick, Ireland (2006). 12. A.A. Frumkin and V.G. Levich, On Surfactants and Interfacial Motion, Zh. Fiz. Khim. 21, 1183 (1947). 13. S. Tasoglu, U. Demirci, and M. Muradoglu, The Effect of Soluble Surfactant on the Transient Motion of a Buoyancy-Driven Bubble, Phys. Fluids, 20, 040805 (2008). 14. M. Muradoglu and G. Tryggvason, A Front-Tracking Method for Computation of Interfacial Flows with Soluble Surfactants, J. Comput. Phys., 227(4), 2238– 2262 (2008). 15. S. Nas and G. Tryggvason, Thermocapillary Interaction of Two Bubbles or Drops, Int. J. Multiphase Flow, 29 (2003). 16. S. Nas, M. Muradoglu, and G. Tryggvason, Pattern Formation of Drops in Thermocapillary Migration, Int. J. Heat Mass Trans., 49(13–14), 2265–2276 (2006). 17. U. Demirci and G. Montesano, Single Cell Epitaxy by Acoustic Picoliter Droplets, Lab on a Chip, 7 (2007). 18. S. Wiggins and J.M. Ottino, Foundations of Chaotic Mixing, Philos. Trans. R. Soc. London, Ser. A 362, 1087 (2004). 19. H. Aref, Stirring by Chaotic Advection, J. Fluid Mech., 143, 1 (1984). 20. G.I. Taylor, Deposition of Viscous Fluid on the Wall of a Tube, J. Fluid Mech., 10, 161 (1961). 21. Z.B. Stone and H.A. Stone, Imaging and Quantifying Mixing in a Model Droplet Micromixer, Phys. Fluids, 17, 063103 (2005). 22. F.P. Bretherton, The Motion of Long Bubbles in Tubes, J. Fluid Mech. 10, 166–188 (1961). 23. M. Muradoglu, Axial Dispersion in Segmented Gas-Liquid Flow: Effects of Channel Curvature, preprint to be submitted (2009). 24. H.A. Stone, Dynamics of Drop Deformation and Breakup in Viscous Fluids, Annu. Rev. Fluid Mech., 26 (1994). 25. M. Faivre, T. Ward, M. Abkarian, A. Viallat, and H.A. Stone, Production of Surfactant at the Interface of a Flowing Drop: Interfacial Kinetics in a

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26. 27. 28. 29. 30. 31. 32. 33. 34.

M. MURADOGLU Microfluidic Device, in: 57th APS Division of Fluid Dynamics Meeting, Seattle, WA, USA (2004). E.A. van Nierop, A. Ajdari, and H.A. Stone, Reactive Spreading and Recoil of Oil on Water, Phys. Fluids, 18(3), Art. No. 03810 (2006). S.L. Anna and H.C. Meyer, Microscale Tip Streaming in a Microfluidic Flow Focusing Device, Phys. Fluids, 18(12), Art. No. 12151 (2006). R. Clift, J.R. Grace, and M.E. Weber, Bubbles, Drops and Particles, Dover, Mineola (2005). A.L. Yarin, Drop Impact Dynamics: Splashing, Spreading, Receding, Bouncing ..., Annu. Rev. Fluid Mech. 38, 159–192 (2006). S. Tasoglu1, G. Kaynak, U. Demirci, A.J. Szeri, and M. Muradoglu, Impact of a Compound Droplet on a Flat Surface: A Model for Single Cell Epitaxi, preprint to be submitted (2009). S.F. Kistler, Hydrodynamics of Wetting, in: Wettability, edited by J.C. Berg, Marcel Dekker, New York (1993). S. Sikalo, H.D. Wilhelm, I.V. Roisman, S. Jakirlic, and C. Tropea, Dynamic Contact Angle of Spreading Droplets: Experiments and Simulations, Phys. Fluids, 17, 062103 (2005). M. Muradoglu and S. Tasoglu, A Front-Tracking Method for Computational Modeling of Impact and Spreading of Viscous, Droplets on Solid Walls, Comput. Fluids (in press) (2009). S.O. Unverdi, G. Tryggvason, A Front-Tracking Method for Viscous Incompressible Multiphase Flows, J. Comput. Phys., 100 (1992).

GAS FLOWS IN THE TRANSITION AND FREE MOLECULAR FLOW REGIMES A. BESKOK

Aerospace Engineering Department Old Dominion University, Norfolk, VA 23529,USA, [email protected]

Abstract. We investigate pressure driven flow in the transition and freemolecular flow regimes with the objective of developing unified flow models for channels and ducts. These models are based on a velocity scaling law, which is valid for a wide range of Knudsen number. Simple slip-based descriptions of flowrate in channels and ducts are corrected for effects in the transition and free-molecular flow regimes with the introduction of a rarefaction coefficient. The resulting models can predict the velocity distribution, mass flowrate, pressure and shear stress distribution in rectangular ducts in the entire Knudsen flow regime.

1. Introduction In this chapter we develop a unified flow model that predicts the velocity profiles, and mass flowrate in two-dimensional channels and ducts in the entire Knudsen regime. Our approach is divided into two main steps: First, we will analyze the nondimensional velocity profile to identify the shape of the velocity distribution. Then, we will obtain the magnitude of the average velocity, and hence, obtain a prediction for the flowrate. 2. Velocity Scaling From the DSMC results and solutions of the linearized Boltzmann equation, it is evident that the velocity profiles in pipes, channels and ducts remain approximately parabolic for a large range of Knudsen number. This is also consistent with the analysis of the Navier–Stokes and Burnett equations in long channels, as documented in Ref. [1]. Based on this observation, we model the velocity profile as parabolic in the entire Knudsen regime, with a consistent slip condition. We write the dimensional form for velocity distribution in a channel of height h, S. Kakaç et al. (eds.), Microfluidics Based Microsystems: Fundamentals and Applications, DOI 10.1007/978-90-481-9029-4_13, © Springer Science + Business Media B.V. 2010

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⎡ ⎛ y ⎞2 ⎛ y ⎞ ⎤ dP U ( x, y ) = F ( , μo , h, λ ) ⎢− ⎜ ⎟ + ⎜ ⎟ + U s ⎥ , dx ⎣⎢ ⎝ h ⎠ ⎝ h ⎠ ⎦⎥ where F (dP/dx, μ0, h, λ) shows the functional dependence of velocity on the pressure gradient, viscosity, channel height, and local mean free path. Temperature is assumed to be constant, and therefore the dynamic viscosity is also a constant. Here Us is the slip velocity, which satisfies the general slip boundary condition given by

Us −Uw =

1 − σ v ⎡ Kn ⎛ ∂U ⎞ ⎤ ⎜ ⎟ , σ v ⎢⎣1 − bKn ⎝ ∂n ⎠ s ⎥⎦

(1)

where b is the general slip coefficient [1]. Using this boundary condition yields

U ( x, y ) = F (

⎡ ⎛ y ⎞ 2 ⎛ y ⎞ ⎛ 2 − σ v ⎞ Kn ⎤ dP ⎟⎟ , μo , h, λ ) ⎢− ⎜ ⎟ + ⎜ ⎟ + ⎜⎜ ⎥. dx ⎢⎣ ⎝ h ⎠ ⎝ h ⎠ ⎝ σ v ⎠ 1 − bKn ⎥⎦

Assuming this form of velocity distribution, the average velocity in the channel ( U = Q& / h ) can be obtained as

U ( x) = F (

⎡ 1 ⎛ 2 − σ v ⎞ Kn ⎤ dP ⎟⎟ , μo , h, λ ) ⎢ + ⎜⎜ ⎥. 6 σ dx v ⎠ 1 − bKn ⎦ ⎝ ⎣

By nondimensionalizing the velocity distribution with the local average velocity, dependence on the local flow conditions F (dP/dx, μ0, h, λ) is eliminated. Therefore, the resulting relation is a function of Kn and y only. Assuming diffuse reflection (σv = 1) for simplicity, we obtain

⎡ ⎛ y ⎞2 ⎛ y ⎞ Kn ⎤ ⎢− ⎜ ⎟ + ⎜ ⎟ + ⎥ h h 1 − bKn ⎥ . U * ( y, Kn) = U ( x, y ) / U ( x) = ⎢ ⎝ ⎠ ⎝ ⎠ Kn 1 ⎢ ⎥ + ⎢ ⎥ 6 1 − bKn ⎣ ⎦

(2)

Equation (2) solely describes the shape of the velocity distribution, but it does not properly model the flowrate, which requires additional corrections, as will be shown in the next section.

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245

In Fig. 1 we plot the nondimensional velocity variation obtained in a series of DSMC simulations for Kn = 0.1, Kn = 1, Kn = 5, and Kn = 10. We also included the corresponding linearized Boltzmann solutions obtained in Ref. [2]. It is seen that the DSMC velocity distribution and the linearized Boltzmann solutions agree quite well. We can now use Eq. (2) and compare with the DSMC data by varying the parameter b, which for b = 0 corresponds to Maxwell’s first-order and for b = −1 to the second-order boundary condition in the slip regime only. Here we find that for b = −1, Eq. (2) results in an accurate model of the velocity distribution for a wide range of Knudsen number. From the figure, it is clear that the velocity slip is slightly overestimated with the proposed model for the Kn = 1 case. To obtain a better velocity slip, we varied the value of the parameter b by imposing, for example, b = −1.8 for the Kn = 1 case. Although a better agreement is achieved for the velocity slip, the accuracy of the model in the rest of the channel is destroyed.

− U(Y) /U

1.2

0.8

0.4

Kn = 0.1 0

0.2

b = −1 b=0 b = −1.8

Kn = 1.0 0.4

0.6

0.8

1 0

0.2

0.4

Y

0.6

0.8

1

Y

− U(Y) /U

1.2

0.8

DSMC Lin. Boltzmann

0.4 Kn = 5.0 0

0.2

Kn = 10.0 0.4

0.6 Y

0.8

1 0

0.2

0.4

0.6

0.8

1

Y

Figure 1. Velocity profile comparisons of the model (Eq. (2)) with DSMC and linearized Boltzmann solutions [2]. Maxwell’s first-order boundary condition is shown with dashed lines (b = 0), and the general slip boundary condition (b = −1) is shown with solid lines.

In Fig. 2 we show the nondimensionalized velocity distribution along the centerline and along the wall of the channels for the entire Knudsen number regime considered here, i.e., 0.01 ≤ Kn ≤ 30. We included in the

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A. BESKOK

plot data for the velocity slip and centerline velocity from 20 different DSMC runs, 15 for nitrogen (diatomic molecules) and 5 for helium (monatomic molecules). The differences between the nitrogen and helium simulations are negligible, and thus this velocity scaling model is independent of the gas type. The linearized Boltzmann solution of Aoki for a monatomic gas is also shown by triangles. This solution closely matches the DSMC predictions. Maxwell’s first-order boundary condition (b = 0) (shown by a solid line) erroneously predicts a uniform nondimensional velocity profile for large Knudsen number. The breakdown of slip flow theory based on the first-order slip boundary condition is realized around Kn = 0.1 and Kn = 0.4 for the wall and the centerline velocity, respectively. This finding is consistent with the commonly accepted limits of the slip flow regime. The prediction using b = −1 is shown by small dashed lines. The corresponding centerline velocity closely follows the DSMC results, while the slip velocity of the model with b = −1 deviates from DSMC in the intermediate range for 0.1 < Kn < 5. One possible reason for this is the effect of the Knudsen layer, a sublayer that is present between the viscous boundary layer and the wall, with a thickness of approximately one mean free path. For small Kn flows the Knudsen layer is thin and does not affect the velocity slip prediction too much. For very large Kn flows, the Knudsen layer covers the entire channel. However, for intermediate Kn values both the fully developed viscous flow (boundary layer) and the Knudsen layer exist in the channel. At this intermediate range, approximating the velocity profile to be parabolic neglects the Knudsen layers. For this reason, the model with b = −1 results in 10% error of the velocity slip at Kn = 1. However, the velocity distribution in the rest of the channel is described accurately for the entire flow regime. For a comparison we also included similar predictions by the secondorder slip boundary condition of Hsia and Domoto (large dashed line). The form of their boundary conditions is similar to Cercignani’s, Deissler’s, and Schamberg’s, and they all become invalid at around Kn = 0.1. This boundary condition performs worse than even the first-order Maxwell’s boundary condition for large Kn values. Only the general slip boundary condition predicts the scaling of the velocity profiles accurately. 3. Flowrate Scaling The volumetric flowrate in a channel is a function of the channel dimensions, fluid properties (μ0, λ), and pressure drop, and it can be written as

⎛ dP ⎞ Q& = G⎜ , μ o , h, λ ⎟ . ⎝ dx ⎠

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247

For a channel of height h, using the Navier–Stokes solution and the general slip boundary condition (1) we obtain

6 Kn ⎤ h 3 dP ⎡ , 1+ Q& = − ⎢ 12 μ o dx ⎣ 1 − bKn ⎥⎦

(3)

where Kn = λ/h. 1.5

−

U/U

1

0.5

Lin. Botz. DSMC Data b=0 b = −1 b = −2 Hsia & Domoto

0 0.01

0.05

0.1

0.5

1

5

10

Kn

Figure 2. Velocity scaling at wall and centerline of the channels for slip and transition flows. The linearized Boltzmann solution of Aoki is shown by triangles, and the DSMC simulations are shown by points. Theoretical predictions of velocity scaling for different values of b, and Hsia and Domoto’s second-order slip boundary condition are also shown.

The flowrate for the continuum and free-molecular flows are both linearly dependent on dP/dx [3], and thus we choose to normalize the flowrate with the pressure gradient. This quantity is computed based on the DSMC simulations and is shown in Fig. 3 for nitrogen. For comparison we present the Q& / |dP/dx| predictions obtained using Maxwell’s first-order slip boundary condition (b = 0, dashed lines) and the general slip boundary condition (b = −1, dashed-dotted lines). In both cases the predictions are erroneous. The general slip boundary condition performs the worst for it is asymptotic to a constant value, while the DSMC data show a considerable

A. BESKOK

248

increase with Kn. The first-order boundary condition follows the DSMC data, however with a significant error. The model in Eq. (1) gives good agreement with DSMC data and the linearized Boltzmann solutions for the nondimensional velocity profile, but it does not predict correctly the flowrate. This is expected, since the Navier– Stokes equations are invalid in this regime. In fact, the dynamic viscosity, which defines the diffusion of momentum due to the intermolecular collisions, must be modified to account for the increased rarefaction effects. The kinetic theory description for dynamic viscosity requires μ 0 ≈ λ v ρ where v is the mean thermal speed. Using mean free path λ in this relation is valid as long as intermolecular collisions are the dominant part of momentum transport in the fluid (i.e., Kn > λ >> h) there are no physical values for α, since the flowrate increases logarithmically with

A. BESKOK

250

Kn. For finite-length channels the flowrate is asymptotic to a constant value proportional to loge(L/h). Therefore, for finite-length two-dimensional channel flows, the coefficient α should smoothly vary from zero in the slip flow regime to an appropriate constant value in the free-molecular flow regime. The physical meaning of this behavior is that the dynamic viscosity remains the standard diffusion coefficient in the early slip flow regime. The value of α increases slowly with Kn in the slip flow regime, and therefore the effect of change of the diffusion coefficient is second-order in Kn. For this reason the experimental slip flow results are accurately predicted by the slip flow theory, which does not require change of the diffusion coefficient length scale from λ to channel height h. Variation of α as a function of Kn can be represented accurately with the following relation:

α = αo

2

π

(

)

tan −1 α1Kn β ,

(7)

where αo is determined to result in the desired free-molecular flowrate. Note that the values for α1 and β are the only two undetermined parameters of the model. 4. Model for Duct Flows The asymptotic values of the flowrate for duct flows at high Knudsen number are constants depending on the duct aspect ratio. This offers the possibility of obtaining a model for the rarefaction coefficient Cr(Kn) and in particular the coefficient α. The objective is to construct a unified expression for α (Kn) that represents the transition of α from zero in the slip flow regime to its asymptotic constant value in the free-molecular flow regime. We consider flows in ducts with aspect ratio (AR = w/h ≡ width/height) of 1, 2, and 4. The data are obtained by linearized Boltzmann solution in ducts with the corresponding aspect ratios. Our previous analysis was valid for the two-dimensional channels, where we reported flowrate per channel width. For duct flows, three-dimensionality of the flow field (due to the side walls of the duct) must be considered. In continuum duct flows, the flowrate formula developed for two-dimensional channel flows is corrected in order to include the blockage effects of the side walls. According to this, the volumetric flowrate in a duct with aspect ratio AR for no-slip flows is (see [5], p. 120)

wh ⎛ dP ⎞ Q& = C ( AR) ⎜− ⎟, 12μ ⎝ dx ⎠ 3

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251

where C(AR) is the correction factor given as

⎡ 192( AR) ∞ tanh(iπ 2( AR)) ⎤ C ( AR) = ⎢1 − ∑ ⎥. 5 5 i π = 1 , 3 , 5 ,... i ⎣ ⎦

(8)

With this correction, aspect ratios of 1, 2, and 4 ducts correspond to 42.17%, 68.60%, and 84.24% of the theoretical two-dimensional channel volumetric flowrate for no-slip flows, respectively. According to the new model, the volumetric flowrate for rarefied gas flows in ducts is

wh 3 ⎛ dP ⎞ 6 Kn ⎞ ⎛ & Q = C ( AR) ⎜− ⎟(1 + αKn)⎜1 + ⎟, 12μ 0 ⎝ dx ⎠ ⎝ 1 − bKn ⎠ where the correction factor C(AR) is independent of the Knudsen number. The variation of α as a function of Kn is calculated by using the correction factors (C(AR)), the linearized Boltzmann solutions, and our model. This variation is given in Fig. 4. The rarefaction coefficient (Cr(Kn) = 1 + αKn) was introduced in order to model the reductions in the intermolecular collisions of the molecules as Kn is increased. In duct flows, both the height and the width of the duct are important length scales, and comparison of these length scales to the local mean free path is an important factor in the variation of α. It is seen in Fig. 4 that the transition in α occurs later for high aspect ratio ducts. An approximate formula can be derived to describe the mass flowrate in ducts of various aspect ratios as

⎛ 6 Kn ⎞ M& ⎟⎟ , = C ( AR)(1 + α Kn)⎜⎜1 + M& c ⎝ 1 − b Kn ⎠ where Kn is evaluated at average pressure. In Fig. 5 we present the variation of flowrate nondimensionalized with the corresponding no-slip value as a function of Kn in the slip and early transitional flow regimes. The linear increase of the flowrate with Kn and complete description of rarefied duct flows with the introduction of the correction factor C(AR) are observed. The slope of the nondimensionalized mass flowrate increases gradually with Kn. This is attributed to the gradual change in the rarefaction coefficient as presented in Fig. 4.

A. BESKOK

252 1.8 1.6 1.4 1.2

a

1 0.8 0.6 0.4 AR = 4 0.2

AR = 2 AR = 1

0 0.01

0.1

1

10

100

Kn

Figure 4. Variation of α as a function of Kn for various aspect ratio ducts.

˙C ˙ /M M

3

2

1 AR = ¥ AR = 4 AR = 2 AR = 1 0

0

0.1

0.2

0.3

0.4

Kn

Figure 5. Normalized flowrate variation in the slip and early transitional flow regimes for various aspect ratio (AR) duct flows. Symbols show the linearized Boltzmann solutions. Comparisons with the proposed model are also presented by lines.

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For the free-molecular scaling of the data we nondimensionalized the flowrate with

h 2 w ΔP , M& FM = 2 RT0 L which gives the correct order of magnitude for the flowrate. The exact value of the free-molecular flowrate in rectangular ducts is given by Thompson and Owens [7]

M& FM (h, w) = ΓM& FM ,

(9)

where 2 2 ⎛h ⎛w ⎛ h ⎞ ⎞⎟ ⎛ w ⎞ ⎞⎟ 2 ⎜ ⎜ Γ = h w log e + 1 + ⎜ ⎟ + w h log e + 1+ ⎜ ⎟ ⎜w ⎜h w⎠ ⎟ ⎝ ⎝ h ⎠ ⎟⎠ ⎝ ⎠ ⎝ , 2 2 3/ 2 3 3 h +w (h + w ) − + 3 3 2

where h and w are the height and width of the rectangular duct. For the aspect ratios (AR) of 1, 2, and 4 the above relation results in 0.8387, 1.1525, and 1.5008 times the free-molecular mass flowrate M& FM , respectively. Nondimensionalizing the model with the free-molecular mass flowrate & ( M FM ), we obtain

M& (1 + α Kn) ⎛ 6 Kn ⎞ ⎜⎜1 + ⎟, = C ( AR) & M FM 6 Kn ⎝ 1 − b Kn ⎟⎠ ___

where Kn is evaluated at channel average pressure. In Fig. 6 we present the variation of the nondimensionalized flowrate as a function of Kn. The duct flow data are due to Sone, and the two-dimensional channel data (shown by AR = ∞) are due to Sone (for Kn ≤ 0.17) and Cercignani (Kn > 0.17). Comparisons are made against the linearized Boltzmann solutions. For duct flows, good agreement of the model with the numerical data in the entire flow regime is obtained. The model is also able to capture Knudsen’s minimum accurately. The parameters used in the model are given in Table 1 for various aspect ratio channels. Note that α0 is

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determined from the asymptotic constant limit of flowrate (9) as Kn → ∞. Variation of α as a function of Kn, is modeled using Eq. (7) with α1 and β values given in Table 1. 5. Conclusions We developed a unified flow model that can accurately predict the volumetric flowrate, velocity profile, and pressure distribution in the entire Knudsen regime for rectangular ducts. The new model is based on the hypothesis that the velocity distribution remains parabolic in the transition flow regime, which is supported by the asymptotic analysis of the Burnett equations [1]. The general velocity slip boundary condition and the rarefaction correction factor are the two primary components of this unified model.

AR = ¥

10 9 8

AR = 4 AR = 2

7

AR = 1

6 5

˙ /M ˙ FM M

4

3

2

1 0.9 0.8 0.7 0.01

0.1

1

10

100

Kn

Figure 6. Free-molecular scaling of linearized Boltzmann solutions for duct flows of various aspect ratio. Comparisons with the proposed model are also presented by lines corresponding to different aspect ratios.

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The general slip boundary condition gives the correct nondimensional velocity profile, where the normalization is obtained using the local channel averaged velocity. This eliminates the flowrate dependence in modeling the velocity profile. For channel flows, we obtain b = −1 in the slip flow regime. Evidence based on comparisons of the model with the DSMC and Boltzmann solutions shows that b = −1 is valid in the entire Knudsen regime. In order to model the flowrate variations with respect to the Knudsen number Kn, we introduced the rarefaction correction factor as Cr =1+α Kn. This form of the correction factor was justified using two independent arguments: first, the apparent diffusion coefficient; and second, the ratio of intermolecular collisions to the total molecular collisions. We must note that α cannot be a constant. Physical considerations to match the slip flowrate require α → 0 for Kn ≤ 0.1, while α → αo in the free molecular flow regime. The variation of α between zero and a known αο value is approximated using Eq. (7) which introduced two empirical parameters α1 and β to the new model. Therefore, the unified model employs two empirical parameters (α1 and β) and two known parameters b = −1 and αo. Although this empiricism is not desired, the α value in Cr varies from zero in the slip flow regime to an order-one value of αo as Kn → ∞. Finally, the model is adapted to the finite aspect ratio rectangular ducts using a standard aspect ratio correction given in Eq. (7). TABLE 1. Parameters of the model for various aspect ratio duct flows. The only free parameters are α1 and β, as α0 is determined from the asymptotic constant limit of flowrate as Kn → ∞ .

(AR) = w/h 1 2 4

C(AR) 0.42173 0.68605 0.84244

α0 1.7042 1.4400 1.5272

α1 8.0 3.5 2.5

β 0.5 0.5 0.5

References 1. 2.

A. Beskok and G.E. Karniadakis. A model for flows in channels, pipes and ducts at micro and nano scales. Microscale Thermophys. Eng., 3(1):43–77 (1999). T. Ohwada, Y. Sone, and K. Aoki. Numerical analysis of the Poiseuille and thermal transpiration flows between two parallel plates on the basis of the Boltzmann equation for hard sphere molecules. Phys. Fluids A, 1(12):2042– 2049 (1989).

256 3. 4. 5. 6. 7.

A. BESKOK E.H. Kennard. Kinetic Theory of Gasses. McGraw-Hill Book Co. Inc., New York (1938). W.G. Polard and R.D. Present. On gaseous self-diffusion in long capillary tubes. Phys. Rev., 73 (7):762–774, April (1948). F.M. White. Viscous Fluid Flow. McGraw-Hill International Editions, Mechanical Engineering Series (1991). S. Loyalka and S. Hamoodi. Poiseuille flow of a rarefied gas in a cylindrical tube: Solution of linearized Boltzmann equation. Phys. Fluids A, 2 (11):2061– 2065 (1990). S.L. Thompson and W.R. Owens. A survey of flow at low pressures. Vacuum, 25:151–156 (1975).

MIXING IN MICROFLUIDIC SYSTEMS A. BESKOK Aerospace Engineering Department Old Dominion University, Norfolk, VA 23529, USA, [email protected]

Abstract. Flow and species transport in micro-scales experience laminar, even Stokes flow conditions. In absence of turbulence, species mixing becomes diffusion dominated, and requires very long mixing length scales (lm). This creates significant challenges in the design of Lab-on-a-chip (LOC) devices, where mixing of macromolecules and biological species with very low mass diffusivities are often desired. The objectives of this chapter are to introduce concepts relevant to mixing enhancement in microfluidic systems, and guide readers in the design of new mixers via numerical simulations. A distinguishing feature is the identification of flow kinematics that enhance mixing, followed with systematic characterization of mixing as a function of the Schmidt number at fixed kinematic conditions. In this chapter, we briefly review the routes to achieve chaotic advection in Stokes flow, and then illustrate the characterization of a continuous flow chaotic stirrer via appropriate numerical tools, including the Poincaré section, finite time Lyapunov exponent, and mixing index. 1. Introduction Mixing is the process of homogenization of species distribution as a result of stirring and diffusion. While stirring brings the constituents to close proximity, and diffusion homogenizes through “blending of the constituents”. Using this simplified definition of mixing, stirring is indicative of flow kinematics that is often determined by the mixer geometry and flow conditions, which are primarily described by Reynolds number (Re), defined as the ratio of inertial and viscous forces (Other dimensionless groups can also exist based on the specific mixer design). The effects of diffusion are determined by the species that is being mixed, which can be characterized as a function of the Schmidt number (Sc) defined as the ratio of momentum and mass diffusivities. Although the characteristic lengths associated with LOC devices are very small − typically on the order of 100 μm − diffusion alone in the case of large molecules does not allow S. Kakaç et al. (eds.), Microfluidics Based Microsystems: Fundamentals and Applications, DOI 10.1007/978-90-481-9029-4_14, © Springer Science + Business Media B.V. 2010

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for sufficiently fast mixing. For example, at room temperature, myosin’s diffusion coefficient in water is about 10−11 m2/s, and the time constant for the diffusion along a length of 100 μm is thus intolerably large, about 103 s. Therefore, mixing several fluids in reactors at the micron scale is not as easy as it might seem at first sight. Since the Reynolds numbers of flows in micro-devices are usually very small (i.e., Re ∼ O(1)), the flows are laminar and mixing enhancement cannot be reached by making use of turbulencelike flow patterns. In order to achieve reasonable speed and yield of chemical reactions and bioassays, micromixers must be necessarily integrated into the chips. The device integration step may bring several limitations regarding to the flow kinematics utilized in the mixer design, where simply increasing the flow rate (or Re) to mix different species may not be compatible with the upstream and downstream components of the LOC device. Given these limitations, one needs to determine the kinematically favorable conditions for mixing by choosing the mixer-geometry and flow conditions (Re, and other relevant dimensionless parameters), and then, ensure efficient mixing for various species by varying Sc under these predetermined kinematic conditions. Various types of micromixers have been designed, fabricated and experimentally characterized using fluorescent dyes to measure the fluorescence intensity at various sections of these mixers. In these studies, the mixing efficiency was quantified using standard deviation of the fluorescence intensity from a perfect mix [1–6]. A remarkable amount of the experiments utilized a single type of dye (i.e., fixed Schmidt number Sc), and the mixing length or mixing time was investigated as a function of the Peclet number (Pe ≡ Sc × Re), which gives the forced convection to diffusion ratio of a system, by varying the Reynolds number. An important overlooked aspect of this approach is that varying Re by keeping Sc fixed changes the flow kinematics. Especially, beyond the Stokes flow regime, significant changes in flow kinematics can be achieved by varying the flow rate, which may lead to different stirring conditions. Therefore, such studies should be interpreted as attempts to identify the flow kinematics that enhance mixing. A fundamentally important, yet mostly underappreciated aspect of mixing is characterization of the stirrer under fixed flow kinematics but for mixing of different species. This approach requires varying the Sc to vary the Peclet number at fixed Re. Only this latter approach should be used to assess the chaotic nature of species mixing based on the fluorescent dye experiments and numerical simulations of the species transport equations. Reasons of this claim will be substantiated in this chapter. The main objective of this chapter is to provide an introductory review on characterization of chaotic stirrers using appropriate numerical tools. The rest of this chapter is organized as follows: Section 2 reviews the

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general routes to achieve chaotic advection and gives examples of chaotic stirrers. Section 3 describes computational tools used for quantification of chaos and mixing efficiency. Finally, the chapter ends with concluding remarks. 2. Routes to Chaotic Advection Chaos was discovered and studied since almost a century ago, and has been mostly thought of in the context of turbulence. The concept of chaotic advection in laminar flows was introduced in the early 1980s by Aref [7]. Since then, a substantial number of investigators have demonstrated that chaotic advection occurs in a wide variety of laminar flows ranging from creeping flow to potential flow, and in different flow systems including unsteady two-dimensional flow, and both steady and time-dependent threedimensional flows [8–12]. The idea underlying chaotic advection is the observation that a certain regular velocity field, u(x, t ) can produce fluid pathlines, x(x o , t ) , which uniformly fill the volume in an ergodic way. The motion of passive tracers is governed by the advection equation:

x& = u(x, t), x(t = 0) = xo ,

(1)

Hereafter, bold letters represent vectors. In such velocity fields, fluid elements that are originally close to one another trace paths that diverge rapidly (exponentially fast in the ideal case), so that the material is dispersed throughout the volume very efficiently. This typically leads to significantly fast mixing. Therefore, chaotic advection in LOC devices can provide the best possibility of achieving efficient and thorough mixing of fluids. Due to the nature of the dynamical system, chaotic advection requires either time-dependent flow in simple 2-D geometries or complex 3-D geometries [9, 12]. Typically, active chaotic micro-mixers which are actuated externally by time-dependent energy sources (i.e., pressure, electric and/or magnetic fields) use time-dependent 2-D flow to achieve chaotic advection for mixing enhancement. On the other hand, passive chaotic micromixers typically use complex three-dimensional twisted conduits fabricated in various substrates such as silicon [13], polydimethylsiloxane (PDMS) [14], ceramic tape [15], or glass [13] to create 3-D steady flow velocity with a certain complexity to achieve chaotic advection. Typical examples of the aforementioned two routes to achieve chaotic advection and mixing in LOC devices are presented in the following.

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2.1. MIXING WITH CHAOTIC ADVECTION IN 2-D

Various active micromixers using 2-D time-dependent flow to achieve chaotic advection have been developed [16–19]. Since electroosmosis is very attractive for manipulating fluids in LOC devices, a chaotic electroosmotic stirrer developed by Qian and Bau [20] is described as an example to achieve chaotic advection and mixing by 2-D time-dependent electroosmotic flow. The electroosmotic chaotic stirrer developed by Qian and Bau [20] consists of a closed cavity (|x| ≤ L and |y| ≤ H) with two electrodes mounted along the walls x= ±L inducing an electric field, E, parallel to the x-axis. Four additional electrodes are embedded in the cavity’s upper and lower walls. These electrodes are not in contact with the liquid, and are used to control the ζ potential at the liquid-solid interface. The cavity contains an electrolytic solution. Various 2-D flow patterns are induced through the modulation of the zeta potentials along the top left, top right, bottom left, and bottom right walls. These flows are, however, highly regular. In the absence of diffusion, trace particles will follow the streamlines with no transport occurring transverse to the streamlines. To induce chaotic advection in the cavity, two different flow patterns, A and B, are alternated with a period of T. In other words, the flow field type A is maintained for a time interval 0< t symbol denotes averaging over the volume of a single mixing block. Based on the initial distribution of the species, a perfect mix would reach C∞ = 0.5. According to the definition in Eq. (8), a perfect mix results in M = 0. Hence, smaller values of M show better mixing. For the continuous flow mixer considered here, the mixing index varies as a function of the channel length, and it can be used as a metric to assess the mixing efficiency. Using the inverse of the mixing index (M−1) instead of itself is more preferable since M−1 → ∞, while M → 0. For example, M−1 = 20 corresponds to (1 − σ/C∞) × 100% = 95% mixing efficiency. Similarly, M−1 = 10 corresponds to 90% mixing. For a theoretical study, the dimensionless concentration is calculated from the species transport equation (4). For high Pe flows, solution of scalar transport equation is quite challenging and requires high accuracy both in time and space [19, 21]. Mixing-length (lm) and mixing-time (tm) is used to assess the mixing efficiency for continuous-flow and closed mixers, respectively. However, Pe dependence of mixing-length or -time must be investigated by varying the Schmidt number (i.e., different molecular dyes) while keeping the Reynolds number constant. The mixing process can be characterized globally by evaluating its lm – Pe behavior at fixed kinematic condition (i.e., constant Re and St). For laminar convective/diffusive transport, mixing length typically varies as lm ∝ Pe0.5. It is possible to reduce the mixing-length drastically by inducing chaotic stirring, which results in lm ∝ ln(Pe) for fully chaotic, and lm ∝ Peβ (with β < 1) for partially chaotic flows. Figure 4 depicts the dimensionless species concentration distribution in the continuous mixer when Pe=500 (a), 1,000 (b), and 2,000 (c), while the kinematic condition is fixed at St = 1/2π and Re = 0.01. Based on the spatial species concentration distribution, the mixing index, M, is then calculated using Eq. (8). Figure 5 depicts M−1 as a function of the dimensionless mixing length, lm/h, under the same kinematic condition (St = 1/2π and Re = 0.01) for Pe = 500 (rectangles), 1,000 (triangles), and 2,000 (circles). The corresponding 95%, 93% and 90% mixing efficiencies are also marked in Fig. 5. (a) (b) (c) Figure 4. Dimensionless species concentration distribution for Pe = 500 (a), 1,000 (b) and 2,000 (c) at St = 1/2π , Re = 0.01 and A = 0.8.

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−1

Figure 5. Mixing index inverse (M ) as a function of the normalized mixing length for Pe = 500, 1,000 and 2,000 at St = 1/2π, Re = 0.01, and A = 0.8.

As a succinct and clear evidence of global chaos, logarithmic relation between the mixing length (lm) and Pe should be investigated under the same kinematic condition. Figure 6 depicts the mixing length for 95%, 93%, and 90% mixing efficiency vs. ln(Pe) under the kinematic condition of St = 1/2π and Re = 0.01. The linear relationship between lm and ln(Pe) indicates fully chaotic flow in the mixer. Figure 6 can also be used to determine the length or number of mixing blocks of the mixer that is required to achieve a certain mixing efficiency. Before finishing this section, we would like to discuss the practical aspects of mixing index calculations. The method requires utilization of the species transport equation along with a flow solver, which presently exists

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Figure 6. Peclet vs. the normalized mixing length at 90%, 93%, and 95% mixing efficiencies for St = 1/2π, Re = 0.01 and A = 0.8 conditions.

in most commercial software packages. Therefore, the mixing index can be the preferred methodology to characterize the mixing efficiency. One must be careful about accuracy of the utilized numerical solver in case of long time integration errors, which have significant impacts on the results of the flow and species distribution. Although the color contour plots are often too forgiving, significant discrepancy in the M −1 values of high-order accurate solver from others is observed at high Pe values, because of the high numerical diffusion of the latter. Finally, the mixing index is relevant with the experimental observations based on mixing of fluorescent dyes. The decision for the desired M−1 value or the mixing efficiency can depend on the application. For example, certain applications may require perfect molecular diffusion for a reaction to take place. Numerical modeling of this situation could be challenging as it would require very large M −1 values, requiring very long numerical integration times and excessive number of mixing blocks for open mixers.

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4. Concluding Remarks We outlined the conditions and benefits of chaotic stirring in LOC devices. Based on Lagrangian particle tracking of passive tracers, the Poincaré sections provide qualitative detection of bad mixing zones, such as islands, and cannot differentiate the stirring performance after the Poincaré sections become featureless. When Poincaré section is featureless, FTLE should be used to quantify the chaotic strength. Strictly positive FTLE values indicate fully chaotic flow in the mixer, and the average value of the FTLE quantifies the chaotic strength. However, the computations of the Poincaré section and FTLE are very expensive since they both require accurate time integration and accurate resolution of the flow field. Alternatively, mixing index and scaling of lm as a function of Pe can be used to characterize the mixing behavior under fixed kinematic conditions by varying the Sc. Spatial distribution of species concentration can be determined either by numerically solving the species transport equation or from imaging analysis of fluorescence images obtained from experiments using confocal microscopy with dye additions. The relationship lm vs. Pe should be evaluated under fixed kinematic conditions (i.e., fixed Re, etc) to check whether the continuous-flow mixer is globally chaotic. Often lm ∝ Peβ with β < 1 is observed. Pure diffusion results in β = 1, while certain convective flows result in β = 0.5. For partially chaotic flows the value of β depends on the extent of the regular flow regions, and β → 0 as the regular flow zones diminish. For fully chaotic flows lm ∝ ln(Pe) is observed. Similarly, the logarithmic relation between the mixing time, tm and Pe should be investigated in a closed mixer at a fixed kinematic condition (i.e., fixed Re, etc.), where tm ∝ ln(Pe) indicates fully chaotic flow in closed mixers [21].

References 1. A.D. Stroock, S.K.W. Dertinger, A. Ajdari, I Mezic, H.A. Stone, G.M. Whitesides, Chaotic mixer for microchannels, Science, 295: 647–651 (2002). 2. N. Sasaki, T. Kitamori, H.B. Kim, AC electroosmotic micromixer for chemical processing in a microchannel, Lab Chip, 6: 550–554 (2004). 3. C. Simonnet, A. Groisman, Chaotic mixing in a steady flow in a microchannel, Physical Review Letters, 94(13): 134501 (2005). 4. S.H. Chang, Y.H. Cho, Static micromixers using alternating whirls and lamination, J. Micromech. Microeng., 15: 1397–1405 (2005). 5. A.P. Sudarsan and V.M. Ugaz, Fluid mixing in planar spiral microchannels, Lab Chip, 6: 74–82 (2006).

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6. H.M. Xia, C. Shu, S.Y.M. Wan, Y.T. Chew, Influence of the Reynolds number on chaotic mixing in a spatially periodic micromixer and its characterization using dynamical system techniques, J. Micromech. Microeng., 16(1): 53–61 (2006). 7. H. Aref, Stirring by chaotic advection, J. Fluid Mech., 143: 1–21 (1984). 8. H. Aref, Chaotic advection of fluid particles, Phil. Trans. R. Soc. Lond. A, 333: 273–288 (1990). 9. H. Aref, The development of chaotic advection, Phys. Fluids, 14: 1315–1325 (2002). 10. J.M. Ottino, The kinematics of mixing: stretching, chaos, and transport, Cambridge University Press, Cambridge, England (1989). 11. S. Wiggins and J.M. Ottino, Foundations of chaotic mixing, Phil Trans. Royal Soc. A, 362 (1818): 937–970 (2004). 12. M.A. Stremler, F.R. Haselton, H. Aref, Designing for chaos: applications of chaotic advection at the micro scale, Phil Trans. Royal Soc. A, 362(1818): 1019–1036 (2004). 13. R.H. Liu, M.A. Stremler, K.V. Sharp, M.G. Olsen, J.G. Santiago, R.J. Adrian, H. Aref, D.J. Beebe, A Passive three-dimensional ‘C-shape’ helical micromixer, J. Microelectromechanical Systems, 9(2): 190–198 (2000). 14. M.A. Stremler, M.G. Olsen, R.J. Adrian, H. Aref, D.J. Beebe, Chaotic mixing in microfluidic systems. Solid-state sensor and actuator workshop, Hilton Head, SC, June 4–8 (2000). 15. M. Yi, H.H. Bau, The kinematics of bend-induced mixing in microconduits. Int. J. Heat Fluid Flow, 24: 645–656 (2003). 16. N.T. Nguyen, Z.G. Wu, Micromixers – a Review, Journal of Micromechanics and Microengineering, J. Micromech. Microeng, 15(2): R1–R16 (2005). 17. S. Qian and J.F.L Duval, Mixers, In: Comprehensive Microsystems, edited by Y.B. Gianchandani, O. Tabata and H. Zappe, 2: 323–374, Elsevier (2007). 18. N.T. Nguyen, Micromixers: Fundamentals, Design and Fabrication, William Andrew Micro & Nano Technologies Series (2008). 19. D.A. Boy, F. Gibou, S. Pennathur, Simulation tools for lab on a chip research: advantages, challenges, and thoughts for the future, Lab Chip, 8: 1424–1431 (2008). 20. S. Qian, H.H. Bau, Theoretical Investigation of Electro-Osmotic Flows and Chaotic Stirring in Rectangular Cavities, App. Math. Modeling, 29: 726–753 (2005). 21. H.J. Kim, A. Beskok, Quantification of chaotic strength and mixing in a micro fluidic system, J. Micromech. Microeng., 17: 2197–2210 (2007). 22. T.J. Johnson, D. Ross, L.E. Locascio, Rapid Microfluidic Mixing, Analytical Chemistry, 74(1): 45–51 (2002). 23. A.D. Stroock, S.K.W. Dertinger, A. Ajdari, I. Mezic, H.A. Stone, G.M. Whitesides, Chaotic mixer for microchannels, Science, 295(5555): 647–651 (2002). 24. P.B. Howell, D.R. Mott, S. Fertig, C.R. Kaplan, J.P. Golden, E.S. Oran, F.S. Ligler, A microfluidic mixer with grooves placed on the top and bottom of the channel, Lab Chip, 5: 524–530 (2005).

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25. H.J. Kim and A. Beskok, Numerical Modeling of Chaotic Mixing in Electroosmotically Stirred Continuous Flow Mixers, ASME J. Heat Transfer 131(9): 092403 (2009). 26. X. Niu, Y.K. Lee, Efficient spatial-temporal chaotic mixing in microchannels, J. Micromech. Microeng., 13: 454–462 (2003). 27. J.C. Sprott, Chaos and Time-Series Analysis, Oxford University Press, Oxford, England (2003). 28. T.M. Antonsen, Z. Fan, E. Ott, E. Garcia-Lopez, The role of chaotic orbits in the determination of power spectra of passive scalars, Phys. Fluids, 8(11): 3094–3104 (1996).

AC ELECTROKINETIC FLOWS A. BESKOK

Aerospace Engineering Department Old Dominion University, Norfolk, VA 23529, USA, [email protected]

Abstract. Alternating current (AC) electrokinetic motion of colloidal particles suspended in an aqueous medium and subjected to a spatially nonuniform AC electric field are examined using a simple theoretical model that considers the relative magnitudes of dielectrophoresis, electrophoresis, AC-electroosmosis, and Brownian motion. Dominant electrokinetic forces are explained as a function of the electric field frequency, amplitude, and conductivity of the suspending medium for given material properties and geometry. Parametric experimental validations of the model are conducted utilizing interdigitated microelectrodes with polystyrene and gold particles. The theoretical model provides quantitative descriptions of AC electrokinetic transport for the given target species in a wide spectrum of electric field amplitude and frequency, and medium conductivity. The presented model, previously published in Ref. [1], can be used as an effective framework for design and optimization of AC electrokinetic devices.

1. Introduction With the advancement of microfabrication methods, AC electrokinetic techniques such as electrophoresis (EP), dielectrophoresis (DEP) and AC electroosmosis (AC-EO) have been widely investigated and utilized for separating, sorting, mixing and detection of colloidal particles and biological species on microscale devices. AC electrokinetic techniques provide a great potential for development of micro total analysis systems (μ-TAS). Since colloidal motion is mainly induced by interaction with AC electric field, manipulation of sub-micrometer scale particles without mechanical moving parts is possible, and the direction and magnitude of the colloidal motion can be controlled by adjusting the frequency and amplitude of the applied electric field. Moreover, AC electrokinetic techniques are well suited for integration with other electronic components on a single chip with small foot print area. However, AC electrokinetic manipulation of colloidal particles is generally limited by the applicable electric field conditions and relative polarizability of the suspending medium compared to that of the particles and S. Kakaç et al. (eds.), Microfluidics Based Microsystems: Fundamentals and Applications, DOI 10.1007/978-90-481-9029-4_15, © Springer Science + Business Media B.V. 2010

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electrodes. Accordingly, design and optimization process of AC electrokinetic devices require performance prediction and validation over specific operational ranges of electric field, which should be considered as a function of the electrode geometry, and electromechanical properties of the target species and suspending medium. For example, when the size and properties of the target species are fixed, DEP forces can be represented as a function of the ionic strength of media, electric field frequency and amplitude, and the electrode geometry. In order to utilize DEP for manipulating colloidal particles, magnitude of the DEP force should be large enough to dominate other forces. If this is induced using large electric fields, electrolysis of the suspending medium can occur. Relative polarizability of suspending medium can be controlled by adjusting molarity of the buffer solution to vary the direction and magnitude of DEP at certain frequency ranges. However, high conductivity media often causes undesirable electrothermal effects. It should be also noted that selection of the buffer conductivity is restrictive in the case of biological samples, since excessive osmotic stress can cause cell damage. Thus, design and development of devices for specific applications require characterization of each AC electrokinetic mechanism over the desired range of electric field strength and buffer concentration. In this chapter, we demonstrate an effective way of predicting the AC electrokinetic motion of colloidal particles in a microscale device. A modified scaling analysis is constructed by considering the relative magnitudes of AC electrokinetic motion (EP, DEP and AC-EO) and Brownian motion of colloidal particles on interdigitated microelectrodes, which have simple planar geometry and analytically obtained electric field. Dominant transport mechanisms at given electric field and material conditions are described using phase diagrams, and effects of particle’s relative polarizability and ionic concentration of buffer solution are explained. Then, the results are validated through parametric experiments for different kinds of colloidal particles (polymeric and metallic particles, and biological species) at various electric field conditions. Dominant transport mechanisms of each particle with different polarization characteristics are observed, and compared with the results of the scaling analysis. As a result, we have shown that the theoretical model can provide quantifiable information for AC electrokinetic motion of colloidal particles over broad ranges of electric field frequencies and amplitudes. 2. AC Electrokinetic Effects In the presence of non-uniform AC electric field, colloidal particles suspended in an aqueous medium experience electrokinetic forces including electrophoresis (EP), dielectrophoresis (DEP), and hydrodynamic drag force due

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to the bulk fluid motion induced by AC-electroosmosis (AC-EO) at a certain frequency range. In addition to electrical forces, the particles are also influenced by the Brownian motion. Lateral motions of colloidal particles are generally driven by interaction of these forces, and precise analysis for each transport mechanism is required for manipulation of particles in microfluidic devices. To reduce the effort involved in detailed numerical simulations and to gain understanding for the order of magnitude of each transport mechanism, we present a scaling analysis that predicts dominant forces in a microscale device based on the maximum displacement of colloidal particles on interdigitated microelectrodes. The scaling map results in prediction of the dominant transport mechanism at a given operational condition. It also enables production of phase diagrams that describe the particle motion as functions of the electric field frequency, amplitude and media conductivity. In the following, we present a simple particle displacement analysis for various AC electrokinetic effects. Assuming co-planar parallel interdigitated electrodes, the electric field between two electrodes can be assumed as halfcircular lines near the electrode surface. Various electrokinetic forces can be represented in simple analytical forms using this simplified electric field distribution. 2.1. AC ELECTROOSMOSIS

AC Electroosmosis is due to the interactions of the tangential electric field with the induced charges on each electrode, which results in electroosmotic force and fluid velocity in the horizontal direction. The AC-EO flow was previously explained in Refs. [2–4]. The tangential AC electric field produces electroosmotic fluid velocity due to the potential drop across double layer on the electrodes, which can be represented as [4] u EO =

(

)

εε 0 εε ∂ 2 Δφ D Et = − 0 Λ Δφ DL , η 4η ∂r

(1)

where ε0 and ε are the absolute permittivity and relative permittivity of the medium respectively, η is the viscosity, ΔφD and ΔφDL are the potential drop across diffuse layer and double layer respectively, and Et is the tangential electric field. The capacitance ratio Λ is given by, Λ = CS/(CS+CD), where CS is the capacitance of the Stern layer, and CD is the capacitance of the diffuse layer. CS = 0.007 F/m2 is used based on the experimental result of impedance measurements [4]. With expressions for resistance of the fluid and capacitance of the double layer, electric circuit analogy can be applied to model the double layer potential drop by [5, 6]

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Δφ DL =

V0 , 2(1 + jΩ)

(2)

where V0 is the applied voltage, j = − 1 , Ω=Λωεε0πr/2σλD, ω is the radian frequency, σ is the conductivity of the fluid, and λD is the Debye length. Then, the resultant displacement due to AC-EO motion can be expressed as [7] 1 εε V Ω2 X AC − EO = Λ 0 0 t. ηr (1 + Ω 2 ) 2 8 2

(3)

AC-EO displacement becomes zero as the non-dimensional frequency Ω goes to zero or infinity, which represents a bell shaped function with both ends approaching zero. 2.2. DIELECTROPHORESIS

Dielectrophoresis is the motion of polarizable particles that are suspended in an ionic solution and subjected to a spatially non-uniform electric field. Polarizability of particle relative to the suspending medium determines the basic direction of DEP force (positive/negative DEP), which also strongly depends on the frequency of the applied electric field. In the case of electric field with constant phase, time-averaged DEP force can be represented as [8] 2

FDEP = 2πεε 0 a 3 Re{K }∇ E ,

(4)

where a is the particle radius, E is the electric field, and K is the ClausiusMossotti (CM) factor. For homogeneous particles suspended in a medium, the CM factor is given by

ε *p − ε * , K (ε , ε ) = * ε p + 2ε * * p

*

(5)

where ε* is the complex electric permittivity of the media, which can be represented as ε* = ε − jσ/ω. Subscript p refers to the particle. The CM factor represents effective polarizability of the particle with respect to the suspending medium, which is a strong function of the applied frequency. The value of Re{K} varies between +1 and −1/2. Depending on the sign of Re{K}, particle motion is induced towards the electrode surface (positive DEP), or away from the electrodes (negative DEP). Figure 1 shows the variation of Re{K} as a function of the electric field frequency and ionic strength of suspending medium for solid spherical dielectric particles with the parameters εp = 2.55, ε = 78.5, and σp = 0.01 S/m. The sign of Re{K} is

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1 1 µS/cm 10 µS/cm 100 µS/cm 1000 µS/cm

0.8 0.6

Re(K)

0.4

+DEP

0.2 0

−DEP

− 0.2 − 0.4 102

103

104

105 106 Frequency (Hz)

107

108

Figure 1. Real part of the Clausius-Mossotti factor for a solid spherical dielectric particle at various medium conductivities (for εp = 2.55, σp = 0.01 S/m, and ε = 78.5). Switch of the sign of Re{K} indicates switch between positive and negative dielectrophoresis.

switched from positive to negative around the crossover frequency (~2 MHz) for low conductivity buffer solution cases (10−5 S/m and 10−4 S/m). However, only negative Re{K} is observed in the whole frequency range for high conductivity buffer case (10−1 S/m), which shows limitation of positive DEP by the conductivity of buffer solution. Since DEP force is proportional to the gradient of electric field, small device scale and high operational voltage are required to amplify the DEP motion of suspended particles. Due to the potential loss induced by electrode polarization, actual potential supplied to the fluid can be expressed as [6] V fluid = V0 − 2Δφ DL = V0

jΩ . 1 + jΩ

(6)

Utilizing the half circular electric field approximation (E = Vfluid /πr) and assuming force balance with Stokes drag for small particles, characteristic DEP displacement can be represented as [7] X DEP =

1 3π 2

Re{K }

a 2 εε 0 β 2V0

η

r3

2

t,

(7)

where β2 = Ω2/(1+Ω2). It can be observed that β goes to unity as Ω approaches to infinity, and thus the effect of electrode polarization can be neglected for large Ω.

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278 2.3. (AC) ELECTROPHORESIS

(AC) Electrophoresis is the motion of electrically charged particles under the influence of an AC electric field. For thin electrical double layers (a/λD  1), dynamic mobility of spherical particles can be expressed as [9]

μd =

εε 0 ς p η

⎛ ωa 2 G⎜⎜ ⎝ ν

⎞ ⎟⎟ , ⎠

(8)

where ζp is the zeta potential of the particle, ν is the kinematic viscosity, and G is a function that represents inertial effects of particle motion as a function of the Womersley number α = a ω /ν , and is given as [9] G (α 2 ) =

1 + (1 + j )α / 2 1 + (1 + j )α / 2 + j (α

2

/ 9)(3 + ( ρ

p

− ρ) / ρ )

,

(9)

where ρp and ρ are the density of the particle and medium, respectively. Electrophoretic displacement can be derived from particle velocity (uEP = μdE) as X EP =

εε 0 ς p η

⎛ ωa 2 G ⎜⎜ ⎝ ν

⎞⎛ βV0 ⎟⎟⎜ ⎠⎝ πr

⎞1 ⎟ sin(ωt ) , ⎠ω

(10)

where (βV0/πr) is an approximation for the half circular electric field with potential drop due to the electrode polarization. The maximum electrophoretic displacement can be determined based on the amplitude of the oscillatory motion as

X EP =

εε 0 ς p ⎛ βV0 ⎞ ⎛ ωa 2 ⎞ 2 ⎟ . ⎜ ⎟G ⎜ η ⎝ πr ⎠ ⎜⎝ ν ⎟⎠ ω

(11)

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2.4. BROWNIAN MOTION

Using Stokes–Einstein relation (D = kBT/6πaη), the expressions for characteristic displacements induced by random Brownian motion in one dimension is given by [7] X Brownian

⎛ k T ⎞ = ⎜⎜ B t ⎟⎟ ⎝ 3πaη ⎠

1/ 2

,

(12)

where kB is Boltzmann constant and T is the temperature. From the expression of each transport mechanism, comparisons of maximum displacements were obtained for scaling analysis. Figure 2 (left) hows the result of scaling analysis using 30 μm electrode spacing, 1 μm polystyrene particle properties, which are εp = 2.55, ρp = 1,050 kg/m3, and σp = 0.01 S/m.30 Homogeneous particle model was used with the parameters, ε = 78.5, D = 1 × 10−9 m2/s, ρ = 1,000 kg/m3, μ = 1 × 10−3 Ns/m2, V = 10 V. Relative magnitudes of characteristic particle displacement for each transport mechanism were compared, and the dominant transport mechanism with the largest displacement magnitude was predicted, as shown Fig. 2 (left). At conductivities less than 10−4 S/m (i.e. typical range of DI water), electrode polarization effects induce dominant AC-EO motion of the fluid at low frequencies (1–10 kHz). However, positive DEP starts to dominate as frequency increases, and negative DEP becomes significant after the crossover frequency (about 2 MHz). At conductivity values more than 10−2 S/m, positive DEP disappears since polarizability of the particle is less than that of medium, and the CM factor is negative over the whole frequency range. The AC-EO and negative DEP motions are relatively small at low frequencies where only Brownian motion is dominant. As frequency increases, AC-EO and negative DEP become dominant consecutively. It should be noted that the scaling map is generated to determine the dominant transport mechanisms based on the two dimensional electric field assumption. Thus, spatial variations for each transport mechanism, especially in three dimensional cases, can not be accounted precisely. However, these results are still applicable in design of more complex electrode systems since the complicated geometry of electrodes can be divided into several sub-regions with different characteristic lengths, allowing predictions of local colloidal motion. Electrokinetic manipulation of particles is not possible in some regions of the scaling maps due to electrolysis effects. We experimentally observed electrolysis at frequencies below 800 Hz and voltages above 1 V. To avoid electrode damage, experimental validations of the scaling maps described in the next section were conducted outside the electrolysis range. We also

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observed that electrothermal effects were insignificant in the ranges of experiments (~10 V). However, electrothermal effects can possibly dominate colloidal motion at higher voltage inputs, especially for cases with high conductivity buffers, since the power dissipation is directly proportional to the conductivity (W ~ σ E2). Although theoretical expressions are available, electrothermal effects are essentially related with three dimensional flow motions, and a different characteristic length scale is required to include electrothermal motions to the scaling analysis. Thus, explicit comparisons with other AC electrokinetic forces are not attempted in the presented study. 3. Experimental Validation of the Scaling Laws The theoretical results are validated through experimental observations of particle motion utilizing interdigitated microelectrodes with 30 μm spacing. Two different types of particles, 1 μm polystyrene particles (polymer), and 800 nm gold particles (metal), were tested for examining the effect of polarizability of each particle. Starting with randomly dispersed particles in initial state, steady state distribution of the particles was observed in each case after applying electric fields. The dominant transport mechanism was determined based on the particle distribution, and was compared with the scaling analysis. Properties of the particles and ionic solutions that were used in the scaling analysis are summarized in Ref. [1]. Figure 2 shows the results of scaling analysis for 1 μm polystyrene particles with experimental observations of particle motion suspended in distilled water, which has conductivity of 2.6 × 10−3 S/m. By feeding a fresh particle solution for each case, a random distribution of particles inside the fluid chamber was established in initial state. After applying 10 V peakto-peak AC electric field for 5 min at specified frequencies, steady state distribution of the particles was captured. Each test case is indicated on the phase diagram. Scaling maps are plotted in a frequency–conductivity plane to demonstrate transition of the dominant transport mechanism as a function of these two parameters. Effects of other parameters can be explained on scaling maps in different planes. We also observed voltage dependence of the dominant transport mechanism utilizing a voltage–frequency phase diagram for same buffer conductivity, and found that the transition is dependent only on the applied frequency, with the exception of low voltage regions (less than 1 V) where Brownian motion was mostly dominant. As predicted from the scaling analysis, transition of dominant transport mechanism can be seen on the experimental results, presented in Fig. 2 (right). AC-EO motion was observed at 1 kHz (case 1 ), where large amount of particles were concentrated on the center of the electrode surface, as predicted by the scaling analysis in Fig. 2. With increased frequency, the particles were forced to move towards the electrode gap and concentrated

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on edges of the electrodes by positive DEP motion. The strength of positive DEP was increased as the frequency was gradually increased up to 100 kHz (cases 2, 3 and 4). However, the DEP motion was decreased at 1 MHz (case 5 ). The increase in positive DEP till 100 kHz frequency can be explained with decrease of AC-EO motion, which competes with the positive DEP force. Since the positive DEP and AC-EO are effective in opposite directions, positive DEP increases as AC-EO decreases. In case 2, small amounts of particles were observed on the center of the electrode surface, while positive DEP motion was dominant on the electrode gap. This can be interpreted as a result of competition between the AC-EO motion of the bulk fluid and the positive DEP, where AC-EO motion is affecting the particle transport far from the electrode edges at 10 kHz frequency. Although the scaling map predicts AC-EO dominant transport of particles at 10 kHz frequency, positive DEP is effective near the electrode gap. In order to obtain more precise theoretical predictions near the region where AC-EO 8

Frequency, log(ω) (Hz)

7

1 kHz

1

100 kHz

4

1 MHz

5

100 MHz

6

negative DEP

6 positive DEP 5

Electrode surface 10 kHz

2

50 kHz

3

4 AC Electroosmosis 3 2 −5

Brownian −4 −3 −2 −1 Conductivity, log(σ) (S/m)

0

Applying AC field after sedimenting for 3 hours

Figure 2. Frequency–conductivity phase diagram for 1 μm polystyrene particles (left). Steady state distribution of polystyrene particles suspended in distilled water (2.6 × 10−3 S/m) after applying 10 V peak-to-peak AC electric field for 5 min at specified frequencies (right). For image 1 , concentrated particles on the center of electrode surface driven by AC-EO mechanism are also shown. Due to the nature of negative DEP that repels particles away from the electrode surface, the particles for case 6 were sedimented for 3 h to capture their lateral motion at the image focal plane.

and DEP are balanced, further correlations with the experimental results for AC-EO motion by deriving an empirical value of capacitance ratio, Λ, in Eq. (1) would be required. Decrease of positive DEP near the crossover

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frequency (about 2 MHz) and negative DEP motion of particles at 10 MHz are well captured by cases 5 and 6. Due to the nature of negative DEP that repels particles away from the electrode surface, particles for case 6 were sedimented for 3 h prior to the experiments, which enabled observation of lateral motions at focal plane of the image. 3

AC-EO

Voltage (V)

2.5

p-DEP

2

7

8

9

1.5

4

5

6

1

2

3

3

4 5 6 Frequency, log(w) (Hz)

1 0.5 0

2

Brownian 7

8

Figure 3. Voltage-frequency phase diagram for 800 nm gold particles (left). Steady state distribution of 800 nm gold particles suspended in 0.1 mM NaHCO3 buffer solution (1.8 × 10−3 S/m) after applying the specified AC electric field for 15 s (right).

Figure 3 shows theoretical and experimental results for 800 nm gold particles suspended in 0.1 mM NaHCO3 buffer solution. Images were captured after applying electric field at specified frequency and voltage for 15 s. Figure 3 (right) shows theoretically predicted dominant displacement map in the frequency–voltage phase plane at buffer conductivity of 1.8 × 10−3 S/m. As shown in the figure, only AC-EO and positive DEP appear as dominant transport mechanisms except in the low voltage region where Brownian motion is also dominant. Unlike the polymeric particles, polarizability variation of gold particles is negligible due to their higher conductivity (4.9 × 107 S/m) compared to that of the buffer solution. Therefore, only positive DEP force appears over 50 kHz. Figure 3 (right) shows experimental results consistent with the scaling map. At 1 kHz frequency (cases 1, 4 and 7 ), the particles were driven to the center of the electrode by AC-EO motion. The strength of the AC-EO motion was increased with increased voltage, and more particles were concentrated on the center of the electrode. For frequencies higher than 1 kHz, particles were concentrated on the edges of electrodes due to positive DEP motion. For cases 2 and 3, weak positive DEP motion was observed near the electrode gap, while Brownian

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motion was observed away from the electrodes as predicted in the phase diagram. With increased voltage, more particles were concentrated and pearl chains of particles were formed between the electrodes. 4. Conclusions A theoretical predictive tool for AC electrokinetic manipulation of micron size particles in a microfluidic device has been presented. Utilizing a scaling analysis that considers relative magnitudes of EP, DEP, AC-EO and Brownian motion, dominant transport mechanisms and their orders of magnitudes were explained over broad ranges of electric field frequency, amplitude and ionic strength of suspending medium. The resultant theoretical model was validated through parametric experimental examination of different types of colloidal particles including polymer (polystyrene), and metal (gold) particles. The AC electrokinetic motion of colloidal particles at various conditions of the electric field and suspending medium were well described in predictive manner. Quantitative information of AC electrokinetic mechanisms for target species and media over a broad range of electric field frequency and amplitude enables configuration of required electric field in early design stages, and provides an easy way to design frequency specific manipulations of various colloidal particles suspended in aqueous media without detailed numerical simulations. Therefore, the presented model can be applied in design and optimization of future AC electrokinetic devices in an effective way.

References 1. S. Park, A. Beskok, Alternating current electrokinetic motion of colloidal particles on interdigitated microelectrodes, Analytical Chemistry, 80(8): 2832– 2841 (2008). 2. N. G. Green, A. Ramos, A. Gonz´alez, H. Morgan, A. Castellanos, Fluid flow induced by nonuniform ac electric fields in electrolytes on microelectrodes. I Experimental measurements, Phys. Rev. E, 61, 4011 (2000). 3. A. Gonz´alez, A. Ramos, N. G. Green, A. Castellanos, H. Morgan, Fluid flow induced by nonuniform ac electric fields in electrolytes on microelectrodes. II A linear double layer analysis, Phys. Rev. E, 61, 4019 (2000). 4. N. G. Green, A. Ramos, A. Gonz´alez, H. Morgan, A. Castellanos, Fluid flow induced by nonuniform ac electric fields in electrolytes on microelectrodes. III Observations of streamlines and numerical simulation, Phys. Rev. E, 66, 026305 (2002). 5. A. Ramos, H. Morgan, N. G. Green, A. Castellanos, AC electric field induced fluid flow in microelectrodes, J. Colloid Interface Sci. 217, 420 (1999).

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6. H. Morgan, N. G. Green, AC Electrokinetics: colloids and nanoparticles; Research Studies Press: Hertfordshire, (2003). 7. A. Castellanos, A. Ramos, A. Gonz´alez, N. G. Green, H. Morgan, Electrohydrodynamics and dielectrophoresis in Microsystems: Scaling laws, J. Phys. D: Appl. Phys. 36, 2584 (2003). 8. T. B. Jones, Electromechanics of Particles, Cambridge University Press: Cambridge (1995). 9. R. W. O’Brien, Electroacoustic equations for a colloidal suspension, J. Fluid Mech., 190, 71 (1988). 10. N. G. Green, H. Morgan, Dielectrophoresis of submicrometer latex spheres. 1. Experimental results, J. Phys. Chem. B, 103 (1), 41–50 (1999).

SCALING FUNDAMENTALS AND APPLICATIONS OF DIGITAL MICROFLUIDIC MICROSYSTEMS R.B. FAIR

Department of Electrical and Computer Engineering, Duke University, Durham, NC 27708, USA, [email protected]

Abstract. With the first experimental demonstration of droplet flow on an electrowetting-on-dielectric (EWD) array platform in 2000, there has been significant interest in droplet actuation for lab-on-a-chip applications. A hydrodynamic scaling model of droplet actuation in a EWD actuator is presented that takes into account the effects of contact angle hysteresis, drag from the filler fluid, drag from the solid walls, and change in the actuation force while a droplet traverses a neighboring electrode. Based on this model, it is shown that scaling models of droplet splitting, actuation, and liquid dispensing all show a similar scaling dependence on [t/εr(d/L)]1/2, where t is insulator thickness and d/L is the aspect ratio of the device. It is also determined that reliable operation of a EWD actuator is possible as long as the device is operated within the limits of the Lippmann–Young equation. Also discussed are fluidic operations possible with digital microfluidics. Significant advances have been made in chip technology that allow for users to access digital microfluidic chips and to program these chips to perform numerous operations and applications on a common array of electrodes. Whereas in the past, microfluidic devices have been application specific, lacking reconfigurability and programmability, today’s digital microfluidic chips enable versatile, reconfigurable chip architectures that are capable of accommodating and adapting to multiple applications on the same platform.

1. Introduction Electrowetting-on-dielectric (EWD) microfluidics is based on the actuation of droplet volumes up to several microliters using the principle of modulating the interfacial tension between a liquid and an electrode coated with a dielectric layer [1]. An electric field established in the dielectric layer creates an imbalance of interfacial tension if the electric field is applied to only one portion of the droplet, which forces the droplet to move [2]. Droplets are usually sandwiched between two parallel plates – the bottom S. Kakaç et al. (eds.), Microfluidics Based Microsystems: Fundamentals and Applications, DOI 10.1007/978-90-481-9029-4_16, © Springer Science + Business Media B.V. 2010

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being the chip surface, which houses an addressable electrode array, and the top surface being either a continuous ground plate or a passive top plate (the nature of the top plate is determined by the chip’s characteristics). Figure 1 diagrams this setup. The chip surface is coated with an insulating layer of Paralyene –C (~800 nm), and both the top and bottom surfaces are covered in a Teflon-AF thin film (~60 nm) to ensure a continuous hydrophobic platform necessary for smooth droplet actuation. A spacer separates the top and bottom plates, resulting in a fixed gap height. The gap is usually flooded with silicon oil which acts as a filler fluid, preventing droplet evaporation and reducing surface contamination [2]. Other insulators have also been used in EWD devices, such as silicon dioxide with Teflon [4, 5] and Teflon alone [6]. NOT TO SCALE

Top-plate (ground) Glass (0.7 mm) ITO (100 nm) Teflon AF (60 nm)

Fluid Layer Teflon AF (60 nm) Parylene C (800 nm) Cr (100 nm) Glass (1.1 mm)

Bottom-plate (control)

Figure 1. Side-view of digital microfluidic platform with a conductive glass top plate (left). A diagram of materials and construction of the actuator is shown (right). By adding a conductive top plate and adding individually addressed buried electrodes in the bottom plate, the droplet can be actuated from one electrode position to the next by the application of voltage.

The basic EWD device is based on charge-control manipulation at the solution/insulator interface of discrete droplets by applying voltage to control electrodes. The device exhibits bilateral transport, uses gate electrodes for charge-controlled transport, has a threshold voltage, and is a square-law device in the relation between droplet velocity and gate actuation voltage. Thus, the EWD device is analogous to the metal-oxide-semiconductor (MOS) field-effect transistor (FET), not only as a charge-controlled device, but also as a universal switching element [3]. Liquid volumes that can be actuated fall in the range of a few microliters and less. Whereas early demonstrations have been made with droplets between 100 nl and 2 µl, there is interest in scaling down to picoliters and below. The EWD parameters that must be considered in scaling actuator dimensions include: (1) threshold voltage for droplet actuation, (2) droplet splitting voltage, (3) droplet dispensing voltage from on-chip reservoirs, (4)

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voltage dependence of droplet velocity, and (5) droplet mixing times. To address the scaling issues of these device parameters requires an integrated analytical model for the fluidic functions of droplets placed between parallel plates in a EWD actuator. A hydrodynamic model of droplet actuation was constructed in a systematic manner that includes the effects of contact angle hysteresis, drag from the filler fluid, drag from the solid walls, and changes in the actuation force while a droplet traverses one electrode to the next. From this model, we have developed scaling rules for EWD parameters. This model is then applied to EWD actuator scaling. In addition, limits on applied actuator voltages are developed for reliable operation based on conditions for contact-angle saturation. 2. EWD Actuator Scaling Model The driving force of droplet transport is due to a change in surface tension when an electric potential is applied between a droplet and an electrode coated with an insulator of thickness t. When a voltage, V, is applied the charges on the surface of the insulator modify the surface tension between the droplet and the insulator. Then, the resulting change in contact angle of the droplet is described by the Lippmann–Young equation:

cos θ(V) = cos θ(0) +

εrεoV2 2tγ lg

(1)

where ε o (8.85 × 10−12 F/m) is the permittivity of vacuum, ε r is the dielectric constant of the insulator layer, V is the applied voltage, θ(0) is the non-actuated contact angle, θ(V) is the droplet contact angle when voltage V is applied, where γlg is the liquid-filler medium interfacial tension. Based on a model of the force balance on the contact line of a droplet and the Lippmann–Young equation, the velocity of a droplet undergoing EWD actuation has been derived, as shown in Eq. (1) [7].

εrεoV2 sin φ { cos α − γ lg sin α [sin θ(V)+ sin θ(0)]} 2t U= μ d 12μ o +2C v d L L d

(2)

where t is the dielectric thickness, α is the contact angle hysteresis, d is the gap of the actuator, L is the electrode pitch, φ is the advancement angle of the droplet, V is the applied voltage, θ(0) is the non-actuated contact angle,

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and θ(V) is the droplet contact angle when voltage V is applied, and VT is the threshold voltage for droplet actuation. The first term in the denominator is due to drag from the filler medium (oil or air), and the second term is due to drag on the droplet by the two opposing plates in the actuator. The velocity model of Eq. (2) is similar to the simplified model of Baird, which does not take into consideration drag from the filler medium or contact line resistance [8]. It is revealed in Eq. (2) that the velocity is proportional to the square of the applied voltage, which agrees with previous observations. Equation (2) also predicts that the droplet velocity will increase with the actuator aspect ratio, d/L, if the viscous drag term dominates over the filler medium drag. This follows since as the gap d increases, the drag on the droplet from the plate surfaces decreases. Such a dependence of droplet velocity on gap height in an air medium has been experimentally observed [9]. 2.1. THRESHOLD VOLTAGE SCALING

We have investigated the way in which VT scales with the physical dimensions of the EWD actuator and with the medium surrounding the droplet (oil or air). We have also explored the upper range of applied voltages and find that reliable actuator operation can only occur of the applied voltage remains below the contact-angle saturation voltage of the droplet. Other fluidic operations whose scaling behavior has been studied include droplet dispensing, splitting, and mixing. The threshold voltage for droplet actuation, VT, occurs when V = VT and U = 0 in Eq. (2). Thus, at the threshold of droplet actuation: VT = {2tγlg/εrεo [tanα(sinθ(VT) + sinθ(0)]}1/2

(3)

If the insulator is a combination of two dielectric layers of thickness t1 and t2 with relative dielectric constant ε1 and ε2 respectively, then t/εr = t1/ε1 + t2/ε2

(4)

Equation (2) can now be written as: U = sinφ εo cosα [V2 − VT2] 2t/εr [12µod/L + 2CvµdL/d]

(5)

With regard to scaling VT for a given filler medium, the dominant variables are insulator thickness and relative dielectric constant. Equation

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100 Oil Data: (parylene C/Teflon):

90

- this study - Pollack

80 (VT) (V)

70 60

Air

50

Oil Air Data: - Pollack - Cho - Moon - Cooney

40 30 20 10 0

0

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 [t/εr]1/2 (µm1/2)

Figure 2. Threshold voltage scaling with insulator thickness (t/εr)1/2 for water droplets in silicone oil and air filler media.

(3) is plotted in Fig. 2 for water droplets in silicone oil. We have used γlg (oil) = 47 mN/m, θ(VT) = 104o, θ(0) = 125o, and α = 2–4o based on OCT measurements of moving droplets [10]. Threshold voltage data are included for actuators fabricated with parylene C insulators of different thicknesses (0.5, 0.8, 1, and 2 µm) with a thin Teflon overcoat. Reasonable agreement is achieved with experimental results. For droplet actuation in an air medium, we have included data in Fig. 2 from a number of sources [11–14]. Equation (3) is plotted in Fig. 2 for γlg (air) = 72.8 mN/m, θ(VT) = 95o, θ(0) = 110o, and α = 9o. Reasonable agreement is achieved with experimental results. 2.2. SCALING DROPLET SPLITTING

Perhaps the simplest fluidic operations in a EWD device are the splitting of a droplet and the merging of two droplets into one. The minimum splitting arrangement involves three serial electrodes [11]. Splitting occurs when the two outer electrodes are turned on and the contact angles θb2 are reduced, resulting in an increase in the radius of curvature, r2. With the inner electrode off, the droplet expands to wet the outer two electrodes. As a result the meniscus over the inner electrode contracts to maintain a constant volume (Fig. 3a). Thus, the splitting process is underway as the liquid forms a neck

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with radius R1. In general, the hydrophilic forces induced by the two outer electrodes stretch the droplet while the hydrophobic forces in the center pinch off the liquid into two daughter droplets [15]. Section B-B’ B R1 P2

A

b1

P1

R2

A’

B’

r1

d

(a)

(b)

Section A-A’ d

r2 on

b2

off

on

(c) Figure 3. Droplet configuration for splitting (Cho et al. [11]).

A static criterion for breaking the neck in Fig. 3a is [16]: 1/R1 = 1/R2 – (cos θb2 – cos θb1)/d

(6)

The symbols are indicated in Fig. 3. According to Eq. (6), necking and splitting are facilitated when the gap height, d, is made smaller or the volume of the droplet is increased. If contact angle hysteresis is included, the condition for splitting in Eq. (6) becomes: 1/R1 = 1/R2 – cosα εrεo[V2 − VT2]/(2dtγlg)

(7)

Generalizing splitting to occur over N electrodes (necking occurs over N′ ≥ 1 electrodes, where N = N′ + 2), the minimum voltage required for splitting is approximated by using Ren’s relation for R1 [17]: V2 − VT2 ≈ 4γlg/εo[t/εr(d/L)] [1 − 1/(N′2+1)]

(8)

It is assumed that cos α = 1. It can be seen that the static splitting voltage depends on N′ and scales with [t/εr(d/L)]1/2.

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2.3. COMBINED SCALING EFFECTS

It has been shown that static models of droplet splitting, protrusion, and dispensing all show a similar dependence on [t/εr(d/L)]1/2 [7]. As a result, curves for splitting and dispensing with N = 3 electrodes are plotted on the same axes in Fig. 4a, b for actuation in silicone oil and in air respectively. Also plotted is EWD actuator threshold voltage versus [t/εr(d/L)]1/2 for d/L = 1 and the optimum mixing condition. It can be seen that all of the important fluidic operations can be scaled. Constant voltage scaling with fixed VT can occur by maintaining constant insulator thickness, t, and d/L. However, the question remains regarding the maximum actuation voltages that can be applied for reliable actuator operation. Instabilities in threshold voltage have been associated with contact angle saturation, insulator charging, and dielectric breakdown [14, 18, 19]. Thus scaling to assure reliable operation is now considered. Optimum Mixing

0 0

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 [t/εr(d/L)]1/2 (µm1/2)

(a)

N= 3 ing en s

70 60

60 ng N= 3

50 30 20

50

VT

40 30

litti

40

20 10

10 0

90 80

Dis p

70

Sp

ing en s Di sp

N= 3

20 10

10 0

50 30

Sp

30 20

60 40

l i tt i ng

40

80

70 VT

50

90

80

VT(V) for d/L=1

60

90 VT(V) for d/L=1

(V2-VT2)1/2 (V)

80

(V2-VT2)1/2 (V)

90 70

Optimum Mixing

100 N= 3

100

0 0

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 [t/εr(d/L)]1/2 (µm1/2)

(b)

Figure 4. Superimposed scaling of droplet splitting, dispensing, protrusion, threshold voltage and mixing in a EWD actuator in an oil filler medium (left) and air (right). (Adapted from [7]).

2.4. LIMITS ON ACTUATOR VOLTAGES

Experiments show that the Lippmann–Young equation (Eq. (1)) is valid for lower voltages, but beyond a critical voltage the contact angle reaches a lower limit, contrary to the prediction of Eq. (1). This phenomenon is known as contact angle saturation [20]. Thus for electrode voltages above the voltage at which contact angle saturation occurs, the scaling results presented here are no longer valid. While there have been numerous proposals regarding the origins of contact angle saturation, it still is not certain which effect prevails [18]. However, it is clear that the associated mechanism depends on the dielectric material used to insulate the buried electrodes of a EWD actuator and its thickness.

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The work of Berry et al. and others has suggested that increasing the applied voltage until contact angle saturation occurs was damaging to the insulator [21, 22]. Berry et al. later proposed that for a composite insulator consisting of an amorphous fluoropolymer coating of thickness t1 on an insulator of thickness t2, charge trapping occurs during contact angle saturation [23]. The onset of charge trapping was proposed to occur when the effective dielectric strength of the fluoropolymer layer, D1, is exceeded. The threshold voltage for this condition is given by the expression: Vtc = ε1D1t/εr = D1[ t1+ t2 (ε1/ε2)]

(9)

where ε1 is the dielectric constant of the amorphous fluoropolymer, and ε2 is the dielectric constant of the underlying insulator. For early actuators fabricated in our lab with composite dielectrics of 0.8 µm thick parylene C and 60 nm Teflon AF, it was observed that an actuator’s threshold voltage exhibited a time-dependent increase for applied electrode voltages of 60–100 V [14]. However, Eq. (9) predicts that insulator charging at V > 60 Vdc would occur in Pollack’s device at Vtc = 14.1 V. This value of charging voltage falls well below the observed threshold voltages reported by Pollack. From the standpoint of electrowetting contact angle saturation, the Lippmann–Young equation (Eq. (1) above) is valid up to V = Vsat at contact angle saturation. Assuming a composite insulator with a fluoropolymer layer over an underlying oxide layer, then at contact angle saturation Eq. (1) can be rewritten as Vsat = {2γlg/εoε1[t1 + t2(ε1/ε2)][cosθ(Vsat) − cosθ(0)]}1/2 200

Saturation Voltage (V)

180 160 140

Air medium

120 100

(10)

Data: (air medium) - Cooney (Tef./parylene) - Welters (Tef./parylene) - Park (cytop/parylene) - Papathanasiou (SiO2) Oil medium - Baviere (Tef./nitride) - Moon (Tef./SiO2) - Moon (Tef./BST) - Quinn (Teflon)

80

Data: (oil medium) - Srinivasan (Tef./parylene) - This study (Tef./parylene)

60 40 20 0

0

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 [t/εr]1/2 (µm1/2)

Figure 5. Calculated and measured contact angle saturation vs. insulator thickness (t/εr)1/2 for water droplets in air and silicone oil media.

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Calculated and measured contact angle saturation vs. insulator thickness (t/εr)1/2 for water droplets in air and silicone oil media are shown above in Fig. 5. It can be seen that the saturation voltage is essentially independent of the filler medium (silicone oil with γlg(oil) = 47 mN/m and air with γlg(air) = 72.8 mN/m), and essentially one curve represents Vsat vs [t/εr]1/2 for a variety of insulator systems. It can be seen above in Fig. 2 that an EWD actuator operating with a silicone oil filler medium has a lower VT for any given value of [t/εr]1/2. Since similar values of Vsat occur in both systems, an air filler medium will afford a smaller reliable operating voltage range than an oil system. 2.5. SECTION SUMMARY

In summary, it has been shown that static models of droplet splitting and liquid dispensing all show a similar dependence on [t/εr(d/L)]1/2. Scaling reduces the amount of linear displacement to dispense a droplet. Thus, the model shows that as long as t/εr(d/L) is held constant while L is decreased, the same number of dispensing electrodes required is fixed for constant (V2 − VT2)1/2. Therefore, scaling to smaller droplet volumes is favorable for droplet pinchoff with a correspondingly smaller linear displacement of liquid from the reservoir. Based on numerous studies reported in the literature, we conclude that reliable operation of a EWD actuator is possible as long as the device is operated within the limits of the Lippmann–Young equation. The upper limit on applied voltage, Vsat, corresponds to contact-angle saturation. For both silicone oil and air media, the values of Vsat vs. (t/εr)1/2 are essentially the same. The minimum 3-electrode splitting voltages as a function of aspect ratio d/L < 1 for an oil medium are less than Vsat. However, it is likely that conditions for uniform droplet splitting may require voltages that exceed Vsat. For an air medium the minimum voltage for 3-electrode droplet splitting exceeds Vsat for d/L ≥ 0.4. This observation implies that reliable splitting in air places tighter limits on the actuator aspect ratio. Similar conclusions also apply to droplet dispensing. 3. Applications Investigators have conducted extensive research on the basic principles and operations underlying the implementation of electrowetting-based digital microfluidic systems. The result is a substantial “microfluidic toolkit”. In biomedical applications it is required to transport biological liquids and beads. The transport of non-biological electrolytes using electrowetting has been demonstrated both in air [24] and in other immiscible media such as silicone oil [25]. And transport of polystyrene beads in solution [10] and

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magnetic beads [26] has been demonstrated. On the contrary, the transport of fluids containing proteins, such as enzyme-laden reagents and human physiological fluids is not as straightforward. This is because most proteins tend to adsorb irreversibly to hydrophobic surfaces, and contaminate them. In addition to contamination, protein adsorption can also render the surface permanently hydrophilic [27]. This is detrimental to transport, since electrowetting works on the principle of modifying the wettability of a hydrophobic surface, unless such contamination is intended for a particular application [28]. Examples of tools in the digital microfluidic toolkit will be reviewed. 3.1. DIGITAL MICROFLUIDIC TOOLKIT

Fluidic I/O: Loading samples and reagents on chip requires an interface between the microfluidic device and the outside world. Strategies for introducing samples and reagents onto a microfluidic chip are usually not discussed at length by workers in the field. Typically droplets are pipetted onto EWD chips and then the top plate is applied to close the system [14, 29]. The key is to provide a continuous-supply external source that keeps the on-chip reservoirs full. On-chip storage and dispensing: Reservoirs can be created on EWD devices in the form of large electrode areas that allow liquid droplet access and egress [10, 29]. Liquids from the I/O ports are stored in reservoirs. The basic lab-on-a-chip should have a minimum of three reservoirs – one for sample loading, one for the reagent, and one for collecting waste droplets, but this depends on the application. A fourth reservoir might be needed for a calibrating solution. Each reservoir should have independent control to allow either dispensing of droplets or their collection. Droplet dispensing refers to the process of aliquoting a larger volume of liquid into smaller unit droplets for manipulation on the electrowetting system. Droplet generation is the most critical component of an electrowetting-based lab-on-a-chip, because it represents the world-to-chip interface. Controlled droplet dispensing on chip can occur by extruding a liquid finger from the reservoir through activation of adjacent serial electrodes [17, 24, 33]. Mixing: Mixing of analytes and reagents in microfluidic devices is a critical step in building a lab-on-a-chip system [4, 41, 42]. Mixing in these systems can either be used for pre-processing, sample dilution, or for reactions between samples and reagents in particular ratios. The ability to mix liquids rapidly while utilizing minimum area greatly improves the throughput of such systems. However, as microfluidic devices are approaching the sub nano-liter regime, reduced volume flow rates and very low Reynolds numbers make mixing such liquids difficult to achieve in reasonable time scales. In an electrowetting-based digital microfluidic device, for example, typical

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times to perform elemental fluidic operations can be compared to passive mixing solely by diffusion of the contents of two coalesced droplets. Droplet splitting and merging: Perhaps the simplest fluidic operations in a EWD device are the splitting of a droplet and the merging of two droplets into one. For splitting a droplet three electrodes are used as described by Cho et al. [11]. During splitting the outer two electrodes are turned on and the contact angles are reduced, resulting in an increase in the radii of curvature. With the inner electrode off, the droplet expands to wet the outer two electrodes. Thus, the splitting process is underway as the liquid forms a neck. In general, the hydrophilic forces induced by the two outer electrodes stretch the droplet while the hydrophobic forces in the center pinch off the liquid into two daughter droplets [15]. Sample dilution and purification: In EWD devices, dilution has been investigated using a binary interpolating mixing algorithm and architecture [17, 43, 44]. Sample purification has been investigated on EWD devices for the specific application of Matrix-Assisted Laser Desorption/Ionization Mass Spectrometry (MALDI-MS) for protein analysis [5]. Sample preparation in EWD devices with a silicone oil medium requires an alternative method to sample drying. One method that has been investigated is the use of magnetic beads with attached analytes or antibodies localized onto the top plate or confined in solution by an external magnet. The beads then are washed with droplets transported to the bead site. This method has been successfully demonstrated in a DNA sequencing application and will be described. Sample washing methods are described. Molecular separation: When mass-limited samples are used in biochemical analysis, it is often required to isolate components that produce a signal of interest so that component can be further processed by amplification, modified, or extracted for identification. Such processes require initial separation followed by fractionation and collection. To date, there have been no reports of the full integration of electrophoresis and electrowetting. However, two papers have demonstrated droplet-based sample loading into a capillary electrophoresis tube [30, 31]. Itegration would require a digitalto-analog (D/A) interface from the EWD device, where a sample containing DNA, for example, would be presented to the input well of a capillary electrophoresis device for sample injection and plug focusing. lity to manipulate magnetic microspheres in solution on a EWD device will expand the variety of tasks that can be performed if the microspheres are used as analyte immobilization surfaces. Because the microspheres can be transported in solution and immobilized by a magnetic field, the use of microspheres on-chip will not alter the reconfigurability or reusability of the chip. The retention of 8 μm diameter magnetic microspheres during droplet splitting has been demonstrated on a digital microfluidic platform through 2,000 wash steps.

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3.2. ARCHITECTURE

The digital microfluidic architecture shown below in Fig. 6 [32] capitalizes on the flexibility of a unit flow grid array. At any given time, the array can be partitioned into “cells” that perform fluidic functions, such as storage, mixing, or transport. If the array is actuated by a clock that can change the voltage at each electrode on the array in one clock cycle, then the architecture has the potential for dynamically reconfiguring the functional cells at least once per clock cycle. Thus, once the fluidic function defined by a cell is completed, the cell electrode voltages can be reconfigured for the next function. Digital microfluidic architecture is under software-driven electronic control, eliminating the need for mechanical tubes, pumps, and valves that are required for continuous-flow systems. The compatibility of each chemical substance with the electro-wetting platform must be determined initially. Compatibility issues include the following: (1) Does the liquid’s viscosity and surface tension allow for droplet dispensing and transport by electrowetting? (2) Will the contents of the droplet foul the hydrophobic surfaces of the chip? (3) In systems with a silicone oil medium, will the chemicals in the droplet cross the droplet/oil interface, thus reducing the content in the droplet? (4) What type of detection method is suitable?

Figure 6. Two-dimensional electrowetting electrode array used in digital microfluidic architecture.

3.3. APPLICATIONS

Demonstrations of numerous applications of digital microfluidics have been made in the past five years. Some examples are presented below.

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3.3.1. Colorimetric Assays On-chip colorimetric assays for determining the concentrations of target analytes is a natural application for digital microfluidics [10, 33, 34]. The specific focus of work in this area has been on multiplexed assays, where multiple analytes can be measured in a single sample. The on-chip process steps include the following: (1) pre-diluted sample and reagent loading into on-chip reservoirs, (2) droplet dispensing of analyte solutions and reagents, (3) droplet transport, (4) mixing of analyte solutions.

Figure 7. Optical absorbance measurement instrumentation used to monitor color change due to colorimetric reactions on chip.

Srinivasan et al. have demonstrated a colorimetric enzyme-kinetic method based on the Trinder’s reaction used for the determination of glucose concentration [33]. At the end of the mixing phase, the absorbance is measured for at least 30 s, using a 545 nm LED-photodiode setup. The mixed droplet is held stationary by electrowetting forces during the absorbance measurement step, depicted in Fig. 7. 3.3.2. Chemiluminescent Assays Chemilumescent detection has been shown to be compatible with the digital microfluidic platform [35] and with diagnostic applications as well as sequencing DNA by synthesis [36]. In general, the on-chip chemistry must result in optical signal generation in the vicinity of a photodetector. Work in this area has been reported by Luan et al. with an integrated optical sensor based upon the heterogeneous integration of an InGaAs-based thin film photodetector with a digital microfluidic system [35].

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DNA sequencing-by-synthesis methods involve enzymatic extension by polymerase through the iterative addition of labeled nucleotides, often in an array format. The cascade begins with the addition of a known nucleotide to the DNA (or RNA) strand of interest. This reaction is carried out by DNA Polymerase. Upon nucleotide incorporation, pyrophosphate (PPi) is released. This pyrophosphate is converted to ATP by the enzyme ATP sulfurylase. The ATP then provides energy for the enzyme lucerifase to oxidize luciferin. One of the byproducts of this final oxidation reaction is light at approximately 560 nm. This sequence is shown in Fig. 8. The light can be easily detected by a photodiode, photomultiplier tube, or a charge-coupled device (CCD). Since the order in which the nucleotide addition occurs is known, one can determine the sequence of the unknown strand by formation of its complimentary strand. The entire pyrosequencing cascade takes about 3–4 s from start to finish per nucleotide added. Pyrosequencing of DNA has been performed on a digital microfluidic platform [36]. The chip was covered with a transparent top plate and filled with oil to create a microfluidic chamber in which droplets were programmably manipulated (dispensed, transported, merged, split) using electrical fields. Using a 211 bp DNA fragment derived from C. albicans genomic DNA, single stranded templates were prepared and attached to 2.8 µm magnetic beads. Results of a 20 bp read are shown in Fig. 9.

Figure 8. Illustration of solid-phase pyrosequencing. After incorporation of a nucleotide (in this case dATP), a washing step is used to remove the excess substrate.

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Figure 9. On-chip pyrosequencing results showing 17-bp sequencing of a 211-bp long C. albicans DNA template.

3.3.3. DNA Hybridization Testing There is significant interest in developing microfluidic systems that can function as portable, chip-scale DNA diagnostic sensors. The testing procedure involves isolating parasitic DNA from blood, cleaning the DNA, and detecting. This protocol is illustrated below in Fig. 10 [37]. The main fluidic functions required to achieve the detection of DNA are given in the flowchart. Using malaria detection as an example, the procedure starts having as input a 1 µl volume of blood. The first step is the sample preparation. This consists of detaching the infected cells, breaking their cellular membrane and extracting the DNA. As the amount of DNA is too scarce for successful detection to be considered, DNA must be replicated by using an amplification technique. Finally, a detection step is integrated in order to determine if an infection with one of the malaria parasites is present in the organism [37]. Magnetic bead separation implemented on a digital microfluidic platform is the first step in separating infected cells from other cells in whole blood [37, 38]. Magnetic beads can be made to selectively tag infected cells using antibody–antigen bonding. By locating the droplet containing beads and other cells over a magnet, separation can be achieved by washing a 2x droplet through the bead droplet. After 5–10 wash droplets pass, the bead droplet is relatively clean, only containing tagged cells on beads. This method does not result in bead loss [36]. Chemical cell lysis of infected cells is carried out to extract parasitic DNA. Droplets containing lysing agents are dispensed from their reservoirs, and are mixed with the bead droplets. After cell lysis, DNA strands need to be extracted from a mixture of the cell contents suspended in a droplet. To facilitate DNA extraction, the droplet is first heated to 95°C to convert the double stranded DNA to single stranded DNA. The droplet is then mixed

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with a droplet containing complementary DNA strands attached to magnetic beads. Magnetic bead separation is then repeated as described previously. After DNA extraction from the lysed cells, the droplet is heated to unbind the DNA from the magnetic beads. This droplet undergoes further magnetic bead separation, to separate the magnetic beads from the DNA strands. The resulting droplet, concentrated with DNA strands then undergoes PCR [39].

Figure 10. Malaria chip flowchart.

Dhar et al. [37] have pointed out that several detection schemes are possible for the malaria chip. A popular technique is flow cytometry, where sample processing is performed on-chip, and the chip is then used in conjunction with a commercial cytrometry device. An advantage of this technique is that it is well-established, but a major drawback is that the detector is rather large and not on-chip. An on-chip detection option is an integrated thin-film semiconductor light source, waveguide and detector capable of measuring changes in transmission. Or, instead of integrating a light source, such a scheme could measure changes in the chemiluminescence of the sample, as shown by L. Luan et al. [35]. Surface plasmon resonance (SPR) may also be a viable detection scheme. However, no one has shown that SPR can be integrated on a digital microfluidic chip [40]. 4. Conclusions Investigators working in the field of digital microfluidics have conducted extensive research on the basic principles and operations underlying the implementation of electrowetting-based microfluidic systems. The result is a substantial “microfluidic toolkit” of automated droplet operations, a sizable

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catalog of compatible reagents, and demonstrations of important chemical and biological assays. However, the lack of good integrated on-chip sensing methods and on-chip sample preparation currently are the biggest impediments to broad commercial acceptability of microfluidic technologies, including digital microfluidics. Other issues include system integration and interfacing to other laboratory formats and devices, packaging, reagent storage, and maintaining temperature control of the chip during field operation. The number and variety of analyses being performed on chip has increased along with the need to perform multiple-sample manipulations. It is often desirable to isolate components that produce a signal of interest, so that they can be detected. Currently, mass separation methods, such as capillary electrophoresis, are not an established part of the digital microfluidic toolkit, and integration of separation methods presents a significant challenge. Nevertheless, we will see the first introduction of commercial digital microfluidic chips into certain laboratory applications in the near future.

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MICROFLUIDIC LAB-ON-A-CHIP PLATFORMS: REQUIREMENTS, CHARACTERISTICS AND APPLICATIONS D. MARK1, S. HAEBERLE1,2, G. ROTH1,2, F. VON STETTEN1,2, AND R. ZENGERLE1,2 1

HSG-IMIT – Institut für Mikro- und Informationstechnik, WilhelmSchickard-Straße 10, 78052 Villingen-Schwenningen, Germany 2 Laboratory for MEMS Applications, Department of Microsystems Engineering (IMTEK), University of Freiburg, Georges-KoehlerAllee 106, 79110 Freiburg, Germany, [email protected]

Abstract. This review summarizes recent developments in microfluidic platform approaches. In contrast to isolated application-specific solutions, a microfluidic platform provides a set of fluidic unit operations, which are designed for easy combination within a well-defined fabrication technology. This allows the implementation of different application-specific (bio-) chemical processes, automated by microfluidic process integration [1]. A brief introduction into technical advances, major market segments and promising applications is followed by a detailed characterization of different microfluidic platforms, comprising a short definition, the functional principle, microfluidic unit operations, application examples as well as strengths and limitations. The microfluidic platforms in focus are lateral flow tests, linear actuated devices, pressure driven laminar flow, microfluidic large scale integration, segmented flow microfluidics, centrifugal microfluidics, electrokinetics, electrowetting, surface acoustic waves, and systems for massively parallel analysis. The review concludes with the attempt to provide a selection scheme for microfluidic platforms which is based on their characteristics according to key requirements of different applications and market segments. Applied selection criteria comprise portability, costs of instrument and disposable, sample throughput, number of parameters per sample, reagent consumption, precision, diversity of microfluidic unit operations and the flexibility in programming different liquid handling protocols. 1. Introduction The increasing number of publications [2] and patents [3] related to microfluidics reveals how relevant the technology has become during the last years, also from a commercial perspective. Consequently, microfluidics has S. Kakaç et al. (eds.), Microfluidics Based Microsystems: Fundamentals and Applications, DOI 10.1007/978-90-481-9029-4_17, © Springer Science + Business Media B.V. 2010

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established itself in academia and industry as a toolbox for the development of new methods and products in life sciences. However, the public visibility of microfluidic products is, with few exceptions, still very low. The question is: will microfluidics remain a toy for academic and industrial research or will it finally make the transition to an end-user product? Looking into the past, the first microfluidic technology was developed in the early 1950s when efforts to dispense small amounts of liquids in the nanoliter and sub-nanoliter range were made, providing the basics of today’s ink-jet technology [4]. In terms of fluid propulsion within microchannels with sub-millimeter cross sections, the year 1979 set a milestone when a miniaturized gas chromatograph (GC) was realized on a silicon (Si) wafer [5]. The first high-pressure liquid chromatography (HPLC) column microfluidic device, fabricated using Si-Pyrex technology, was published in 1990 by Manz et al. [6]. By the end of the 1980s and the beginning of the 1990s, several microfluidic structures, such as microvalves [7] and micropumps [8, 9] have been realized by silicon micromachining, providing the basis for automation of complex liquid handling protocols by microfluidic integration [10, 11]. This was the advent of the newly emerging field of “micro total analysis systems” (µTAS [12]), also called “lab-on-a-chip” [13]. At the same time, much simpler yet very successful microfluidic analysis systems based on wettable fleeces emerged: First very simple “dipsticks” for e.g. pH measurement based on a single fleece paved the way for more complex “test strips” that have been sold as “lateral-flow tests” in the late 1980s [14]. Examples that are still on the market today are test strips for pregnancy [15], drug abuse [16–18], cardiac markers [19] and also upcoming bio-warfare protection [20]. Among the devices that completely automated a biochemical analysis by microfluidic integration into one miniature piece of hardware, the test strips became the first devices that obtained a remarkable market share and still remain one of the few microfluidic systems which is sold in high numbers. Until today, most of the revenue in the field of lab-on-a-chip is created on a business-to-business, but not on a business-to-consumer basis [21], as the vast majority of research in the field only approaches the stage of demonstrators and is not followed by the development of products for endusers. Among the hurdles for market entry are high initial investments and running fabrication costs [22]. Furthermore, the multitude of individual labon-a-chip solutions developed so far cannot compete with the flexibility of state of the art liquid handling approaches, e.g. with pipetting robots. Instead of the time-consuming and expensive developments of applicationspecific microfluidic solutions, we propose to base microfluidic developments on a microfluidic platform approach, where a combinable set of liquid handling steps together with a suitable fabrication technology enable the flexible and affordable implementation of biochemical protocols in a market-relevant

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framework. Hence, the intention of this review is to provide an overview on lab-on-a-chip applications that are based on a microfluidic platform approach. According to their actuation scheme, we subdivide microfluidic platforms into five groups, namely: capillary, pressure driven, centrifugal, electrokinetic and acoustic systems, as depicted in Fig. 1. After providing a short general introduction to unique properties, requirements, and applications for microfludic platforms, the review focusses on a detailed discussion of the microfluidic platforms listed in Fig. 1. First, the defintion and the general principle of the microfluidic plaform is presented. Afterwards, already implemented unit operations as well as application examples are briefly discussed for each platform. This is summed up by highlighting the strengths and limitations of each platform, mainly with respect to the selection criteria. The review is concluded by an attemp to provide a selection scheme for microfluidic platforms which is based on platform characteristics and application requirements. This review contains examples of microfluidic platforms for lab-on-a-chip applications which were selected as fitting to our platform definition and no comprehensiveness is claimed. The review should, however, provide the reader with some orientation in the field and the ability to select platforms with appropriate characteristics on the basis of application-specific requirements.

Figure 1. Microfluidic platforms classified according to actuation method.

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2. The Framework for Microfluidic Platforms: Unique Properties, Requirements and Applications 2.1. MICROFLUIDICS AS AN ENABLING TECHNOLOGY: FROM CLASSICAL LIQUID HANDLING TO SINGLE-CELL HANDLING

A number of classical, macroscopic liquid handling systems for perfoming analytical and diagnostic assays have been in use for many decades. Examples are petri dishes, culture bottles and microtitre plates (also called microplates). Petri dishes have been first described in 1887 [23] and culture bottles [24] are in use since around 1850. Since roughly 60 years ago, they are manufactured as plastic disposables. In comparison, microtiter plates are quite “modern,” having first been described in 1951 [25]. Based on these standards, highly automated high throughput solutions have been developed within the last decades (“pipetting robots”) and are the current “gold standard” in the market. They offer a huge potential for many applications since they are very flexible as well as freely programmable. Microfluidic platforms have to test themselves against these established systems and offer new opportunities. Expectations quoted in this context are [26]: • Higher sensitivity • Lower cost per test • Shorter time-to-result • Less laboratory space consumption Additionally, scaling effects lead to new phenomena and permit entirely new applications that are not accessible to classical liquid handling platforms, such as: 6 • High grade of parallelization (up to around 10 ) • Laminar flow with liquid gradients down to single-cell length scales • High-speed serial processing (at single cell level) Structures of the size of a cell or smaller In the following, the effects and phenomena leading to the abovementioned expectations and the potential for new applications will be outlined briefly. It is obvious that the amount of reagent consumption can be decreased significantly by scaling down the assay volume. Additionally, by reducing the footprint of each individual test, a higher degree of parallelization can be achieved in a limited laboratory space. A prime example for microfluidic tests with minimal reagent consumption are parallel reactions in hundreds of thousands individual wells with picoliter-volumes [27], which took genome sequencing to a new level [28] hardly achievable by classical liquid handling platforms. With decreasing length scales, capillary forces become increasingly dominant over volume forces. This permits purely passive liquid actuation

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used in the popular capillary test strips. Another effect is the onset of laminar flow at low Reynolds numbers in small channels. This enables the creation of well-defined and stable liquid–liquid interfaces down to cellular dimensions. Therefore, large concentration gradients can be applied and the effects monitored at the single cell level [29] (Fig. 2). In summary, laminar flow conditions and controlled diffusion enable temporally and spatially highly resolved reactions with little reagent consumption. A different paradigm using the possibility of controlling interfaces in microfluidic applications is the concept of droplet-based microfluidics, also called “digital microfluidics” [30]. The on-demand generation of liquid micro-cavities either in air or a second immiscible liquid enables the manipulation of small quantities of reagents down to single cells at high throughput [31]. Control and manipulation of such droplets can be achieved by another favorable aspect of the high surface-to-volume ratio in microfluidics: the possibility to control the liquid flow by electrically induced forces or electrowetting [32]. Having the huge background of theoretical and practical knowledge in electronics, this is obviously a desirable property. Additional helpful properties of small assay volumes are fast thermal relaxation and low power consumption for liquid manipulation and thermal control. This can speed up assays that require thermocycling, such as PCR, which was realized in numerous microfluidic applications [33].

Figure 2. Concept of differential manipulation in a single bovine capillary endothelial cell using multiple laminar flows. (a, b), Chip layout: 300 × 50 µm channels are used to create laminar interfaces between liquids from different inlets. (c) Fluorescence image of a cell locally exposed to red and green fluorophores in a laminar flow. (d) Migration of fluorophores over time (scale bars, 25 µm). This shows the high potential for accurate spatial control and separation of liquids achievable in microfluidic laminar flows. (Adapted by permission from Macmillan Publishers, Ltd: Nature [29], copyright 2001.)

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This short summary shows that there is the potential for many novel applications and improvements over the state-of-the-art within the abovementioned criteria of sensitivity, cost, time, and size. However, despite a myriad of publications about microfluidic components, principles and applications, very few successful products with a relevant market share have emerged from this field so far. In the next chapter, we will outline probable reasons and present emerging paradigm changes for the future research in microfluidics. 2.2. THE NEED FOR THE MICROFLUIDIC PLATFORM APPROACH

Definition of a Microfluidic Platform: A microfluidic platform provides a set of fluidic unit operations, which are designed for easy combination within a well-defined fabrication technology. A microfluidic platform allows the implementation of different application-specific (bio-)chemical processes, automated by microfluidic process integration. In the last two decades, thousands of researchers spent a huge amount of time to develop micropumps [34–37], microvalves [38], micromixers [39, 40], and microfluidic liquid handling devices in general. However, a consistent fabrication and interfacing technology as one prerequisite for the efficient development of lab-on-a-chip systems is very often still missing. This missing link can only be closed by establishing a microfluidic platform approach which allows the fast and easy implementation of analytical assays based on common building blocks. The idea follows the tremendous impact of platforms in the ASIC industry in microelectronics, where validated elements and processes enabled faster design and cheaper fabrication of electronic circuitries. Conveying this to the microfluidic platform approach, a set of validated microfluidic elements is required, each able to perform a certain basic liquid handling step or unit operation. Such basic unit operations are building blocks of laboratory protocols and comprise fluid transport, fluid metering, fluid mixing, valving, separation or concentration of molecules or particles (see Table 1) and others. Every microfluidic platform should offer an adequate number of microfluidic unit operations that can be easily combined to build application-specific microfluidic systems.

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TABLE 1. Common features of microfluidic platforms.

Microfluidic unit operations • Fluid transport • Fluid metering • Fluid valving • Fluid mixing • Separation • Accumulation • Reagent storage • Incubation, etc.

Fabrication technology • Validated manufacturing technology for the whole set of fluidic unit operations (prototyping and mass fabrication) • Seamless integration of different elements … preferable in a monolithic way … or by a well defined easy packaging technique

This concept, however, does not imply that every microfluidic platform needs to provide a complete set of all the unit operations listed in Table 1. It is much more important that the different elements are connectable, ideally in a monolithically integrated way or at least by a well defined, ready-to-use interconnection and packaging process. Therefore at least one validated fabrication technology is required to realize complete systems from the individual elements within a microfluidic platform. 2.3. MARKET REQUIREMENTS AND PLATFORM SELECTION CRITERIA

The requirements on microfluidic platforms differ largely between different market segments. Following a roadmap on microfluidics for life sciences [41], the four key market segments for microfluidic lab-on-a-chip applications are, according to their market size: in vitro diagnostics, drug discovery, biotechnology and ecology. The largest market segment, in vitro diagnostics, can be subdivided into point-of-care testing (e.g. for self-testing in diabetes monitoring or cardiac marker testing in emergency medicine) and central laboratory based testing (e.g. core laboratory in a hospital). Especially the self- and point-of-care testing segments offer huge potential for microfluidics, since portability is an important requirement. Drug discovery in the pharmaceutical industry is the second largest segment. Here, enormous effort is undertaken to identify new promising drug candidates in so called high-throughput screening (HTS) or massively parallel analysis [42]. After screening promising candidates, so-called hits have to be validated and characterized (hit characterization). Also cell-

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based assays received increasing interest over the last years [43, 44]. These assays often require the handling of single cells, which becomes possible using microfluidic approaches. This market segment requires high sample throughput and low costs per test. The third segment is the biotech market with the fermentation-based production (e.g. for biopharmaceuticals or food). This industry shows a great demand for on-line process monitoring and analyses in the field of process development. Here, low sample volumes and programmability are important factors. Ecology is another market segment, comprising the field of agriculturaland water-analysis, either as spot tests or as continuous monitoring. Included are also applications related to homeland security, e.g. the detection of agents that pose biological threats. This market benefits from portable systems with preferably multi-parameter capabilities. These diverse fields of applications are associated with a number of analytical and diagnostic tasks. This outlines the field for the microfluidic technology, which has to measure itself against the state-of-the-art in performance and costs. Table 2 gives an exemplary overview on some important requirements of the different market segments and application examples, with respect to the following selection criteria: • Portability: miniaturized, handheld device with low energy consumption • Sample throughput: number of samples/assays per day • Cost of instrument: investment costs of the instrument (“reader”) • Cost of disposables: defining the costs per assay (together with reagent consumption) • Number of parameters per sample: number of different parameters to be analyzed per sample • Low reagent consumption: amount of sample and / or reagents required per assay • Diversity of unit operations: the variety of laboratory operations that can be realized • Precision: the volume and time resolution that is possible • Programmability: the flexibility to assay adaptations • These criteria will be discussed for each of the platforms described in this review.

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TABLE 2. Market segments for microfluidic lab-on-a-chip applications and their requirements*.

2.4. REQUIREMENTS FROM APPLICATIONS AND ASSAYS ON LIQUID HANDLING PLATFORMS

Here, a short overview of the fields of applications that are typically addressed by microfluidic platforms is presented. A first field of application is biotransformation, the breakdown and generation of molecules and products by the help of enzymes, bacteria, or eucariotic cells cultures. This comprises fermentation, the break down and re-assembly of molecules (e.g fermentation of sugar to alcohol), and (bio)synthesis the build-up of complex molecules (e.g. antibiotics, insulin, interferon, steroids). Especially in the field of process development challenges are to handle a large number of different liquids under controlled conditions such as temperature or pH, in combination with precise liquid control down to nL or even pL volumes. Some examples of microfluidic liquid handling platforms are given for fermentation in micro bioreactors [45–52], the biosynthesis of radiopharmaceuticals [53], and antibody screening, phage- and ribosome-display technologies [54, 55].

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Another major field of application is analytics. The analysed molecule (analyte) can be from a variety of biomolecules, including proteins and nucleic acids. Here, the main requirements are effective mixing strategies and highly precise liquid handling for quantitative results. Also, automation and portability combined with a large set of unit operations for the implementation of complex analytical protocols are required. As an emerging field, cellular assays are the most challenging format, since the cells have to be constantly kept in an adequate surrounding to maintain their viability and activity (control of pH, O2, CO2, nutrition, etc.). Cellular tests useful to assess the effect of new pharmaceutical entities at different dosing concentrations on toxicity, mutagenity, bioavailability and unwanted side effects. The most exciting prospect is the establishment of assays with single-cell analyses [56, 57]. Requirements on cellular assays include high-througput solutions as well as a low reagent consumption per test. After this short overview, the next chapter will summarize the liquid handling challenges that arise from the different liquids associated with these fields of applications. 2.5. REQUIREMENTS FROM (BIO)CHEMISTRY ON LIQUID HANDLING PLATFORMS

A great challenge of biochemical applications for microfluidics is the handling of a large variation of liquids and their respective properties such as surface tension, contact angle on the substrate material (non-Newtonian) viscosity and so on. Also, an inter-sample variation e.g. due to physiological differences between patients has to be managed by a robust microfluidic system. In the following, a short summary of typical sample materials and their interactions with the microfludic substrate is given. Also, strategies to prevent unfavorable interactions are outlined. In general, the microfluidic substrates should be inert against the expected sample and assay reagents which might comprise organic or inorganic solvents or extreme pH values [58]. Likewise, the sample must not be affected by the microfluidic substrate in any way that could influence the analytical result. For example, nucleic acids are critical molecules because of their negative charge and tendency to adhere to charged surfaces such as metal oxides. Similar problems occur with proteins or peptides which exist in a variety of electrical charges, molecular sizes, and physical properties. In addition to possible adsorbtion onto the surfaces, their catalytic (enzymatic) activities can be influenced by the substrate [59–62]. A general countermeasure against the interaction of biomolecules and microfluidic substrates is the blocking of substrates with another suitable biomolecule which is added in excess. For instance bovine serum albumine (BSA) adsorbs to nearly any surface thus passivating it [63, 64]. Another significant challenge

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in microfluidic production technology is to retain the activity of pre-stored proteins. Thermal bonding [65, 66] or UV curing steps might destroy the proteins and render the assay useless. Experience shows that this set of challenges needs to be considered at the very beginning of a fluidic design, since the listed problems can jeopardize the functionality of the whole system if addressed too late. 3. Lateral Flow Tests Definition of lateral flow tests: In lateral flow tests, also known as test strips (e.g. pregnancy test strip), the liquids are driven by capillary forces. Liquid movement is controlled by the wettability and feature size of the porous or microstructured substrate. All required chemicals are pre-stored within the strip. The presence of an analyte is typically visualized by a colored line. 3.1. GENERAL PRINCIPLE

The first immunoassay performed in a capillary driven system was reported in 1978 [67]. Based on this technique, the commonly known “over-thecounter pregnancy test” was introduced into the market in the middle of the 80’s. Today, this microfluidic platform is commonly designated as a “lateral flow test (LAT)” [14]. Other terms are “test strip”, “immunochromatographic strip”, “immunocapillary tests” or “sol particle immunoassay (SPIA)” [68]. Astonishingly, hardly any publications from a microfluidic point of view or in terns of material classification exist, and apparently many “company secrets” are kept unpublished [69]. The “standard LAT” consists of an inlet port and a detection window (Fig. 3a). The core comprises several wettable materials providing all biochemicals for the test and enough capillary capacity to wick the sample through the whole strip. The sample is introduced into the device through the inlet into a sample pad (Fig. 3b), which holds back contaminations and dust. Through capillary action, the sample is transported into the conjugate pad, where antibodies conjugated onto a signal-generating particle are rehydrated and bind to the antigens in the sample (Fig. 3c). This binding reaction continues as the sample flows in the incubation and detection pad. On the test line a second type of antibody catches the particles coated with antigens, while a third type of antibodies catch particles which did not bind to an analyte on the control line. The control line shows a successfully processed test while the detection line shows the presence or absence of a specific analyte (Fig. 3d). Typically the result becomes visible after 2–15 min.

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Over the last decades, LAT transformed from a simply constructed device into a more and more sophisticated high-tech platform with internal calibrations and quantitative readout by a hand-held reader (Fig. 4) [70].

Figure 3. Schematic design of a lateral flow test (According to [69]): (a) sample pad (sample inlet and filtering), conjugate pad (reactive agents and detection molecules), incubation and detection zone with test and control lines (analyte detection and functionality test) and final absorbent pad (liquid actuation). (b) Start of assay by adding liquid sample. (c) Antibodies conjugated to colored nanoparticles bind the antigen. (d) Particles with antigens bind to test line (positive result), particles w/o antigens bind to the control line (proof of validity).

3.2. UNIT OPERATIONS

The different pads in the test strip represent different functions such as loading, reagent prestorage, reaction, detection, absorbtion and liquid actuation. The characteristic unit operation of LATs is the passive liquid transport via capillary forces, acting in the capillaries of a fleece, a microstructured surface, or a single capillary. The absorption volume of an absorption pad defines how much sample is wicked through the strip and provides metering of the sample [69]. The sample pad usually consists of cellulose or cross-linked silica and is used for filtering of particles and cells as well as separating the analyte from undesired or interfering molecules, which is absorbed in the pad [71]. The conjugation pad is made of cross-linked silica and is used as dry-reagent storage for antibodies specific to the antigen conjugated to the signal generating particle. The conjugates are typically colored or fluorescent nanoparticles with sizes up to 800 nm, which unobstructedly flow through the fleeces together with the sample. Most often colloidal gold [20] or latex

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[72] and more rarely carbon, selenium, quantum dots, or liposomes [73] are the choice of nanoparticles. The length, material (mainly nitro-cellulose) and pore-size (50 nm to 12 µm, depending on the applied nanoparticles) of the detection and incubation pad define the incubation time [69]. The detection and enrichment of the conjugates is achieved on the antibody-bearing lines. Analyte detection is performed on the test line and proof of assay validity on the control line. The readout is typically done by naked eye for absence (1 colored line) or presence (2 colored lines) of a minimum analyte amount. A readout with a reader enables quantitative analyte detection [70, 74]. For multi-analyte detection [69] or semi-quantitative setups [75] several test lines are applied. Within the last years, new LAT designs have been developed in combination with the device-based readout in handheld systems. Here a complex capillary channel network provides the liquid actuation (Fig. 4). Antibodies conjugated to nanoparticles or special enzymes are prestored at the inlet. The incubation time is defined by the filling time of the capillary network. Typically, readout is done quantitatively by fluorescence or electrochemical detection. The time-to-result is usually several seconds. Blood glucose or coagulation monitoring are the most common applications for such quantitative readouts [70]. To accommodate aging, batch-to-batch variations and sample differences and also to achieve higher precision and yield of the assay, several internal controls and calibrations are automatically performed during analysis by the readout device.

Figure 4. LAT for blood coagulation with handheld read-out according to Cosmi et al. [70, 74]. (Image (a) courtesy of Roche Diagnostics.) (a) Loading of blood, (b) the blood flows from the inlet into the fluidic network rehydrating the coagulation chemistry. The “drop detect” electrodes detect whether blood is applied and measure the incubation times. Several capillaries are filled and the filling is monitored with according electrodes. A Ag/AgCl electrode is used as standard electrode for calibration and analysis. Finally the analyte gets quantified by optical or electrochemical detection.

3.3. APPLICATION EXAMPLES

Lateral flow tests were among the first successfully commercialized microfluidic products. A huge amount of assays has been developed on the capillary test strip platform during the past 30 years [76]. Today, they serve a wide

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field of applications, including health biomarkes (pregnancy [14, 77], heart attack [71], blood glucose [78], metabolic disorders [79]), small molecules (drug abuse [80], toxins [81], antibiotics [82]), infectious agents (anthrax [83], salmonella [84], viruses [85]), pre-amplified DNA [86] and RNA applications [83], and even whole bacteria [87]. Some of the more recent designs and publications show even the detection of DNA [85] without the need of amplification by PCR, which would open yet another vast field of new applications. First trials for massively parallel screening in combination with microarrays were made in lateral flow tests [71, 83]. 3.4. STRENGTHS AND LIMITATIONS

The fact that 6 billion glucose test strips were sold in 2007 [88] already indicates that the LAT may be seen as a gold-standard microfluidic platform in terms of cost, handling simplicity, robustness, market presence and the number of implemented lab-on-a-chip applications [69]. The amount of sample and reagent consumption are quite low, and the concept is mainly used for qualitative or semi-quantitative assays. Especially the complete disposable test carriers with direct visual readout, easy handling, and a time-to-result between seconds and several minutes are predestined for untrained users. The simplicity of the test strip is also its major drawback. Assay protocols within capillary driven systems follow a fixed process scheme with a limited number of unit operations, imprinted in the microfluidic channel design itself. Highly precise liquid handling and metering is also extremely challenging [69]. The depenency of the purely capillary liquid actuation on the sample properties can also be a major problem, leading to false positive or negative results [15] or decreased precision. New designs allow applications with quantitative analysis, but require a readout device (mainly handheld) [70, 74]. High-throughput or screening applications are possible, but quite difficult to implement. In total, the lateral flow test is a well established platform with a large but limited field of applications and consequently a benchmark for the home-care and IVD sector in terms of cost per assay and simplicity. 4. Linear Actuated Devices Definition of linear actuated devices: Linear actuated devices control liquid movement by mechanical displacement (e.g. a plunger). Liquid control is mostly limited to a one-dimensional liquid flow (no branches or alternative paths) with the corresponding possibilities and limitations to assay implementation. The degree of integration is very high, with liquid calibrants and reaction buffers pre-stored in pouches.

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4.1. GENERAL PRINCIPLE

One of the first examples of a linear actuated device was the i-STAT® for quantitative bedside testing, introduced in the early 1990s by Abbott Point of Care Inc., NJ, USA. It relied on active liquid actuation by displacement [89]. Compared to lateral flow tests, this principle was one step ahead in result quantification and possible applications, but also in complexity of the processing device and disposable. The characteristic actuation principle of the linear actuated platform is the mechanical linear propulsion of liquids with no branching. Normally, the liquid actuation is performed by a plunger which presses on a flexible pouch, displacing its content. Another common attribute is the prestorage of all required reagents (liquid and dry) on the disposable test carrier (cartridge). Systems based on this platform thus offer fully integrated sample-to-result processing in relatively short time. 4.2. UNIT OPERATIONS

Basically, the linear actuated platform relies on only two unit operations: Liquid transport and reagent storage. Liquid transport is achieved by mechanical displacement (e.g. with a plunger). By pressing on flexible compartments of the disposable, the liquid can be transported between reservoirs [89]. Alternatively, a weakly bonded connection to an adjacent reservoir can be disrupted, or the connection to a neighbouring cavity selectively blocked [90]. Liquid reagent storage can easily be implemented by integrating pouches into the cartridge. Mixing can also be realized on the linear actuated platform by moving liquids between neighbouring reservoirs [90]. 4.3. APPLICATION EXAMPLES

One example of a linear actuated device is of course the previously mentioned i-STAT® analyzer from Abbott Point-of-Care [91]. Using different disposable cartridges, several blood parameters (blood gases, electrolytes, coagulation, cardiac markers, and hematology) can be determined with the same portable handheld analyzer for automated sample processing and read-out (Fig. 5a). Since only the disposable polymer cartridge is contaminated with the blood sample and thus has to be disposed after performing the diagnostic assay, the analyzer device itself is reusable. Typical response times of the system are in the order of a few minutes. The system features an integrated calibration solution that is prestored in the disposable. The analysis process takes only a few steps: As depicted in Fig. 5, the blood sample (a few drops) is filled into the cartridge by capillary

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forces (b) and placed into the analyzer (c). First, the calibrant solution is released and provides the baseline for an array of thin-film electrodes integrated in the disposable. Then the sample is pushed into the measuring chamber and displaces the calibrant. Thereby, the blood parameters which can be determined by the sensor array of the specific disposable are measured and presented at the integrated display of the handheld analyzer. Several studies showed good agreement between laboratory results and this POCsystem [89, 92, 93]. A second example is the Lab-in-a-tube (Liat™) analyzer from IQuum [94]. This bench-top device with disposable test tubes contains all necessary reagents for amplification-based nucleic acid tests. It integrates sample preparation, amplification and detection and is a fully integrated sample-toresult platform with response times between 30 and 60 min. Handling of the platform requires only a few steps: The sample (e.g. 10 µL of whole blood) is collected in the collection tube that is integrated into the disposable, the barcode on the disposable is scanned, and the tube is then inserted into the analyzer. The disposable features compartmentalized chambers in a tube which contain different reagents and can be connected via peelable seals (Fig. 6). Liquid control is performed by actuators that compress the compartments, displacing the liquid into adjacent chambers [90]. Sample preparation includes a nucleic acid purification step: Magnetic beads serve as solid nucleic acid binding phase and are controlled by a built-in magnet. For nucleic acid amplification, compartments can be heated and the liquid is transferred between two different temperature zones thus cycling the sample. The system is capable of real-time fluorescence readout.

Figure 5. Images and handling procedure of the i-STAT® analyzer. (a) Photograph depicting the portable i-STAT® analyzer for clinical blood tests [91]. (b) Depending on the blood parameters to be measured, a certain disposable cartridge is filled with blood by capillary forces from the finger tip. (c) Afterwards loaded into the analyzer for assay processing and readout. (Images courtesy of Abbott Point of Care.)

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Figure 6. Functional principle and exemplary processing steps in a nucleic acid test in the Lab-in-a-tube analyzer according to Chen et al. [90]. The disposable contains pouches with reagents (light blue) which are actuated by plungers while clamps open and close fluidic connections to adjacent pouches. (a) Sample is inserted (red). (b) Sample is mixed with prestored chemicals containing magnetic capture-beads. (c) Unwanted sample components are moved to a waste reservoir while the capture-beads are held in place by a magnet. (d–e) Further processing steps allow sequential release of additional (washing)-buffers and heating steps (red block) for lysis and thermocycling demands. The system allows optical readout by a photometer (PM).

4.4. STRENGTHS AND LIMITATIONS

The presented commercially available examples show that automation and time-reduction by microfluidic systems with active processing devices can indeed be achieved in a market-relevant context. The potential of the linear actuated device platform certainly lies in its simplicity and the ability for long-term liquid reagent storage. The presented application examples are portable and show a high degree of assay integration, requiring no external sample pre- or post processing steps. Typical liquid (sample) volumes handled on the platform are in the range of 10–100 µL, which is adequate for pointof-care diagnostic applications (capillary blood from finger tip). While disposables can generally be mass-produced, these can become somewhat expensive due to the integration of sensors (i-STAT®) and liquid reagents (iSTAT® and Liat™). Time-to-result varies between minutes and approximately 1 h, depending on the assay. The advantage of full integration with pre-stored reagents comes at the price of an imprinted protocol that cannot be changed for a specific test carrier. The number of unit operations is somewhat limited, in particular separation, switching, and aliquoting as well as precise metering are difficult to realize. This hinders the implementation of more complex assays and laboratory protocols in linear actuated systems, such as integrated genotyping with a plurality of genetic markers or multiparameter assays.

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5. Pressure Driven Laminar Flow Definition of pressure driven laminar flow: The laminar flow platform comprises liquid handling and (bio-) chemical assay principles, based on the stable hydrodynamic conditions in pressure driven laminar flows through microchannels. The samples are processed by injecting them into the chip inlets using external pumps or pressure sources, either batch-wise or in a continuous mode. 5.1. GENERAL PRINCIPLE

As mentioned earlier, liquid flow in microchannels is typically strictly laminar over a wide range of flow rates and channel dimensions. Pressure driven laminar flow offers several opportunities for assay implementation: − − −

Predictable velocity profiles Controllable diffusion mixing Stable phase arrangements, e.g. in co-flowing streams

These advantages have been utilized for several lab-on-a-chip applications in the past. Probably the oldest example is the so-called “hydrodynamic focusing” technology [95], used to align cells in continuous flow for analysis and sorting in flow cytometry [96, 97]. Today, many technologies still use laminar flow effects for particle counting [98] or separation [99–103]. However, pressure driven laminar flow can also be utilized to implement other (bio-)chemical assays for lab-on-a-chip applications as described within this section. Especially nucleic acid based diagnostic systems received a great deal of interest in the last decade, since the first introduction of a combined microfluidic PCR and capillary electrophoresis in 1996 by Woolley et al. [104]. 5.2. UNIT OPERATIONS

The basic unit operation on the pressure driven laminar flow platform is the contacting of at least two liquid streams at a microfluidic channel junction (see Fig. 7). This leads to controlled diffusional mixing at the phase interface, e.g. for initiation of a (bio-) chemical reaction [105]. It can also be applied for the lateral focusing of micro-objects like particles or cells in the channel [95]. The required “flow focusing” channel network consists of one central and two symmetric side channels, connected at a junction to form a common outlet channel. By varying the ratio of the flow rates, the lateral width of the central streamline within the common outlet channel can be adjusted very accurately. Consequently, micro-objects suspended in the liquid flowing

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through the central channel are focused and aligned to this well-defined streamline position. If the available duration for a (bio-) chemical reaction needs to be limited, the contacted liquid streams can again be separated further downstream as shown in [105]. For the separation of micro-objects like living cell or micro-beads from a liquid stream, several technologies have been presented relying either on geometrical barriers [105], or magnetic forces [106, 107]. Sorting of microobjects, i.e. the selective separation based on size or any other feature, was implemented using magnetic forces [108, 109], acoustic principles [110], dielectrophoresis [111], or hydrodynamic principles [99–101, 112] on the pressure driven laminar flow platform. The common principle of all these technologies is a force acting selectively on the suspended micro-objects (particles or cells), while the liquid stream stays more or less unaffected.

Figure 7. Contacting on the laminar flow platform. Three different liquid streams are symmetrically contacted at an intersection point. This microfluidic structure is also referred to as “flow focusing structure” [95].

A great number of valving principles exists on the pressure driven laminar flow platform, summarized in a review by Oh and Ahn [38]. Active as well as passive solutions have been presented. However, no standards have emerged so far, so the choice and implementation of valves remains a difficulty on this platform. A possible approach is to transfer the valving functionality off-chip [113], thus decreasing the complexity and cost of the disposable. 5.3. APPLICATION EXAMPLES

One recently established technology on the pressure driven laminar flow platform is the so called “phase transfer magnetophoresis (PTM)” [106]. Magnetic microparticles flowing through a microfluidic channel network are attracted by a rotating off-chip permanent magnet, and can consequently be transferred between different co-flowing liquid streams. As a first application, DNA purification with magnetic beads was successfully

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demonstrated with a yield of approximately 25% [106] (first prototype). Thus, this system provides continuous DNA-extraction capability which could serve as an automated sample preparation step for flow-through PCR, in e.g. bioprocess monitoring (of fermentation) applications. Other microfluidic applications based on the manipulation of magnetic microparticles with external permanent magnets have been shown. One example is the free-flow magnetophoresis [108, 109], which can be utilized to sort magnetic microparticles by size. A large number of microfluidically automated components for batchwise nucleic acid diagnostics based on pressure driven laminar flow chips have been published and summed up in several reviews [33, 114, 115]. However, a totally integrated system remains a challenge, since the integration of sample preparation proved difficult [115], although it seems to be in reach, as the next two examples show. Easley et al. showed integrated DNA purification, PCR, electrophoretic separation and detection of pathogens in less than 30 min [116]. The assay was performed on a pressure driven four layer glass/PDMS chip with elastomeric valves. Temperature cycling for PCR was achieved by IR radiation. Only the sample lysis step was not integrated in the microfluidic chip. Detection of Bacillus anthracis from infected mice and Bordetella pertussis from a clinical sample was successfully demonstrated. An integrated µTAS system for the detection of bacteria including lysis, DNA purification, PCR and fluorescence readout has also been published recently [113]. A microfluidic plastic chip with integrated porous polymer monoliths and silica particles for lysis and nucleic acid isolation was used for detection (Fig. 8). A custom-made base device provided liquid actuation and off-chip valving by stopping liquid flow from the exits of the chip, utilizing the incompressibility of liquids. Detection of 1.25 × 106 cells of B. subtilis was demonstrated with all assay steps performed on-chip. 5.4. STRENGTHS AND LIMITATIONS

One strength of the platform lies in its potential for continuous processing of samples. Continuous sample processing is of utmost importance for online monitoring of clinical parameters, process control in fermentation, water quality control or cell sorting. Typically one or a few parameters are monitored. The application examples showed one system capable of continuous DNA extraction as well as other implementations that integrated complex batchwise protocols such as nucleic acid analysis. The platform is in principle compatible to polymer mass-production technologies such as injection molding, enabling inexpensive disposable microfluidic chips. A difficulty of the platform is the necessity to connect the pressure source to the (disposable) chip, which decreases the portability and requires additional

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manual steps. Another challenge is Taylor dispersion [117] of streamwise dispersed samples which can make it hard to accurately track analyte concentrations. Unit operations on the platform are optimized for mixing and separation processes and somewhat limited in other aspects such as aliquoting.

Eluate Propulsion Buffer

SPE Column

PCR Mix Mixer 2 Reservoir 2 PCR Channel Air In

Waste 1 Mixer 1 Exhaust GuSCN Sample In Sample Reservoir Reservoir 1 Mixer 1 Detection Well

Mixer 2 Exhaust Elution Buffer

Waste 2 70% EtOH

Figure 8. Chip for integrated detection of bacteria including lysis, DNA isolation and PCR published by Sauer-Budge et al. [113].

6. Microfluidic Large Scale Integration Definition of microfluidic large scale integration: Microfluidic large scale integration describes a microfluidic channel circuitry with chip-integrated valves based on a flexible membrane between a liquid-guiding and a pneumatic control-channel layer. The valves are closed (opened) by applying an overpressure (underpressure) on the controlchannel, leading to deflection (withdrawal) of the membrane into the liquid-guiding channel.

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6.1. GENERAL PRINCIPLE

The microfluidic large scale integration platform (LSI) arose in the year 1993 [118]. At the same time, a novel fabrication technology for microfluidic channels, called soft lithography made its appearance. Soft lithography is based on the use of elastomeric stamps, molds and conformable photomasks to fabricate and replicate microstructures [119]. Using this technology, the monolithic fabrication of all necessary fluidic components within one single elastomer material (Polydimethylsiloxane, PDMS) became possible, similar to the silicon-based technology in microelectronics. PDMS, also known as silicone elastomer, is an inexpensive material offering several advantages compared to silicon or glass. It is a cheap, rubber-like elastomer with good optical transparency and biocompatibility. A detailed review on the use of PDMS for different fields of applications can be found in [120]. The strength of the technology became obvious, when Stephen Quake’s group expanded the technology towards the multilayer soft-lithography process, MSL [121]. With this technology, several layers of PDMS can be hermetically bonded on top of each other resulting in a monolithic, multilayer PDMS structure. This enables the fabrication of microfluidic chips with densely integrated microvalves, pumps and other functional elements. Today, this technology is pushed forward by the company Fluidigm Corp., CA, USA. 6.2. UNIT OPERATIONS

Based on the high elasticity of PDMS, the elementary microfluidic unit operation is a valve which is typically made of a planar glass substrate and two layers of PDMS on top of each other. One of the two elastomer layer contains the fluidic ducts while the other elastomer layer features pneumatic control channels. To realize a microfluidic valve, a pneumatic control channel crosses a fluidic duct as depicted in Fig. 9a. A pressure p applied to the control channel squeezes the elastomer into the lower layer, where it blocks the liquid flow. Because of the small size of this valve in the order of 100 × 100 µm2, a single integrated fluidic circuit can accommodate thousands of valves. Comparable to developments in microelectronics, this approach is called “microfluidic large scale integration” (LSI) [122]. The valve technology called NanoFlex™ (Fluidigm) is the core technology of the complete platform. For example, by placing two such valves at the two arms of a T-shaped channel a fluidic switch for the routing of liquid flows between several adjacent channels can be realized. Liquid transport within the fluid channels can be accomplished by external pumps while the PDMS multilayer device merely works passively as integrated valves, or an integrated pumping mechanism can be achieved by combining several microvalves and actuating them in a peristaltic sequence (Fig. 9d).

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Metering of liquid volumes can be achieved by crossed fluid channels and a set of microvalves. Therefore, the liquid is initially loaded into a certain fluid channel and afterwards segmented into separated liquid compartments by pressurizing the control channel.

Figure 9. Realization of the main unit operations on the multilayer PDMS based LSI platform [123]. The NanoFlex™ valve (a) can be closed (b) by applying a pressure p to the control channel. Therewith, microfluidic valves (c), peristaltic pumps (d) and mixing structures (e) can be designed.

Also mixing can be realized using the above described pumping mechanism by the subsequent injection of the liquids into a fluidic loop (Fig. 9e) through the left inlet (right outlet valve is closed). Afterwards, the inlet and outlet valves are closed and the three control channels on the orbit of the mixing loop are displaced with a peristaltic actuation scheme leading to a circulation of the mixture within the loop [124]. Thereby the liquids are mixed and can be flushed out of the mixer by a washing liquid afterwards. Using this mixing scheme, the increase of reaction kinetics by nearly two orders of magnitude has been demonstrated in surface binding assays [125]. However, the key feature to tap the full potential of the large scale integration approach is the multiplexing technology allowing for the control of N fluid channels with only 2 log2 N control channels. Based on this principle, a microfluidic storage device with 1,000 independent compartments of approximately 250 pL volume and 3,574 microvalves has been demonstrated [122]. 6.3. APPLICATION EXAMPLES

One application example on the microfluidic LSI platform is the extraction of nucleic acids (NA) from a small amount of cells [126, 127] for cell-based assays. For the extraction of NA from a cell suspension, the cell membrane has to be destroyed first (chemical lysis of the cell). Afterwards, the NA are specifically separated from the residual cell components using a solid phase extraction method based on an NA affinity column (paramagnetic beads). This extraction protocol is completely implemented on the microfluidic

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platform using the basic unit operations for valving, metering, mixing and switching of liquids. Measurable amounts of mRNA were extracted in an automated fashion from as little as a single mammalian cell and recovered from the chip [126]. Based on this technology, the development of a nucleic acid processor for complete single cell analysis is under way [128–130]. Also many other applications have been implemented on the LSI platform over the last years: protein crystallization [131], immunoassays [132], automated culturing of cells [133] or multicellular organisms [134] and DNA synthesizing [135]. From a commercial perspective, Fluidigm Corp. has launched three different products based on the large scale integration platform within the last years: the BioMarkTM technology for molecular biology (e.g. TaqMan® assay), the TOPAZ® system for protein crystallography, and the Fluidigm® EP1 system for genetic analysis. Especially the EP1 system bears a large potential for high-throughput screening applications such as sequencing [136], multiparallel PCR [137], single-cell analysis [138], siRNA- [139] or antibody-screening [140], kinase- [141] or expression-profiling [142]. 6.4. STRENGTHS AND LIMITATIONS

The microfluidic LSI platform certainly has the potential to become one of the most versatile microfluidic platforms especially for high-throughput applications. It is a flexible and configurable technology which stands out by its suitability for large scale integration. The PDMS fabrication technology is comparably cheap and robust, and thus suitable to fabricate disposables. Reconfigured layouts can be assembled from a small set of validated unit operations and design iteration periods for new chips are in the order of days. Some of the system functions are hardware defined by the fluidic circuitry but others like process sequences can easily be programed externally. Limitations of the platform are related to the material properties of PDMS: for example, chemicals which the elastomer is not inert to cannot be processed, and elevated temperatures such as in micro-reaction technology are not feasible. Also for the implementation of applications in the field of point-of-care diagnostics, where a handheld device is often required, the LSI platform seems not to be beneficial at the moment. Thereto external pressure sources and valves would have to be downsized to a smaller footprint, which is of course technically feasible, but the costs would be higher in comparison to other platform concepts. However, as a first step towards downsizing the liquid control equipment, the use of a Braille system was successfully demonstrated [143].

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7. Segmented Flow Microfluidics Definition of segmented flow microfluidics: Segmented flow microfluidics describes the principle of performing an assay within small liquid droplets immersed in a second immiscible continuous phase (gas or liquid). For process automation, the droplets are handled within microchannels, where they form alternating segments of droplets and the ambient continuous phase. 7.1. GENERAL PRINCIPLE

The segmented flow microfluidic platform relies on a multiphase fluid flow through microchannels. Generally, the applied technologies can be divided into the following categories: • Two-phase gas–liquid • Two-phase liquid–liquid • Three-phase liquid–liquid In principal, droplets of a dispersed liquid phase are immersed in a second continuous gas (two-phase gas–liquid) or liquid (two-phase liquid– liquid) phase within a microchannel. Thereby, the inner liquid droplets are separated by the continuous carrier liquid along the channel. If the size of the inner phase exceeds the cross sectional dimensions of the channel, the droplets are squeezed to form non-spherical segments, also called “plugs”. Following this flow scheme, the platform is called segmented flow microfluidics. In some applications, the stability of the phase-arrangement is increased by additional surfactants as the third phase, stabilizing the plug interface (three-phase liquid–liquid) [144]. An external pressure is applied for the transport of the plugs. A comprehensive general discussion of the platform can also be found in recent review papers [30, 145, 146]. 7.2. UNIT OPERATIONS

The most elementary unit operation on the segmented flow platform is the initial generation of the droplets (see Table 3). This step can also be considered a metering, since the liquid volumes involved in the subsequent reaction within the droplet are defined during the droplet formation process. Generally, two different microfluidic structures have been reported for a controlled and continuous generation of droplets: the flow focusing structure as depicted in Fig. 7 [147, 148] and the T-shaped junction [149, 150], respectively. The size of the droplet is influenced by the strength of the shear forces at the channel junction (higher shear forces lead to smaller droplets) for both droplet formation mechanisms.

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To use droplets inside channels as reaction confinements, the different reactants have to be loaded into the droplet. Therefore, a method to combine three different sample liquid streams by a sheath flow arrangement with subsequent injection as a common droplet into the carrier fluid has been shown by the group of Rustem F. Ismagilov at the University of Chicago, IL, USA [151] (see Fig. 10). Different concentrations and ratios of two reagent sub-streams plus a dilution buffer merge into one droplet and perform a so called on-chip dilution [152]. The mixing ratios can be adjusted by the volume flow ratio of the three streams. Using a combination of two opposing T-junctions connected to the same channel, the formation of droplets of alternating composition has been demonstrated [153]. Using a similar technique, the injection of an additional reactant into a liquid plug moving through the channel at an additional downstream T-junction has been demonstrated [154]. Not only liquid chemical reagents but also other components like cells have been loaded into droplets [155]. The merging of different sized droplets showing different velocities to single droplets has been demonstrated successfully [151]. In the same work, the controlled splitting of droplets at a channel branching point has been shown. Using a similar method, the formation of droplet emulsions with controlled volume fractions and drop sizes has been realized [156]. Mixing inside the droplets can be accelerated by a recirculating flow due to shear forces induced by the motion along the stationary channel wall [157]. This effect is even more pronounced if two liquids of differing viscosities are mixed within the droplet [158]. Based on the recirculating flow, a mixing scheme for the segmented flow platform has been proposed using serpentine microchannels [159]. Within each channel curvature the orientation between the phase pattern in the droplet and the direction of motion is changed so that the inner recirculation leads to stretching and folding of the phases. Under favorable conditions, sub-millisecond mixing can be achieved and has been employed for multi-step synthesis of nanoparticles [154]. A detailed and theoretical description of this mixing effect is given in [160]. Besides the mixing within liquid droplets dispersed into another liquid carrier phase, also mixing within the carrier phase can be accelerated by a segmented flow. The injection of gas-bubbles into a continuous liquid stream forming a segmented gas–liquid flow has been described by Klavs Jensen and his group at MIT [161, 162]. The gas bubbles are introduced into the liquid flow and initiate recirculation flows within the liquid segments in between due to the motion along the channel wall. The gas bubbles can be completely separated from the liquid stream using a planar capillary separator after the reaction is finished. Using that technology, the synthesis of colloidal silica particles has been demonstrated [163]. Another microfluidic mixing

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scheme based on a gas–liquid segmented flow uses an additional repeated separation and re-combining of the channel [164]. TABLE 3. Overview and examples of unit operations and applications on the segmented flow microfluidic platform.

Microfluidic unit operations Droplet generation Droplet merging Droplet splitting Droplet sorting Droplet internal mixing Droplet sorting

Reference [30, 144, 146–149, 168, 169] [30] [151] [30] [30, 161, 162] [170]

Applications

Reference

(Single) cell analysis Single organism analysis DNA assays Drug screening Protein crystallization Chemical synthesis

[31, 145, 168, 171] [170, 172] [173–175] [169] [176–181] [146, 154, 157]

The incubation time of the reagents combined inside a droplet at the injection position can easily be calculated at a certain point of observation from the traveling distance of the droplet divided by the droplet velocity. Thus, the incubation time can be temporally monitored by simply scanning along the channel from the injection point to farther downstream positions. This is a unique feature of the platform and enables the investigation of chemical reaction kinetics on the order of only a few milliseconds [152]. On the other hand, also stable incubation times on the order of a week have been demonstrated [165]. This is enabled by separating the droplet compartments with a carrier fluid that prevents evaporation and diffusion. Using this approach, several 60 nL liquid droplets containing one or a few cells were generated within a microfluidic chip and afterwards flushed into a Teflon capillary tube for cultivation. The cell densities were still as high as in conventional systems after 144 h of growth within the droplets. Additional unit operations based on charged droplets and electric fields have been added to the segmented flow platform by David A. Weitz and coworkers [166]. Using dielectrophoresis, the sorting of single droplets out of a droplet train (switching) at rates up to 4 kHz has been shown [167]. The segmented flow technology augmented with electric field based unit operations is currently commercialized by the company Raindance Technologies, MA, USA.

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7.3. APPLICATION EXAMPLES

Table 3 gives an overview of the microfluidic unit operations and applications that have been already implemented on the segmented flow platform. They all take advantage of the enclosed reaction confinement within the droplets, either for analytical applications (cell analysis, single organism analysis, DNA assays, drug screening, protein crystallization) or chemical synthesis. Protein crystallization, for example, is realized on the segmented flow platform by forming droplets out of three liquids, namely the protein solution, a buffer and the precipitant within oil as the carrier phase [176, 182]. The precipitant concentration inside the droplet is adjusted via the buffer and precipitant flow rates respectively. Therewith, different concentrations are generated and transferred into a glass capillary for later X-ray analysis [177]. The effect of mixing on the nucleation of protein crystallization has been investigated by combining the described crystallization structure with a serpentine mixing channel [181]. Fast mixing has been found to be favorable for the formation of well-crystallized proteins within the droplets [180]. Recently, also a chip for rapid detection and drug susceptibility screening of bacteria has been presented [169] as one example of a high-throughput screening application. The channel design is depicted in Fig. 10. Plugs of the bacterial solution, a fluorescent viability indicator, and the drugs to be screened are injected into the carrier fluid. The different drug solutions (antibiotics: vancomycin (VCM), levofloxixin (LVF), ampicillin (AMP), cefoxitin (CFX), oxicillin (OXA), and erythromycin (ERT)) are separated by an air spacer plug within the drug trial channel. Plugs containing VCM were used as baseline, because VCM inhibited this S. aureus strain in macroscale experiments. No plugs containing VCM or LVF had a fluorescence increase greater than three times the baseline, indicating that MRSA was sensitive to these antibiotics.

Figure 10. Droplet based drug screening. The plugs containing the drugs (D1–D4) get mixed with a bacterial solution and a viability dye. In case of potent drugs the bacteria die and the droplet shows no staining. (Image adapted from Boedicker et al. [169].)

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7.4. STRENGTHS AND LIMITATIONS

The main advantages of the segmented flow microfluidic platform are the small volume liquid segments (controllable with high precision in the nanoliter range), acting as reaction confinements. This leads to little reagent consumption as well as a high number of different experiments that can be performed within a short period of time, which makes the platform a promising candidate for high throughput screening applications, e.g. in the pharmaceutical industry. Therefore, also the quasi-batch-mode operation scheme within nanoliter to microliter sized droplets is beneficial since it represents a consistent further development of classic assay protocols in e.g. well plates. The large number of existing unit operations enables the effective manipulation of the liquid segments. Furthermore, the completely enclosed liquid droplets allow the incubation and storage of liquid assay results over a long period of time without evaporation. However, a limitation of the platform is that handling of small overall sample volumes is not possible due to the volume consumption during the runin phase of the flow within the microchannels. This and the manual connection to external pumps renders the platform less suitable for point-of-care applications. Another drawback is the need for surfactants that are required for high stability of the plugs. They sometimes interfere with the (bio-) chemical reaction within the plugs and thus can limit the number of possible applications on the platform. 8. Centrifugal Microfluidics Definition of centrifugal microfluidics: The centrifugal microfluidic platform uses inertial and capillary forces on a rotating microstructured substrate for liquid actuation. Relevant inertial (pseudo-) forces include the centrifugal force, Euler force and Coriolis force. The substrate is often disk-shaped. Liquid flow is possible in two dimensions but with the limitation that active liquid transport is always directed radially outwards. Active components can be limited to one rotational axis. 8.1. GENERAL PRINCIPLE

The approach of using centrifugal forces to automate sample processing dates back to the end of the 1960s [183]. At that time, centrifugal analyzers were first used to transfer and mix a series of samples and reagents in the volume range from 1 to 110 µL into several cuvettes, followed by spectrometric monitoring of reactions and real-time data processing. Controlling microfluidic networks by just one rotary axis has an obvious charm to it, since no connections to the macro-world, such as pumps, are required. Moreover, the

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required centrifugal base devices can be simple and therefore robust. Rotational frequencies can be controlled very well and a radially constant centrifugal pseudo-force guarantees pulse-free liquid flow. Scientific work and applications based on centrifugal microfluidics have continuously been published since these early beginnings, although the most attention to the topic arose again in the last two decades, as summarized in several reviews [1, 184, 185]. However, the concept is still somewhat exotic compared to the large number of pressure driven systems existing today, possibly attributed to the difficulty of monitoring liquid flow under rotation and the dependency of liquid flow on microchannel surface quality [186]. This results in high initial investment in monitoring equipments and prototyping lines. Nevertheless, considerable advances towards integrated systems have been made in the last decades. In the beginning of the 1990s, the company Abaxis [187] developed the portable clinical chemistry analyzer [188, 189]. This system consists of a plastic disposable rotating cartridge for processing of the specimen, preloading of dried reagents on the cartridge, and an analyzer instrument for actuation and readout. A next generation of centrifugal devices emerged from the technical capabilities offered by microfabrication and microfluidic technologies [190– 193]. Length scales of the fluidic structures in the range of a few hundred micrometers allow parallel processing of up to hundred units assembled on a single disk. This enables high throughput by highly parallel and automated liquid handling. In addition, assay volumes can be reduced to less than 1 µL. Particular fields such as drug screening [191], where precious samples are analyzed, benefit from these low assay volumes. Today, many basic unit operations for liquid control on the centrifugal microfluidic platform are known and new ones are continuously being developed, enabling a number of applications in the fields of point-of-care testing, research, and security. 8.2. UNIT OPERATIONS

Liquid transport is initiated by the centrifugal force fω directed outwards in the radial direction. The centrifugal force can be scaled over a wide range by the frequency of rotation ω. Together with a tunable flow resistance of the fluidic channels, small flow rates in the order of nL/s as well as high throughput continuous flows up to 1 mL/s [194] can be generated. Therefore, scaling of flow rates over six orders of magnitude independent from the chemical composition, ionic strength, conductivity or pH value of the liquid can be accomplished, opening a wide field of possible applications. Also, liquid transport at rest can be achieved by capillary forces, depending on the channel geometry and the wetting properties of the liquid.

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Liquid valves can be realized by several different microfluidic structures on the centrifugal platform. In general, they can be purely passive, as depicted in Fig. 11, or require an active component outside the microfluidic substrate. First, the passive valves will be summarized: A very simple valve arises at the sudden expansion of a microfluidic channel e.g. into a bigger reservoir: the geometric capillary valve (Fig. 11a). The valving mechanism of this capillary valve is based on the energy barrier for the proceeding of the meniscus, which is pinned at the sharp corner. This barrier can be overcome under rotation due to the centrifugal pressure load of the overlying liquid plug [191, 195, 196]. For a given liquid plug position and length, i.e. for a given set of geometric parameters, the valve is influenced by only the frequency of rotation, and a critical burst frequency ωc can be attributed to every valve structure. Another possibility to stop the liquid flow within a channel is the local hydrophobic coating of the channel walls [197–200] (hydrophobic valve) (Fig. 11b). This valve is opened as soon as the rotational frequency exceeds the critical burst frequency ωc for this geometry and surface properties. A third method (Fig. 11c) utilizes the stopping effect of compressed air in an unvented receiving chamber. This centrifugo-pneumatic valve stops liquid up to much higher pressures than capillary valves for small receiving chamber volumes (≤40 µL). The air counter-pressure in the unvented receiving chamber can be overcome at high centrifugal frequencies, at which the liquid–air interface becomes unstable and enables a phase exchange, permitting liquid flow [201, 202]. Another method is based on a hydrophilic S-shaped siphon channel (hydrophilic siphon valve), wherein the two liquid–gas interfaces are leveraged at high frequencies of rotation [188] (Fig. 11d). Below a critical frequency ωc however, the right-hand meniscus proceeds beyond the bend, thus allowing the centrifugal force to drain the complete liquid from the siphon.

Figure 11. Passive centrifugal microfluidic valves. (a) Positioning of valves relative to center of rotation and centrifugal force, (b) geometric capillary valve [191], (c) hydrophobic valve [197], (d) centrifugo-pneumatic valve [201]and (e) hydrophilic siphon valve [188].

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One example of an active valve is an irradiation-triggered “sacrificial” valve published by Samsung Advanced Institute of Technology (Laser Irradiated Ferrowax Microvalve, LIFM) [203]. A ferrowax plug is used to close channels off during the fabrication of the microfluidic network. A laser source in the processing device can be utilized to melt the ferrowax plug and thus allow liquid passage (normally-closed valve). A modification of this technique also allows closing channels off by illuminating a ferrowax reservoir that expands into a channel and seals it (normally-open valve). An advantage of this valve is that it allows liquid control depending solely on the moment of the laser actuation, so it does not depend on the rotational speed or liquid properties. This comes at the cost of a more complex production process and base device. An alternative approach for the active control of liquid flows on the centrifugal platform is followed by the company Spin-X technologies, Switzerland. A laser beam individually opens fluidic interconnects between different channel layers on a plastic substrate (Virtual Laser Valve, VLV). This enables online control of the liquid handling process on the rotating module for adjusting metered volumes and incubation times within a wide range. Due to this, the Spin-X platform works with a standardized fluidic cartridge that is not custom made for each specific application, but can be programed online during a running process. Combining one of the above-mentioned valve principles at the radially outward end of a chamber with an overflow channel at the radially inward end results in a metering structure [204]. The metered liquid portion is directly set by the volume capacity of the chamber. With highly precise micro-fabrication technologies, small coefficients of variations (CV, standard deviation divided by mean value), e.g. a CV < 5% for a volume of 300 nL [205] and also metered volumes of as little as 5 nL have been achieved [198]. By arranging several metering structures interconnected via an appropriate distribution channel, simple aliquoting structures can be realized [201, 206]. These structures split a sample into several defined volumes, enabling the conduction of several assays from the same sample in parallel. Different mixing schemes have been proposed on the centrifugal platform. Considering mixing of continuous liquid flows within a radially directed rotating channel, the perpendicular Coriolis force automatically generates a transverse liquid flow [194]. A continuous centrifugal micromixer, utilizing the Coriolis stirring effect, showed an increasing mixing quality towards very high volume throughputs of up to 1 mL/s per channel [194] (Coriolis mixer). Besides the mixing of continuous liquid flows, also the homogenization of discrete and small liquid volumes located in chambers is of importance especially when analyzing small sample volumes (batch-mode mixing), since homogenous mixing obviously speeds up diffusion-limited chemical and biological reactions due to the close proximity between analytes. One possibility to enhance the mixing is the active agitation of the liquid within

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a mixing chamber by inertia related shear forces (Euler force), induced by a fast change of the sense of rotation (shake-mode-mixing) [204] or change of rotational frequency (unidirectional shake-mode-mixing) [207]. Shakemode mixing leads to reduced mixing times in the order of several seconds compared to several minutes for pure diffusion based mixing. A further downscaling of mixing times below 1 s using magnetic microparticles, located in the mixing chamber, has also been demonstrated [208]. Accelerated mixing can also be achieved by an interplay of capillary and intermittent centrifugal forces [209]. For routing (switching) of liquids, a switch utilizing the transversal Coriolis force to guide liquid flows between two outlets at the bifurcation of an inverse Y-shaped channel [210] or at nozzle leading into a chamber [211] has been presented. Depending on the sense of rotation, the Coriolis force is either directed to the left or to the right, guiding the liquid stream into one of two downstream reservoirs at the bifurcation. Another method for liquid routing based on different wetting properties of the connected channels has been reported by Gyros AB, Sweden [212]. The liquid stream is initially guided towards a radial channel, exhibiting a hydrophobic patch at the beginning. Therefore, the liquid is deflected into a branching non-hydrophobic channel next to the radial one. For high frequencies of rotation, the approaching liquid possesses enough energy to overcome the hydrophobic patch and is therefore routed into the radial channel [213]. A further possibility to switch liquid flows is to utilize an “air cushion” between an initial first liquid entering a downstream chamber and a subsequent liquid. The centrifugally generated pressure of the first liquid is transmitted via the air cushion to the subsequent liquid and forces it via an alternative route into a chamber placed sideways to the main channel [214]. The separation of plasma from a whole blood sample is the prevalent first step within a complete analytical protocol for the analysis of whole blood. Since blood plasma has lower density compared to the white and red blood cells it can be found in the upper phase after sedimentation in the artificial gravity field under rotation. The spatial separation of the obtained plasma from the cellular pellet can be achieved via a capillary channel that branches from the sedimentation chamber at a radial position where only plasma is expected [189]. Another method uses preseparation of the cellular and plasma phase during the sample flow through an azimuthally aligned channel of 300-µm radial width [199]. The obtained plasma fraction is thereafter split from the cellular components by a decanting process. Another concept enables plasma separation of varying blood sample volumes in a continuous process. The sedimentation occurs in an azimuthally curved channel due to centrifugal- and Coriolis forces, enabling up to 99% separation efficiency between two outlets for a diluted sample with 6% hematocrit

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[215]. An overview over centrifugal microfluidic unit operations and related applications can be found in Table 4. 8.3. APPLICATION EXAMPLES

Table 4 shows some applications that have been realized on the centrifugal microfluidic platform. At the top of the applications section, sample preparation modules (plasma separation, DNA extraction) are shown. This is followed by assays based on the detection of proteins, nucleic acids and small molecules (clinical chemistry). Two additional applications are presented at the end of the table, demonstrating chromatography and protein crystallization. Some instructive examples are discussed in more detail below. TABLE 4. Overview and examples of unit operations and applications for the centrifugal microfluidic platform.

Microfluidic unit operations Capillary valving Hydrophobic valving Siphon valving Laser-triggered valve Centrifugo-pneumatic valving Metering Aliquoting Mixing Coriolis switching Reagent storage Applications Integrated plasma separation Cell lysis and/or DNA Extraction Protein based assays Nucleic acid based assays Clinical chemistry assays Chromatography Protein crystallization

Reference [185, 191, 193, 195, 196, 216–223] [185, 197–199] [185, 188, 189, 207, 224, 225] [203, 226–228] [201, 214] [185, 189, 193, 197–199, 203–205, 224, 225, 227] [183, 185, 188, 189, 197, 201, 229] [183, 185, 188, 189, 193, 194, 203–205, 207, 208, 220, 224, 225, 227, 229–232] [185, 204, 210, 214, 215, 233] [220, 234] Reference [185, 199, 204, 215, 224–227, 235] [227, 233, 236] [183, 191, 197, 204, 216, 220, 222, 224–226, 229, 237] [216, 221, 238] [188, 189, 204, 205, 217–219, 225, 232, 239] [240] [198]

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Madou et al. from the University of California, Irvine showed a series of capillary valves to perform enzyme-linked immunosorbent assays (ELISAs) on the centrifugal platform [222]. The different assay liquids are held back in reservoirs connected to the reaction chamber via valves of different burst frequency. The capillary valves are opened subsequently by increasing the frequency of rotation. It was shown that in terms of detection range the centrifugally conducted assay has the same performance as the conventional method on a 96-well plate, but with less reagent consumption and shorter assay time. Gyros AB, Sweden [212] uses a flow-through sandwich immunoassay at the nanoliter scale to quantify proteins within their Gyrolab™ Workstation. Therefore, a column of pre-packed and streptavidin-coated microparticles is integrated in each one of 112 identical assay units on the microfluidic disk. Each unit has an individual sample inlet and a volume definition chamber that leads to an overflow channel. Defined volumes (200 nL) of samples and reagents can be applied to the pre-packed particle column. The laser induced fluorescent (LIF) detector is incorporated into the Gyrolab™ Workstation. Using this technology, multiple immunoassays have been carried out to determine the imprecision of the assay result. The day-to-day (total) imprecisions (CV) of the immunoassays on the microfluidic disk are below 20% [197]. The assays are carried out within 50 min with sample volumes of 200 nL. In comparison, the traditional ELISA performed in a 96-well plate typically takes several hours and requires sample volumes of several hundred microliters. A fully integrated colorimetric assay for determination of alcohol concentrations in human whole blood has been shown on the centrifugal Bio-Disk platform [205]. After loading the reagents into the reagents reservoir, a droplet of untreated human blood taken from a finger tip is loaded into the inlet port of the microstructure. By mixing the blood sample with the reagents, an enzymatic reaction is initiated, changing the color of the mixture depending on the alcohol concentration. After sedimentation of the residual blood cells, the absorbance is monitored in a real-time manner via a laser beam that is reflected into the disk plane on integrated V-grooves [232]. Using this automated assay and readout protocol the concentration of alcohol in human whole blood was determined within only 150 s. The results were comparable to common point-of-care tests and required a minute blood volume of just 500 nL. Also a protein crystallization assay has been demonstrated on the centrifugal microfluidic platform [198]. First, a defined volume of the protein solution is dispensed into the protein inlet and transported into the crystallization chamber. Afterwards, the preloaded precipitant is metered under rotation and transferred into the crystallization chamber as soon as a hydrophobic valve breaks. In the last step, the preloaded oil is released at

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yet a higher frequency and placed on top of the liquid stack within the crystallization chamber, to prevent evaporation. The successful crystallization of proteinase K and catalase could be demonstrated. Samsung Advanced Institute of Technology showed a fully integrated immunoassay for Hepatitis B- and other antibodies, starting from 150 µL whole blood on a centrifugal base device including a laser for controlling ferrowax valves and a read-out-unit [226]. A limit of detection comparable to a conventional ELISA and an assay time of 30 min were reported. On the same platform, enrichment of pathogens and subsequent DNA extraction was also shown (Fig. 12) [227]. The microfluidic structure features an integrated magnet that controls the position of coated magnetic particles which are used to capture target pathogens and lyse them by laser irradiation. With a total extraction time of 12 min, down to 10 copies/µL DNA concentration in a spiked blood sample of 100 µL could be specifically extracted and detected in a subsequent external PCR. Reagents are loaded by the operator prior to the process.

Figure 12. centrifugal microfluidic structure for pathogen-specific cell capture, lysis and DNA purification [227]. The microfluidic network comprises structures for plasma separation, mixing, and laser-triggered valves. For manipulation of the magnetic capture-beads, a movable magnet is integrated into the cartridge.

8.4. STRENGTHS AND LIMITATIONS

Two major advantages of the centrifugal microfluidic platform are the modular setup of the system with disposable and easily exchangeable plastic cartridges and the many existing unit operations, which allow highly precise liquid handling. The fabrication costs of the disposables are governed by the specific

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implementation of unit operations. Necessary global or local surface modification or the integration of active (ferrowax) valves, post-replication treatment, assembly and reagent pre-storage steps can increase the cost of the disposables. Mostly, they are made out of plastic and thus suitable for mass-production. The presented unit operations allow the automation of complex assay protocols. The cost for the base instrument depends heavily on read-out and temperature control modules. The motor required for liquid control is generally required to be able to achieve very stable and defined rotational speed and acceleration, also adding to the costs. However, compared to (several) high-precision syringe pumps, this solution is generally cheaper and allows a higher degree of integration. Due to the rotational symmetry of the disks, optionally some degree of parallelization can be achieved. Also, the rotational symmetry is beneficial for fast readout and temperature uniformity between cavities at the same radial position. However, as soon as any additional actuation or sensing function is required on the module during rotation and if a contact free interfacing is not applicable, things become challenging from a technical point of view. Especially interfacing to electric readout modules on the disk is difficult, since the rotating setup does not allow for wire connections between the disposable and the base instrument. The platform also lacks flexibility compared to others that allow online programming of fluidic networks within one piece of hardware that fits all, since most of the logic functions as well as their critical frequencies are permanently imprinted into the channel network. However, the Virtual Laser Valve technology is an exception in this respect and allows online programming in a centrifugal system. Space restrictions are also an issue, since the required footprint (disk surface) increases quadratically with the number of connected unit operations (radial length). The low centrifugal forces near the center of rotation and the difficulty of transporting liquids radially inward are other challenges in the fluidic design process. Also, completely portable solutions are currently still only a vision. 9. Electrokinetics Definition of electrokinetics: The electrokinetic platform uses electric charges, fields, field gradients or temporally fluctuating electrical fields for liquid actuation. The actuation is provided between different electrodes, and several effects (eletrophoresis, dieletrophoresis, osmotic flow, polarization) superimpose each other, depending on the sample liquid. Besides liquid actuation, the effects can also be used for separation of molecules and particles, detection, and catalysis.

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9.1. GENERAL PRINCIPLE

One of the first applications for electrokinetics was the analysis of chemical compounds via electrophoretic separation within capillaries in 1967 [241], long before the term “microfluidics” emerged. In the beginning, glass capillaries made from drawn glass tubes were used, whereas today well defined microchannels are established and commonly used. The actuation principle of the electrokinetic platform relies on the movement of liquid in an induced electric double layer and charged particles (ions) in an electric field applied along a microfluidic channel. The simple setup of electrokinetic systems consisting of microfluidic channels and electrodes without moving parts explains the early advent of electrokinetic platforms for microfluidic lab-on-a-chip applications. 9.2. UNIT OPERATIONS

In a microfluidic channel, a charged solid surface induces an opposite net charge in the adjacent liquid layer (electric double layer). As soon as an electric potential is applied along the channel, the positively charged liquid molecules are attracted by electrostatic forces and thus move towards a corresponding electrode (Fig. 13a). Due to viscous coupling, the bulk liquid is dragged along by the moving layer and liquid actuation with a planar velocity profile is generated (electroosmotic flow (EOF) [242]). The velocity profile is constant and dispersion only occurs by molecular diffusion. This motion is superimposed by the movement of ions and charged molecules, which are attracted or repelled by the electrodes depending on their charge (Fig. 13b). The velocity of the molecule depends on its charge and hydrodynamic radius and enables the distinction between different molecular entities. This effect is used for separation of charged molecules and is called electrophoresis.

Figure 13. Basic electrokinetic effects. (According to Atkins et al. [242].) (a) Electroosmotic flow (EOF), (b) electrophoresis (EP), (c) dielectrophoresis (DEP).

Based on the electroosmotic flow, metering of volumes down to the picoliter range can be achieved. While the sample liquid is injected and crosses an intersection point of two perpendicular channels, the electrodes

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and therefore the flow along the main channel is switched off. Then, the electrodes in the side channel are activated. This displaces a small plug at the intersection into the side channel, resulting in metering of a sample volume depending on the geometry of the intersection area. The mixing of two co-flowing streams was shown on the electrokinetic platform by applying an AC voltage [241]. A 20-fold reduction in mixing time compared to molecular diffusion has been reported. Also complete biological assays comprising cell lysis, mixing, and DNA amplification have been presented [243]. A modification to electrophoresis is free-flow electrophoresis, which enables the continuous separation of a mixture according to charge with subsequent collection of the sample band of interest [244]. For this, an transverse electric field is applied in pressure driven flow within a broad and flat microchamber. While passing this extraction chamber, the species contained in the sample flow are deflected depending on their charge and thus exit the chamber through one of several outlets. Another electrokinetic effect is based on polarization of particles within an oscillating electrical field or field gradient (dielectrophoresis), as depicted in Fig. 13c. Dielectrophoresis is applied in many fields, e.g. for the controlled separation and trapping of submicron bioparticles [245], for the fusion and transport of cells [246], or the separation of metallic from semiconducting carbon nanotubes [13, 247–249]. Other applications are cell sorting [250, 251] and apoptosis of cells [252, 253]. 9.3. APPLICATION EXAMPLES

Capillary electrophoresis systems were the first micro total analysis systems and emerged as single chip solutions from the analytical chemistry field in the 1990s [254]. Several companies utilize microfluidic capillary electrophoretic chips for chemical analysis, with capillaries of typically 10–100 µm diameter [255]. Today, Caliper Life Sciences, MA, USA [255] and Agilent Technologies, CA, USA [256] offer microfluidic chips for DNA and Protein analysis. Liquid propulsion is provided via electroosmosis and combined with capillary electrophoretic separation. The sample is electroosmotically transported and metered inside the chip, then separated via capillary electrophoresis and analysed by fluorescence detection. (Fig. 14). The whole assay is performed within minutes, instead of hours or days. First combinations of microfluidic integrated electrophoresis with microarrays were published in 1998 by Nanogen Inc., CA, USA [257]. This approach resulted in a 20-fold faster hybridization and more specific binding of DNA onto the microarray. This was the first step into the direction of a platform for massively parallel analysis.

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Figure 14. Microfluidic realization of capillary electrophoresis analysis on the electrokinetic platform. (Adapted from [123]. (© Agilent Technologies, Inc. 2007. Reproduced with permission, courtesy of Agilent Technologies, Inc.) After the sample has been transported to the junction area (a) it is metered by the activated horizontal flow and injected into the separation channel (b). Therein, the sample components are electrophoretically separated (c) and readout by their fluorescence signal (d). The complete microfluidic CE-chip is depicted in the center.

9.4. STRENGTHS AND LIMITATIONS

Electroosmotic actuation of liquids enables pulse-free pumping without any moving parts. Liquid manipulation at high precision can be achieved by the existing unit operations. In addition, electroosmotic flow does not lead to Taylor dispersion [117] as in pressure driven systems and thus enables high yield chromatographic separations. The seamless integration with electrophoresis, an established technology in use since 100 years [258], is another obvious strength. In microfluidic systems, applications can benefit from faster heat dissipation, better resolution, and faster separation. Miniaturization of electrophoretic analysis enables the automation and parallelization of tests with small dead volumes, thus reducing the required amount of sample. A technical problem in capillary electrophoresis systems is the changing pH-gradient due to electrolysis or electrophoresis itself. Also streaming currents which counteract the external electric field or gas bubbles as a result of electrolysis at the electrodes are problematic. Also a massively parallel setup cannot be constructed due to the heat generated by the electrophoresis itself. In addition, handheld devices are almost impossible due to the necessity of high voltages in combination with high energy consumption. Overall, miniaturized electrophoresis is established as a fast and efficient method for the separation and analysis of bio-molecules.

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10. Electrowetting Definition of electrowetting: The electrowetting platform relies on the movement of liquid droplets due to electrically induced local changes in wettability. This is normally achieved by applying a voltage to individual electrodes of an electrode-array. Increasing the voltage at an electrode decreases the local contact angle, and a droplet placed at the edge of the activated electrode will move towards it. 10.1. GENERAL PRINCIPLE

The electrowetting effect was first described by Lippmann in 1875 [259]. Interest in this effect was spurred again in the 1990s, when researchers started placing thin insulating layers on the metallic electrodes to separate it from the often conductive liquids in order to eliminate electrolysis [260]. The basic electrowetting effect is depicted in Fig. 15a. The wettability of a solid surface increases due to polarization and electric fields as soon as a voltage is applied between the electrode and the liquid droplet above (separated by the dielectric insulating layer) [260]. This so-called “electrowetting-ondielectric” (EWOD) [261] effect is therefore a tool to control the contact angle of liquids on surfaces.

Figure 15. The electrowetting effect. (According to Mugele et al. [260].) (a) If a voltage V is applied between a liquid and an electrode separated by an insulating layer, the contact angle of the liquid–solid interface is decreased and the droplet “flattens”. (b) Hydrophobic surfaces enhance the effect of electrowetting. For “electrowetting on dielectrics” (EWOD) several individual addressable control electrodes (here on the bottom) and a large counter-electrode are used. The droplet is pulled to the charged electrodes.

This invention paved the way for the application of the electrowetting effect as a liquid propulsion principle for lab-on-a-chip systems [262, 263]. To utilize the EWOD technology for programable liquid actuation, a liquid droplet is placed between two electrodes covered with insulating, preferably hydrophobic, dielectric layers (Fig. 15b). The liquid droplet is steered by the electrode array on one side and by a large planar ground electrode on the opposite side. Activating selected electrodes allows programing of a path which the droplet follows. The droplet needs to be large enough to cover

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parts of at least four addressable electrodes at all times, allowing twodimensional movement. If a voltage is applied to one of the control electrodes covered by the droplet, it moves onto the activated electrode pad. Successive activation of one electrode after the other will drag the droplet along a defined path. This freedom to program the liquid movement enables the implementation of different assays on the same chip. The universal applicability of moving droplets by EWOD was shown with several media such as ionic liquids, aqueous surfactant solutions [264], and also biological fluids like whole blood, serum, plasma, urine, saliva, sweat, and tear fluid [265]. 10.2. UNIT OPERATIONS

The droplet formation, i.e. initial metering, is the elementary unit operation of the platform. Metered droplets can be produced from an on-chip reservoir in three steps [265]. First, a liquid column is extruded from the reservoir by activating a series of adjacent electrodes. Second, once the column overlaps the electrode on which the droplet is to be formed, all the remaining electrodes are turned off, forming a neck in the column. The reservoir electrode is then activated during the third and last step, pulling back the liquid and breaking the neck, leaving a droplet behind on the metering electrode. Using this droplet metering structure, droplets down to 20 nL volume can be generated with a standard deviation of less than 2% [265]. A similar technology can be used for the splitting of a droplet into several smaller droplets [32]. Since the droplet volume is of great importance for the accuracy of all assays, additional volume control mechanisms such as on-chip capacitance volume control [266] or the use of numerical methods for the design of EWOD metering structures [267] have been proposed. Once the droplets are formed, their actuation is accomplished by the EWOD effect as described above. Also the merging of droplets can be achieved easily with the use of three electrodes. Two droplets are individually guided to electrodes separated from each other by a third one. Deactivating these two electrodes and activating the third separation electrode pulls the droplets together [268]. The most basic type of mixing within droplets on the EWOD platform is an oscillation, forwards and backwards, between at least two electrodes. Another mixing scheme is the repetitive movement of the droplet on a rectangular path. The shortest mixing time for two 1.3 µL droplets in linear oscillation on 4 electrodes was about 4.6 s [269]. In another work, the mixing times of 1.4 µL droplets could be further reduced to less than 3 s using two-dimensional arrays [270].

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10.3. APPLICATION EXAMPLES

Applications based on EWOD are in the development phase and quite close to market products. For example, an enzymatic colorimetric assay for (pointof-care) diagnostic applications has been successfully implemented, and glucose concentration in several biological liquids (serum, plasma, urine, and saliva) was determined with comparable results to standard methods [265]. The microfluidic chip layout for the colorimetric glucose assay is depicted in Fig. 16. It features reservoirs, injection structures (metering) and a network of electrodes for droplet transport, splitting and detection.

Figure 16. Electrowetting platform (EWOD). Implementation of a colorimetric glucose assay in a single chip. Four reservoirs with injection elements are connected to an electrode circuitry, where the droplets are mixed, split and transported to detection sites for readout. (Adapted from Srinivasan et al. [265].)

Also the use of an EWOD system for the automated sample preparation of peptides and proteins for matrix-assisted laser desorption–ionization mass spectrometry (MALDI-MS) was reported. In that work, standard MALDIMS reagents, analytes, concentrations, and recipes have been demonstrated to be compatible with the EWOD technology, and mass spectra comparable to those collected by conventional methods were obtained [271]. Also a PCR assay has been realized on the platform by temperature cycling of a droplet at rest [272]. Additional informations about the EWOD platform can be found in a comprehensive review [273]. 10.4. STRENGTHS AND LIMITATIONS

The strengths of the platform are the very small liquid volumes in the nanoliter range that can be handled with high precision, and the freedom to program the droplet movement. This cuts down sample and reagent consumption and allows a maximum of flexibility for the implementation of different assay

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protocols. The simple setup without any moving parts can be fabricated using standard lithographic processes. The programmable control of small droplets has its particular potential in assay optimization, since it allows varying the protocal over a certain range on the same chip. However, although the sample and reagent consumption is low, portable systems for e.g. point-of-care applications have not yet been demonstrated due to the bulky electronic instrumentation required to operate the platform. Another drawback is the influence of the liquid properties on the droplet transport behaviour, i.e. different patient materials will show different wetting abilities and thus lead to differences in volume or movement speed. Also the long-term stability of the hydrophobic surface coatings and the contamination risk is problematic, since every droplet can potentially contaminate the surface and thus lead to false results and also change the contact angle for the successor droplets. Another issue is the possible electrolysis caused by the electric fields themselves. Strategies for high throughput applications have not been demonstrated to date. In summary, the EWOD technique bears great potential to manipulate many single droplets in parallel. While first applications have been shown, the EWOD concept is still at a stage of development, shortly before entering the IVD markets [273]. 11. Surface Acoustic Waves Definition of surface acoustic waves: Surface acoustic waves (SAW) are acoustic shock waves on the surface of a solid support. An emitted SAW induces an acoustic pressure inside a droplet placed on the surface. If this pressure exceeds a critical value, the droplet is moved away from the SAW source. The surface is hydrophobically coated to facilitate droplet movement. By placing several SAW sources around an area, the droplet can be freely maneouvered. 11.1. GENERAL PRINCIPLE

An alternative to the electrowetting based transportation of droplets on a plane surface has been proposed by the group of Achim Wixforth at the University of Augsburg, Germany [274]. The approach is based on surface acoustic waves (SAW), which are mechanical waves with amplitudes of typically only a few nanometers. The surface acoustic waves are generated by a piezoelectric transducer chip (e.g. quartz) fabricated by placing interdigital electrodes (interdigital transducer, IDT) on top of a piezoelectric layer. Liquid droplets situated on the hydrophobic surface of the chip can be moved by the SAWs if the acoustic pressure exerted on the liquid droplet is

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high enough (Fig. 17) [275]. The actuation of small amounts of liquids with viscosities extending over a large range (from 1 to 1,000 mPa·s) has been shown [276]. This approach is also sometimes referred to as “flat fluidics”, because no cover or slit is required as in the EWOD approach.

Figure 17. Surface acoustic wave (SAW). (According to Tan et al. [277].) The shock waves induce a stream on the solid–liquid interface and lead finally to a movement of the droplet (amplitude of acoustic wave not to scale).

11.2. UNIT OPERATIONS

Metering is accomplished by moving a liquid droplet over a small hydrophilic “metering spot” via surface acoustic waves, leaving behind a small metered liquid portion due to the interplay between the surface tension force (keeping the droplet on the spot) and the acoustic force (pushing the droplet forward). Since those two forces scale differently over the droplet size, the splitting of the initial droplet into two droplets (one sitting on the metering spot and the other propagating forward) occurs. The smaller droplet is not transported since it stays unaffected by the acoustic wave. Also aliquoting has been shown by moving the initial droplet over a hydrophobic/hydrophilic checkerboard pattern [274]. Mixing is an intrinsic unit operation of the SAW platform. A droplet which is placed on the substrate and is influenced by a SAW shows internal liquid circulation due to the vibrating forces of the wave. This internal circulation leads to mixing [274]. 11.3. APPLICATION EXAMPLES

A PCR protocol has been implemented on the SAW plaform, based on 200 nL droplets and an additional heating element placed underneath the substrate surface for temperature cycling while the droplet is at rest [278]. However, since the nanoliter-sized droplet possesses a high surface-to-volume ratio,

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the liquid volume would decrease rapidly due to evaporation at the elevated temperatures required for the PCR reaction. Therefore, the aqueous liquid droplet is covered with a droplet of immiscible mineral oil with a smaller contact angle. This droplet-in-droplet configuration can still be moved via surface acoustic waves on the substrate surface. The concentration of DNA could be monitored by online fluorescent measurement providing a sensitivity of 0.1 ng [278]. 11.4. STRENGTHS AND LIMITATIONS

As in the EWOD platform, the SAW platform also allows the handling of small nanoliter sized liquid volumes in droplets on planar surfaces. The transport mechanism using surface acoustic waves though is more flexible since it depends only on the viscosity and surface tension of the liquid. However, the programmability is in turn limited since the position of the interdigital electrodes and especially the hydrophobic/hydrophilic areas determine the possible liquid handling processes. Another disadvantage is the long-term stability and the complexity of these hydrophobic and hydrophilic surface coatings, and thus costs of the disposable chip as well as the instrument. 12. Systems for Massively Parallel Analysis Definition of massively parallel analysis: Massively parallel analysis or “high throughput screening” allows the parallel handling of several hundred to up to billions of assays or samples within one run, and performs an according readout for each assay in parallel. Main application examples are microarrays, bead based assays and picowellplates. 12.1. GENERAL PRINCIPLE

In this chapter, solutions for highly parallel assay processing are presented. These are not per se microfluidic platforms by our definition, since they do not offer a set of easily combined unit operations and are quite inflexible in terms of assay layout. They are nevertheless presented here, since the small reaction volumes per assay and partly the liquid control systems are based on microfluidic platforms. The significant market for repetitive analyses, which allows high development costs for proprietary, optimized systems, does not necessarily require a platform approach, but can benefit from microfluidic production technologies and liquid handling systems.

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The massively parallel assay systems are a result of the increasing demand of the pharmaceutical industry for repetitive assays [279, 280] to cover the following objectives: − − − −

Screening of chemical libraries with millions of compounds [281] Screening of known drugs against new targets, different cell lines or patient material [282, 283] Multiparameter analysis of cell signaling and single cell analysis [284] All omic analyses such as genomics, transcriptomics, proteomics, glucomics, metabolomics [285]

With every newly discovered receptor or protein, all known drugs, predrugs, and chemical compounds should be tested for interaction in means of binding, activity change, or enzymatic activity. Also the analysis of gene activity or gene sequencing requires new and massively parallel testing in numbers of hundred thousands to billions. These tests consume a lot of time, material, effort, and money, but could lead to precious results (e.g. in case of a new blockbuster-drug) [286]. The challenging task to monitor millions of different binding reactions is partially solved by microarrays [287] (mainly in the case of DNA and RNA) or bead based assays in combination with picowell plates. Microarrays [287] are matrices with spots of different chemical compounds on a surface (Fig. 18a). The number of spots ranges from a few dozen to up to several millions. The microarray is incubated with the sample and each spot interacts with the sample in parallel, leading to as many parallel assays as there are spots on the microarray. Typically a microarray is read out by fluorescence and used for nucleic acid or protein analysis. Picowell plates [288, 289] consist of millions of small wells (2,000,000 unique compounds. The fluidic system is quite simple. The sample is manually loaded with a pipette into the chip, and capillary forces transfer the sample to the incubation chamber. Incubation and mixing is enhanced by a moving air bubble actuated by slow rotation. The company 454 Life Sciences offers picowell plate systems for the performance of massively parallel gene sequencing [289]. Beads containing

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roughly 10 million identical DNA copies are loaded into the picowell plate with a pressure driven system, where each beads sediments into one cavity. Different biomolecules are washed over the wells, interacting with the beads inside. In the case of a positive reaction, a quantitative enzymatic reaction, the pyro-sequencing [296], results in the emission of light. This system allows for parallel sequencing of 106 beads in a single run. 12.2.2. Bead Based Assays For bead based assays, liquid actuation and metering is most often pressure driven or performed with a pipetting robot in a microtiter plate. Mixing can be performed by any kind of mixing process according to the different actuation principles (diffusion, sonication, SAW, shaking, electrokinetic, electrophoretic, pressure driven pumping through microchannels etc.). The beads are separated from the liquid by centrifugation or with the help of magnetic fields and can then be transferred into another liquid. Typically, detection and readout are enabled with a fluorescent marker. The beads are then analyzed either sequentially or in parallel. For sequential analysis the beads are transferred into a capillary and cross several laser beams and detectors one after the other. In that case, the beads bear a coding to identify them [292, 293]. For the massively parallel analysis the beads are transferred onto a planar surface or into a picowell plate (Fig. 18b, c). Bead based assays are commercialized by Luminex since 1997 [292]. A microtiterplate is used for incubation and a capillary for bead transfer into the reader. Illumina [294, 295] expanded this concept radically by the use of 3 µm silica spheres, each bearing a unique DNA strand. The spheres are deposited on one end of a glass fiber connected to a detector. The spheres are incubated with a DNA sample, and in case of a binding event, the according sphere emits a light signal into the glass fiber. The current system allows handling of millions of unique compounds [297]. 12.3. STRENGTHS AND LIMITATIONS

Today, many manual steps and skilled personnel are required for the described systems and a “real” microfluidic platform is still not reached. However, microarrays, picowell plates and bead based assays are a very useful combination of solid phase and liquid handling for massively parallel assays in the number of millions. The material consumption per assay is quite low and the reaction time quite fast. The time-to-result is longer compared to a single assay, but several magnitudes faster compared to serially performing the same number of assays. A strong limitation of this systems is the reliability, reproducibility, and identification of artefacts. Therefore a positive binding event in these systems is always counterchecked in a microtiter plate experiment to verify

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the binding event. The whole system itself cannot be designed as handheld and is quite expensive (several 10,000€ per run for sequencing), but is inexpensive in terms of cost per assay and material consumption (less than a cent per sequenced base) [298]. 13. Criteria for the Selection of a Microfluidic Platform After the previous discussion of the platform approach and the presentation of some prominent examples for microfluidic platforms, this section will attempt to summarize the strengths and limitations of each platform presented in Fig. 1. This should provide the reader with some guidance to select platforms based on the selection criteria presented in Table 2. The given platform characteristics are based on the reviewed literature and the experience of the authors, taking into consideration properties such as material of the TABLE 5. Characteristics of microfluidic platforms with respect to certain selection criteria.

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disposable, necessary processing equipment, production technologies, published variety of unit operations, published data concerning precision, throughput, or multiparameter-testing. Beneficial platforms can be selected by identifying imperative requirements of a certain application, e.g. portability, low reagent consumption and high precision for point-of-care diagnostics, which are then compared to the characterisitcs of the available platforms. The platform characteristics are compiled in Table 5, also showing the potential of classical liquid handling technologies using pipetting robots. It is obvious that some of the microfluidic platform approaches are dedicated to certain fields of application. For example, the classical liquid handling technology enables high sample throughput and has a high programmability, but the main drawback is the lack of portability and the high equipment costs for complex automated workstations. These properties limit its use to large laboratories. The lateral flow test platform fulfills the requirements for point-of-care diagnostic applications quite well (low reagent consumption, good portability, and additionally low costs). However, as soon as the diagnostic assay requires higher precision or exceeds a certain level of complexity (e.g. if an exact metering of the sample volume or sample aliquoting is required), also new approaches like linear actuated devices and centrifugal microfluidics become advantageous for point-ofcare applications. They enable more sophisticated liquid handling functions, which is for instance required for nucleic acid based tests. The pressure driven laminar flow platform is especially interesting for online monitoring applications, since it enables continuous flows compared to the merely “batch-wise” operation of most of the other microfluidic platforms (i.e. handling discrete liquid volumes). Some of the platforms can also be considered as “multi-application” platforms, which is of special interest in the field of research instrumentation. Here, portability is of less importance, and the number of multiple parameters per sample as well as programmability (potentially also during an assay run) gains impact. The microfluidic large scale integration and the droplet based electrowetting and surface acoustic waves platforms are such versatile examples. For high-throughput screening applications, on the contrary, a high number of assays need to be performed within an acceptable period of time. Consequently flexibility is less important, and throughput and costs are the main issues. Thus, approaches like segmented flow and systems for massively parallel analysis are interesting candidates for these applications. An increasing number of application examples is based on the transfer of unit operations and fabrication technologies between research groups by literature or collaboration. This shows the advance of the platform approach in the research community. We strongly believe that this trend of platform-

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based development will continue in the field of microfluidics. If research time and development costs of microfluidic applications can be reduced significantly by this approach, and the spectrum of applications increases correspondingly, this could finally lead to the commercial breakthrough of microfluidic products. Acknowledgements We would like to thank our colleagues Junichi Miwa and Sven Kerzenmacher for their helpful suggestions and assistance during the preparation of this manuscript.

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MICROFLUIDIC LAB-ON-A-CHIP DEVICES FOR BIOMEDICAL APPLICATIONS DONGQING LI Department of Mechanical & Mechatronics Engineering University of Waterloo, Waterloo, Ontario, Canada N2L 3G1, [email protected]

Abstract. Microfluidics is key to miniaturize bio-chemical and biomedical methods and processes into chip based technology. Basics of electrokinetic microfluidics will be reviewed first. Three types of lab-on-a-chip devices, PCR lab-on-a-chip, flow cytometer lab-on-a-chip and immunoassay lab-ona-chip are discussed here. The working principle, key microfluidic processes and the current status of these lab-on-a-chip devices are reviewed.

1. Introduction Lab-on-a-chip devices are miniature laboratories built on a thin glass or plastic chip of several centimeters in dimension, with a network of microchannels (e.g., 100 μm in width). These small chips can duplicate the specialized functions as their room-sized counterparts in clinical diagnoses. The advantages of these lab-on-a-chip devices include markedly reduced reagent consumption, short analysis time, automation and portability. Generally, a lab-on-a-chip device must perform many microfluidic functions such as pumping, flow switching, incubating, sequentially loading solutions and washing. A very large pressure gradient is required to generate liquid flow in microchannels since the flow resistance is reversely proportional to the fourth power of transverse channel dimension. It would be unpractical and difficult to use pressure-driven flow to control the sequential loading and washing processes in a portable microfluidic system. Alternatively, electrokinetic forces can be used to drive liquid flow in microchannels. All solid surfaces acquire electrostatic charges when they are in contact with an aqueous solution. The surface charge in turn attracts the counterions in the liquid to the region close to the surface, forming the electric double layer. Under a tangentially applied electrical field, the excess counter-ions in the double layer region will move, resulting in a bulk liquid

S. Kakaç et al. (eds.), Microfluidics Based Microsystems: Fundamentals and Applications, DOI 10.1007/978-90-481-9029-4_18, © Springer Science + Business Media B.V. 2010

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motion via viscous effect. This is known as the electroosmotic flow [1]. Generally, the electroosmotic flow velocity is given by:

ε ε ζ veof = − r o E μ

(1)

where ε and ε0 are the dielectric constants in the medium and in the vacuum, respectively; μ is the viscosity of the liquid; ζ is the zeta potential of the channel wall surface; and E is the applied electric field. In a microfluidic chip, there are a number of wells at the ends of the microchannel branches. These wells provide not only reservoirs for samples and reagents, but also the connection of electrodes to liquid in the microchannels. The liquid flow control is realized by applying different voltages to different wells simultaneously. In this way one can control the flow rate, and let one solution flowing through a microchannel in the desired direction while keeping all other solutions stationary in their wells and channels. A charged particle will move relatively to the surrounding stationary liquid under the influence of applied electric field; this is generally referred to as electrophoresis. The particle’s electrophoretic velocity:

vep =

ε r ε oζ p E μ

(2)

where ζp is the zeta potential of the particle. In a microchannel, the motion of the particles/cells is determined by the combined effect of electroosmosis (the liquid motion) and electrophoresis. Understanding of the net motion of the particles or cellsin a microchannel is important for transporting and separating particles/cells in a lab-on-a-chip device [1, my book]. In a non-uniform electrical field, a dielectric particle in a dielectric liquid will be polarized and subject to non-symmetric electrical force. Consequently, the particle is induced to move under the net electric force. Such a motion of the particle is known as dielectrophoresis. Dielectrophoresis has been used to concentrate and separate particles/cells in microchannels. In the development of lab-on-a-chip technology, a key is to develop the ability to pump the liquids and transport sample/reagent molecules as well as biological cells in a microchannel network. This can be achieved by using the electroosmotic flow and electrophoresis. Mixing of different solutions and dispensing a specified amount of one solution from one microchannel into another microchannel are important to many microfluidic chips. There are extensive research works done in these areas [1]. Furthermore, precise control of temperature is often critical to on-chip biochemical reactions. In the following the PCR lab-on-a-chip, flow cytometer lab-on-a-chip and immunoassay lab-on-a-chip will be reviewed.

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2. Real-Time PCR Lab-on-a-Chip Many biological identification processes and biomedical diagnosis processes utilize deoxyribonucleic acid (DNA) analysis based methods, such as DNA sequencing to identify a specific DNA for forensic applications. However, all these analyses have to start with a sufficient amount of DNA molecules. To do so, a molecular biology method, the polymerase chain reaction (PCR) is used. Generally speaking, the polymerase chain reaction (PCR) is a technique to amplify a single or few copies of a piece of a DNA molecule to generate millions or more copies of the same DNA molecule. In addition to the chemistry involved, the PCR method relies on thermal cycling, i.e., repeated heating and cooling of the reaction for DNA melting and enzymatic replication of the DNA. Typically, PCR thermal cycling involves the following: Denaturation step: This step is the first regular cycling event and consists of heating the reaction to about 95°C for 20–30 s. It generates single strands of DNA by melting of DNA template and primers, disrupting the hydrogen bonds between complementary bases of the DNA strands. Annealing step: The reaction temperature is lowered to 50–65°C for about 30 s allowing annealing of the primers to the single-stranded DNA template. Stable DNADNA hydrogen bonds are only formed when the primer sequence very closely matches the template sequence. The polymerase binds to the primertemplate hybrid and begins DNA synthesis. Extension/elongation step: The temperature at this step depends on the DNA polymerase used; in the case of Taq polymerase, a temperature of 72°C is used with this enzyme. At this step the DNA polymerase synthesizes a new DNA strand complementary to the DNA template strand by adding dNTPs (Deoxynucleoside triphosphates) that are complementary to the template in 5′ to 3′ direction, condensing the 5′-phosphate group of the dNTPs with the 3′-hydroxyl group at the end of the nascent (extending) DNA strand. Theoretically, after each PCR thermal cycle, the amount of DNA target is doubled, leading to exponential amplification of the specific DNA fragment in the solution. The above described PCR can only amplify the number of copies of a DNA molecules in the sample. In order to know what DNA or specific DNA sequence it is, however, one has to perform additional analyses, such as using gel electrophoresis or DNA sequencing method to find the answer. A direct DNA identification method, called the real-time PCR, combining both the PCR with fluorescent detection, is most useful in this regard. Real-time PCR uses a fluorescently labeled oligonucleotide probe, which eliminates the need for laborious and time-consuming post-PCR processing (e.g., gel electrophoresis). In real-time PCR, a reporter fluorescence dye and a quencher dye are attached to an oligonucleotide probe. Negligible fluorescence from the reporter dye’s emission is observed when both dyes

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are attached to the probe. Once PCR amplification begins, DNA polymerase cleaves the probe, and the reporter dye is released from the probe, separated from the quencher dye during every amplification cycle, and generates a sequence-specific fluorescent signal. Real-time PCR detection is based on monitoring the fluorescent signal intensity produced proportionally during the amplification of a specific PCR product (e.g., an influenza DNA); therefore, it is a direct and quantitative method with high sensitivity. However, there are limitations to the applications of the real-time PCR technique. Currently, the instruments for conducting real-time PCR are bulky and expensive, are available only in large hospitals and major medical centers, and are not available for field or point-of-testing applications. In addition to the initial capital cost, the cost of reagents in real-time PCR is significantly high, partially because of the relatively large reagent consumption. The average thermal cycling speed of some PCR machines is as low as about 1°C/s. In order to apply the real-time PCR technology as a rapid, accurate, and direct detection tool for field or point-of-testing applications, it is highly desirable to miniaturize the real-time PCR instrument. To miniaturize the real-time PCR and make it a lab-on-a-chip method, one must realize the following two key functions: (1) Control the on-chip thermal cycling, i.e., control the temperature of the PCR reaction wells on the chip. (2) Detect the fluorescent signals during the PCR. There are many reported works on conducting PCR on small chips. Both static chamber PCR chips and dynamic flow-through PCR chips were reported. PCR chips have been made by various materials such as silicon, glass, polycarbonate, polyamide and PMMA. Contact and non-contact heating as well as Joule heating were used to power the thermal cycling [2]. However, in these efforts, although PCR reactions were conducted on chips in micro wells or microchannels, to analyze the amplified PCR products, it still requires using the conventional gel electrophoresis or desk-top fluorescence microscopes. For example, among the static chamber PCR chip devices, Yang et al., reported a micro PCR system in which the temperature of the micro reactor was controlled by two Peliter thermolelectric devices sandwiching the reactor [3]. The PCR chip is made of polycarbonate, and fabricated by a direct laser writing method. A commercial fluorescence analyzer was used to detect the amplified products after the thermal cycling. Lin and Lee et al developed a PCR system with a reaction well fabricated in a silicon wafer sealed with a glass substrate and placed a heater at the bottom of the silicon wafer [4]. In their design, a small reaction volume was used to increase the temperature uniformity. Gel electrophoresis was employed to analyze the amplifications. Nagai’s group and Matsubara’s group presented micro array PCR chips patterned on silicon wafer. A commercial thermal cycler was used to conduct the PCR and a fluorescence microscope or micro scanner was employed to measure the fluorescence intensity of the

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PCR products [5, 6]. In dynamic flow-through PCR devices, PCR reactants were heated and cooled by transporting the reactants through different temperature zones. A typical flow-through thermal cycler was presented in literature with thin film platinum heaters and sensors patterned onto a silicon wafer to generate three different temperature zones [7–10]. PCR reactions were also achieved in a continuous flow mode in a ring chamber with controlled temperature regions [11, 12]. Comparing with the static chamber PCR systems, the flow-through PCR can reduce the heating and cooling time and thus shorten the total time of PCR reaction. However, it is difficult to insulate the different temperature zones, to exam the PCR results and to collect the PCR product for further analysis. Another hindrance for flow-through systems is the unalterable number of cycles dependent upon chip design. Recently a portable real-time PCR device was demonstrated [13, 14]. This device has a miniature thermal cyclyer performing the PCR thermal cycling operation. The disposable PCR reaction chip is made of polydimethylsiloxane (PDMS) and glass chips, and has four reaction wells. The well size can be as small as 0.5 μL. A miniature laser-fiber optic system is developed for detecting the fluorescent signals from the four wells during the PCR process. Precise control of the temperature at the three levels and the holding time at each temperature level is critical for a successful PCR. In this device, the heating is achieved by using an external heater under the PCR chip, and the cooling is realized by using a cooling fan. Figure 1 shows the typical temperature profile in a PCR thermal cycling process. The temperature in this figure was measured by using thermal couples embedded in the wells. 110 100

Temperature

90 80 70 60 50 Well Temperature Denaturing (94C) Extension (72C) Annealing (55C)

40 30

800

900

1000

1100

1200

1300

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Figure 1. The actual temperature of the reactants in the wells of the PCR chip. This temperature was measured by thermocouple embedded in the well.

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Figure 2. An example result of on-chip real-time PCR detection of E. coli O157 H7.

Figure 2 shows a typical fluorescent detection result. The optic fiber sensors delivered excitation laser and received the emission fluorescent light signals from each well, and pass the fluorescent signals through an optic filter and to a photo-detector. The signals are then processed by a PDA. In this particular example, The DNA concentration is 12.5 ng/μl in well 1, 1.25 ng/μl in well 2 and 3, and 0.0 ng/μl in well 4 (negative control). For the cases with the same initial concentration of a template DNA of 1.25 ng/μl (well 2 and well 3), the measured fluorescent intensity started to increase at essentially the same cycle number, the 20th cycle. The fluorescence intensity started to increase earlier (17th cycle) for well 1 than well 2 and 3 due to its higher DNA concentration (12.5 ng/μl). In addition, the curve for the negative control is flat, which is expected. The plateau phase intensity of well 1 is different from that of well 2 (well 3). This may be due to the optic loss difference of fiber optical switch from channel to channel. In real-time PCR, it is the slope of the intensity–cycle number curve that is important. The loss difference does not affect the slop of the curve, and affect only the final intensity value. Real-time PCR Lab-on-a-Chip technology has wide spectrum of applications in biomedical diagnosis of pathogen infections, food safety and bio-defense. The major advantages include significantly smaller amount of sample and reagent consumption, high speed and portability. For example, Fig. 3 shows an example of detecting Flu virus H5 (birds flu) on a chip. It took only about 8–10 min to generate positive detection results. In comparison with the 3 h required for the same tests done in a conventional real-time PCR instrument, this is a significant saving in the testing time.

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0.18 0.16 0.14

Intensity (a. u.)

0.12 0.10

Conc=0.1ng/uL

0.08

Conc=1.0ng/uL

0.06 0.04 0.02 0.00 0

5

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Cycle

Figure 3. Examples of the detected fluorescent signals from a real-time PCR chip for detecting Flu virus H5.

3. Flow Cytometer Lab-on-a-Chip Flow cytometer is a device that measures certain physical and chemical characteristics of cells as the cells travel in suspension one by one passing a sensing point. By labeling the cells with fluorescent molecules that bind with high specificity to one particular cellular constituent, it is possible to measure the contents of the constituent. The flow cytometer is capable of rapid, quantitative, multi-parameter analysis of heterogeneous cell populations on a cell-by-cell basis.

Sample solution Fluidic system

Optic detector

Laser Optic filters

Figure 4. Illustration of the working principle of flow cytometer.

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In the operation of a flow cytometer, a fluidic handling system will first pump the sample solution containing biological cells into the instrument. The key function of the fluidic system is to focus the flow, that is, using laminar flow streams from the side to squeeze the central sample solution stream. The objective of the flow focusing is to make the central stream so thin that its diameter is close to the size of a single cell. In this way, cells in the sample solution will move in a single line, one following another. Another key component in the flow cytometer is the optic detection system, as illustrated in Fig. 4. The cells will move through a sensing point where a laser beam shines. The cells pass through the laser beam will be detected by using, for example, light scattering method so that the number of cells in the sample will be counted. Some cells may be labeled with a specific fluorescent dye. When they pass through the sensing point, the laser will excite the dye, the emitted fluorescent light will pass through the optic filter and be detected by the photo-detector. The signal will be sent to a computer to be analyzed. In this way, the number of a specific type of cells labeled with that dye can be determined. Some flow cytometers have another function – cell sorting. After the fluorescent detection point, a vibrating mechanism is used to cause the stream of cells to break into individual droplets. An electrical charging ring is placed just at the point where the stream breaks into droplets. A charge is placed on the ring based on the immediately-prior fluorescence measurement result, and the opposite charge is trapped on the droplet as it breaks from the stream. The charged droplets then fall through an electrostatic deflection system that diverts droplets into containers based upon their charge. However, the flow cytometers are bulky and expansive, and are available only in large reference laboratories. In addition, the required sample volumes are quite large, usually in the 100 µL range. Many clinical applications require frequent blood tests to monitor patients’ status and the therapy effectiveness. It is highly desirable to use only small amount of blood samples from patients for each test. Furthermore, it is highly desirable to have affordable and portable flow cytometry instruments for field applications, point-of-care applications and applications in resource-limited locations. To overcome these drawbacks and to meet the increasing needs for versatile cellular analyses, efforts have been made recently to apply microfluidics and lab-ona-chip technologies to flow cytometric analysis of cells. From the working principle of the conventional flow cytometers as described above, we see that a flow cytomete on a chip must have the following functions: (1) Flow focusing. (2) Counting and detecting cells/ particles. (3) Sort the cells/particles. The general idea of flow focusing is to use one or more laminar flow streams to “compress” the stream of the sample solution. By controlling the flow rates of the side streams, the size of the sample stream can be controlled to a size close to that of the to-be-

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measured cells. As shown in Fig. 5, the flow focusing can be realized in a cross-shaped microchannel. The sample solution is colored with a dye (green) and carries particles. The sample solution is transported from left to right by using electroosmotic flow. A buffer solution is also driven by electroosmotic flow and enters the intersection from the two perpendicular channels and then flow to the downstream (the left). The two side streams squeeze the sample solution stream so thin that the particles in the sample stream have to move in a single line, one following another.

Figure 5. Electrokinetic flow focusing of particles through a crossing microchannel in a microfluidic chip.

Development of microchannel-based flow cytometers has been reported recently. Tung et al. produced a flow cytometer chip using PDMS (polydimethylsiloxane) for fluorescence-labeled particle detection using a two-color, multi-angle detection system via embedded fibers [15]. While a remarkable accomplishment, their chip unfortunately lacks portability as it requires a manually operated external liquid handling system (e.g., two syringe pumps, tubing and valves) to focus the cell-carrying stream in the detection channel. A flow cytometer chip using electrokinetic flow focusing was reported by Fu et al. [16]. This chip consists of a glass plate with a pair of embedded optical fibers for counting particles moving through a microchannel. All these reports demonstrate only one function, i.e. counting the number of the single-sized particles. However, a practical flow cytometer must be able to handle mixtures of diverse cells that must be differentiated

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and counted by size and by their fluorescent dye tags. Significant research is needed to develop these functions for microfluidic flow cytometer chips. For this purpose, Li’s group reported a simple multi-functional particle detection PDMS chip [17]. This chip generates liquid flow and particle motion electrokinetically, and uses two pairs of parallel optical fibers embedded in the chip to measure particle speed and size, and to count particles. More recently, a new microfluidic method was developed to counting the particles flowing through microchannels, not by the optic method as described previously, but by an electric method. This method is called the microfluidic differential resistive pulse sensor method [18]. Figure 6 below illustrates the principle of this method. C A

VD1 B

D

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V+

R1

R3 R2

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Figure 6. Chip design and system setup for one-stage differential amplification. A DC voltage (V1 – V–) is applied to drive the particles from A to B. Trans-aperture voltage (VD1 and VD2) modulation are sensed by the two gate branches to C and D, which are the positive and negative inputs of the differential amplifier, respectively. The resistances of the three sections in the main channel are denoted by R1, R2, R3, respectively.

The PDMS microfluidic chip was fabricated on a glass substrate following the standard soft lithography protocol. The chip consists of a pair of mirrorsymmetric channels (with sensing apertures) that are separated by a wall of 100 mm in thickness and share the same sample input (A) and waste reservoirs (B), as shown in Fig. 6. The fluidic conduit is connected to the electronic circuits by platinum-wire electrodes submerged in four reservoirs. A DC bias (V1 –V–) was applied across the channel to induce the electroosmotic flow, which drove the particles through the sensing apertures from reservoir A to reservoir B. There are two gate branches connected to the differential amplifier at the upstream ends of both sensing apertures to detect the transaperture voltage modulation when particles are translocated.

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For microchip-detection system developed in this study, there are two major types of noise sources. One is the from the electrical power system, such as the system power supply and the ambient illumination, which has a characteristic frequency of 60 Hz. The other is from the intrinsic noise of the electronic components, such as the thermal fluctuation in a resistor, which can generate various interferences from several hundred hertz to over several megahertz. The major advantage of the symmetric dual channel design is that it renders identical noise level for the output signals (VD1 and VD2) from both gate branches. The voltage component common to the amplifier inputs (Vin1 and Vin2) are called “common-mode voltage” (CMV). Obviously, the various noises coupled in VD1 and VD2 constitute the CMV of the amplifier. When the two branches are connected to a differential amplifier of high “common-mode rejection ratio” (CMRR), the noise comprised in the CMV can be rejected significantly at the final output (Vout). Ideally, when there is no particle passing through either of the two sensing apertures, ideally Vin1 is equal to Vin2 in amplitude for a perfectly symmetric fluid circuit. Thus, the two inputs will cancel each other and the amplified output is zero. When a particle passes through either one (but only one at a time) of the two sensing apertures, on top of the DEV, the resulting voltage modulation causes an additional input difference DV between Vin1 and Vin2, which is amplified by the differential gain. That is why this method can largely increase the signal to noise ratio. The lowest volume ratio of the particles detected to the sensing aperture is 0.0004% using twostage amplification, which is about ten times lower than that of current commercial Coulter counters and similar devices reported in literature so far. 1

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Figure 7. Example result of detecting 520 nm and 1 μm particles by the microfluidic resistive pulse sensor.

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Figure 7 is an example of detecting 520 nm and 1 μm particles by the microfluidic resistive pulse sensor. Combining the above described microfluidic differential resistive pulse sensor method with a miniature laser-fiber optic fluorescent detector, the simultaneous detection of fluorescent and non-fluorescent particles has been demonstrated [19]. This method is simple, inexpensive, and easy to operate, and can achieve highly sensitive and accurate detection without relying on any conventional bulky instruments. Excellent agreement was achieved by comparing the results obtained by this chip system with the results from a commercial flow cytometer for a variety of samples of mixed fluorescent and non-fluorescent particles. In a recent work, Li’s group reported a fluorescence-activated particle counting and sorting system based on the electrokinetic flow switching [20]. Figure 8 below illustrates the experimental system. The chip has a crossmicrochannel. When a particle labeled with a specific fluorescent dye passes the intersection, it will be detected by a fiber optic system. A DC electric pulse is triggered by pre-set fluorescent threshold to automatically dispense the particles into the side collection reservoir. Otherwise, if the particle does not carry the correct fluorescent dye, it will be continuously transported to the downstream waste collection well with the electrokinetic flow. It has been proved that this system responses fast and accurately and 15 μm fluorescent particles can be sorted from a mixture with non-fluorescent particles. Figure 9 shows the automatic sorting of 15 μm fluorescent particles from 4.85 and 25 μm non-fluorescent particles in this chip.

Figure 8. Schematics of the flow cytometer chip system.

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Figure 9. Trajectories of a 15 μm fluorescent particle and 4.85 and 25 μm non-fluorescent particles. They are obtained by superposing a series of consecutive images of the moving particles. The 15 μm particle shows longer streak because of its increased velocity in the dispensing branch D. Under the same exposure time, faster motion causes longer streaks.

It has been widely recognized that AIDS is becoming one of the leading epidemic causes of adult deaths globally, especially in developing countries where the prohibitive expenses of the conventional assay technology limits the access for the vast majority of the HIV-infected individuals. Among the most important clinical parameters, enumeration of the peripheral blood CD4+ T lymphocytes is a key factor for determining disease progression and monitoring efficacy of the treatment. A decrease in the total count of CD4+ T lymphocytes, the critical immune cells infected by HIV, is one of the hallmarks of HIV disease. In addition to absolute CD4+ T cell number, the CD4+ percentage (ratio of the CD4+ T cells to the total lymphocytes) is also an important clinical parameter, especially in pediatric HIV infection. Therefore the CD4 percentage provides more accurate prediction for the risk of opportunistic infection than does the absolute CD4 cell number. Recently, the above-described microfluidic differential resistive pulse senor method was combined with a miniaturized fluorescent fiber optic detection method to detect CD4+ cells from blood samples [21]. Figure 10 shows an example of such a detection. The results were compared with the commercial flow cytometer, and the agreement was excellent.

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Figure 10. Detection of 50% stained CD4 cells by the Resistive Pulse Sensing (RPS) current signal and by the fluorescence signal. The upper plot and left axis indicate the RPS signal; the lower plot and right axis indicate the fluorescent signal.

4. Immunoassay Lab-on-a-Chip Immunoassay (IA) is a biochemical method to measure the presence and the concentration of a substance in a biological liquid, typically serum or urine, using the reaction of an antibody to its antigen. The assay takes advantage of the specific binding of an antibody to its antigen. Generally antigens are proteins carried by bacteria and viruses. They prompt the generation of antibodies and can cause an immune response. Antibodies are gamma globulin proteins that are found in blood or other bodily fluids of vertebrates, and are used by the immune system to identify and neutralize foreign objects, such as bacteria and viruses. The binding of an antibody to an antigen is type specific, i.e., they are like a key and lock; they must match each other exactly or will not bind. Immunoassay (IA) is the predominant analytical technique for the determination of a variety of pathogens. However, conventional plate-based heterogeneous IA is a multistage, labor-intensive process that requires sequential loading different reagents, washing and incubation. It takes 4–5 h, and requires skilled technicians. In order to reduce the human error during the bench-top immunoassay processes, automation of immunoassay has focused on the development of robotic systems for solution handling in microarray-based immunoassay. However, the microarray immunoassays depend on a complex robotic system for solution manipulation, and hence are limited to be used in large hospitals only. Miniaturization of the immunoassay has been researched and different assay formats have been tested in microfluidic systems since late 1990s.

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Stokes et al. [22] used sandwiched immunoassay with mixed cellulose membrane for solid support. The antigens were immobilized into an array pattern, resembling the dot-ELISA strategy, to detect multiple bacteria. However, their method involves using mechanical pumps that are prone to breakdown and leakage, and has no portability. Dodge et al. [23] utilized electroosmotically-pumped flow for a microchannel immunoassay. In their experiments the entire channel was first coated with an antibody layer, which subsequently reacted with each component of the immunoassay. The final product was detected by laser excitation of a Cy5 conjugate. This strategy lacks the multiplex capability of the dot-ELISA array design because the microchannel was coated with only one concentration of antibody. It should be pointed out that, in Dodge’s work, the assay was done manually for all the steps. Similarly, in the works of Sia et al. [24] and Kartalov et al. [25], other than the reaction occurred in a microchannel, the fluid manipulation was done manually for all the steps, and complex external steel tubes, valve arrays, and plumbing were required to supply reagents to the channels. They used a fluorescence microscope for detection. Therefore, the whole IA system depends on a conventional lab, and is not a portable device. The critical issues to develop a practical immunoassay lab-on-a-chip technology are integration, automation, multiplexity and portability. An immunoassay lab-on-a-chip device must perform the following microfluidic functions: pumping, flow switching, incubating, sequentially loading solutions and washing. A very large pressure gradient is required to generate liquid flow in microfluidic devices since the flow resistance is reversely proportional to the fourth power of transverse channel dimension. It will be impractical and difficult to use pressure-driven flow to control the sequential loading and washing processes in a portable microfluidic system. Alternatively, electrokinetic forces can be used to drive liquid flow in microchannels. In a microfluidic chip, there are a number of wells at the ends of the microchannel branches. These wells provide not only reservoirs for samples and reagents, but also the connection of electrodes to liquid in the microchannels. The liquid flow control is realized by applying different voltages to different wells simultaneously. In this way we can control the flow rate, and let one solution flowing through a microchannel in the desired direction while keeping all other solutions stationary in their wells and channels. In a recent work, Li’s group has developed a simple electrokineticallycontrolled IA chip, as shown in Fig. 11, for detecting H. pylori and E. coli [26–28]. In this chip, an H-shaped microchannel network was fabricated using PDMS. The operation parameters (i.e., the applied voltage at each electrode and the duration) obtained from numerical simulation were applied to a desktop DC voltage sequencer to control the IA chip operation. Multiantigen immobilization was accomplished by adsorbing the antigen molecules onto a PDMS-coated glass slide with the aid of a microfluidic network.

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Immobilized lysate antigen of E. coli O157: H7 at different concentrations was assayed and the low detection limit was 3 μg/mL. The assay also demonstrated very good specificity: different microbial lysate antigens were immobilized, including E. coli and H. pylori, and the primary and secondary antibodies were mixtures of different species. The assay time is only 25 min (the conventional lab based assay requires over 3 h); the sample consumed was less than 12 μL. While still an un-optimized chip, this IA chip shows a great potential in detecting multiple pathogen efficiently. More recently, the development of an electrokinetically-controlled, highthroughput immunoassay for testing multiple clinical samples against PDMS layer

Glass slide

Figure 11. Picture of an immunoassay chip with a H-shaped microchannel, and the sequential steps of an automatic IA processes. The surface of the reaction channel wall is coated with probing antigens. The solution delivery occurs in the dark colored channels whereas in the light colored channels, the solution remains stationary. The arrows indicate the flow direction. (a) Dispensing and incubation of the primary antibody; (b) washing off the primary antibody by a buffer solution; (c) dispensing and incubation of the secondary antibody; (d) washing off the secondary antibody by a buffer solution.

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multiple pathogen targets was reported [29]. The microfluidic design of this immunoassay chip can be seen from Fig. 12. The automatically controlled sequential microfluidic processes are shown in Fig. 13. With effective control of the microfluidic transport process in a compact microfluidic network, this microfluidic immunoassay lab-on-a-chip is capable of detecting ten samples simultaneously in 22 min. E. coli O157:H7 antibody and H. pylori antibody in buffer solutions were detected down to 0.02 μg/mL (130 pM) and 0.1 μg/mL (670 pM), respectively. The microfluidic immunoassay was also applied to screen for E. coli O157:H7 antibody or H. pylori antibody from human serum. In the 18 samples of human serum tested, E. coli O157:H7-positive or H. pylori-positive sera were accurately distinguished from the corresponding negative sera. Simultaneous screening of both antibodies from human serum was also proved feasible. With non-specific binding effectively suppressed by 10% (w/v) BSA, the assay results showed no evidence of adsorption of serum proteins to channel walls and consequent disturbance to electrokinetic transport. These results, thus, prove the applicability of electrokineticallydriven heterogeneous immunoassay chip to clinical environments (Fig. 14).

Immobilized probing

Figure 12. Illustration of the microchannel network in the multiplex immunoassay chip.

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Figure 13. Steps in the electrokinetically-controlled immunoassay. Arrows indicate flow direction. Solid arrows stand for major flows, and dashed arrows, minor flows. (a) Loading and incubation of samples. Sample solutions were dispensed from the sample wells to the reaction region and discharged into the waste well. (b) Washing of samples. Buffer solution flushed sample solutions from the reaction region back into the sample wells. (c) Second washing of samples. Sample solutions having entered the antibody channel during the previous three steps were flushed into the waste well. (d) Loading and incubation of detection antibody. (e) Washing of detection antibody.

Figure 14. Simultaneous detection of both antibodies from human serum. Antigens of H. pylori and E. coli O157:H7 were coated alternately, as indicated at the bottom of the image. Samples are labeled from S1 to S10 and the contents of the each sample are indicated on the right side of the image. Capital “P” or “N” denotes a positive or negative sample, respectively. For S1 to S7, the dilution of serum was 1:100. S8 and S9 were mixed samples of H. pylori-positive and E. coli O157:H7-positive serum. The overall serum dilution was 1:50 for S8 and S9, in order to match the concentration of each antibody to that in the corresponding unmixed serum. For example, the concentration of H. pylori antibody in S1 and S8 were equivalent.

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5. Summary Electrokinetic microfluidics provides important tools for transforming many processes of conventional labs into on-chip processes, making it possible to miniaturize many biochemical and biomedical methods and control the operation of the lab-on-a-chip devices. This article does not intend to provide a comprehensive review on the three lab-on-a-chip devices discussed here. By reviewing the real-time PCR lab-on-a-chip device (or bio-chemical reactor chip), flow cytometer lab-on-a-chip device and immunoassay labon-a-chip device, this article attempts to illustrate how biochemistry, microfluidics, optic detection and electronic control can be integrated to develop lab-on-a-chip technology for practical applications such as in medical diagnosis, and food safety. It is clear that significant advances are needed before we cam reach this goal, particularly in integration, automation, multiplexity and portability.

References 1. Dongqing Li, “Electrokinetics in Microfluidics”, Academic, London, 2004. 2. G. Hu, Q. Xiang, R. Fu, B. Xu, R. Venditti, and D. Li, Electrokinetically controlled real-time PCR in microchannel using Joule heating effect. Analytica Chimica Acta, 557, 146–151 (2006). 3. Y. Liu, C. B. Rauch, R. L. Stevens, R. Lenigk, J. Yang, D. B. Rhine, and P. Grodzinski, DNA amplification and hybridization assays in integrated plastic monolithic devices, Analytical Chemistry, 74, 3063 (2002). 4. Y. C. Lin, C. Yang, and M. Y. Huang, Simulation and experimental validation of micro polymerase chain reaction chips, Sensors and Actuators B: Chemical, 71, 127 (2000). 5. H. Nagai, Y. Murakami, K. Yokoyama, E. Tamiya, and Y. Morita, Development of microchamber array for picoliter PCR. Analytical Chemistry, 73, 1043 (2001). 6. Y. Matsubara, K. Kerman, M. Kobayashi, S. Yamamura, Y. Morita, Y. Takamura, and E. Tamiya, On-chip nanoliter-volume multiplex TaqMan polymerase chain reaction from a single copy based on counting fluorescence released microchambers. Analytical Chemistry, 76, 6434 (2004). 7. M. U. Kopp, A. Mello, and A. Manz, Chemical amplification: continuous-flow PCR on a chip, Science 280, 1046 (1998). 8. I. Schneegass, R. Brautigam, and J. M. Kohler, Miniaturized flow through PCR with different temperature types in a silicon chip thermocycler. Lab on a Chip, 1, 42–9 (2001). 9. P. J. Obeid, T. K. Christopoulos, H. J. Crabtree, and C. J. Backhouse, Microfabricated device for DNA and RNA amplification by continuous-flow polymerase chain reaction and reverse transcription polymerase chain reaction with cycle number selection, Analytical Chemistry, 75, 288 (2003).

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10. M. Hashimoto, P. C. Chen, M. W. Mitchell, D. E. Nikitopoulos, S. A. Soper, and M. C. Murphy, Rapid PCR in a continuous flow device, Lab on a Chip 4, 638 (2004). 11. J. Liu, M. Enzelberger, and S. Quake, A nanoliter rotary device for polymerase chain reaction, Electrophoresis, 23, 1531 (2002). 12. K. Sun, A. Yamaguchi, Y. Ishida, S. Matsuo, and H. Misawa, A heaterintegrated transparent microchannel chip for continuous flow PCR, Sensors and Actuators B: Chemical, 84, 283 (2002). 13. Q. Xiang, B. Xu, and D. Li, Miniature real time PCR on chip with multichannel fiber optical fluorescence detection module, Biomedical Microdevices, 9, 443–449 (2007). 14. Q. Xiang, B. Xu, R. Fu, and D. Li, Real Time PCR on Disposable PDMS chip with a miniaturized thermal cycler, Biomedical Microdevices, 7, 273–279 (2005). 15. Y. C. Tung, M. Zhang, C. T. Lin, K. Kurabayashi, and S. J. Skerlos. PDMSbased opto-fluidic micro flow cytometer with two-color, multi-angle fluorescence detection capability using PIN photodiodes. Sensors and Actuators B: Chemical, 98, 356–367 (2004). 16. L. M. Fu, R. J. Yang, C. H. Lin, Y. J. Pan, and G. B. Lee, Electrokinetically driven micro flow cytometers with integrated fiber optics for on-line cell/particle detection. Analytica Chimica Acta, 507, 163–169 (2004). 17. Q. Xiang, X. Xuan, B. Xu, and D. Li, Multi-functional particle detection with embedded optical fibers in a poly(dimethylsiloxane) chip, Instrumentation Science & Technology, 33, 597–607 (2005). 18. X. Wu, Y. Kang, Y. N. Wang, D. Xu, Deyu Li, and Dongqing Li, Microfluidic differential resistive pulse sensor, Electrophoresis, 29, 2754–2759 (2008). 19. X. Wu, C. Chon, Y. Kang, Y. Wang, and D. Li, Simultaneous particle counting and detecting on a chip, Lab-on-Chip, 8, 1943–1949 (2008). 20. Y. Kang, X. Wu, Y. Wang, and D. Li, On-chip fluorescence-activated particle counting and sorting system, Analytica Chimica Acta, 626, 97–103 (2008). 21. Y. N. Wang, Y. Kang, D. Xu, L. Barnett, S. A. Kalams, Deyu Li, and Dongqing Li, On-chip total counting and percentage determination of CD4+ T lymphocytes, Lab-Chip, 8, 309–315 (2008). 22. D. L. Stokes, G. D. Griffin, and T. Vo-Dinh, Detection of E. coli using a microfluidics-based antibody biochip detection system, Fresenius Journal of Analytical Chemistry, 369, 295–301 (2001). 23. A. Dodge, K. Fluri, , E. Verpoorte, and N. F. de Rooij, Electrokinetically driven microfluidic chips with surface-modified chambers for heterogeneous immunoassays, Analytical Chemistry, 73, 3400–3409. 24. S. K. Sia, V. Linder, B. A. Parviz, A. Siegel, and G. M. Whitesides, An integrated approach to a portable and low-cost immunoassay for resource-poor settings, Angewandte Chemie-International Edition, 43, 498–502 (2004). 25. E. P. Kartalov, J. F. Zhong, A. Scherer, S. R. Quake, C. R. Taylor, and W. F. Anderson, High-throughput multi-antigen microfluidics fluorescence immunoassays, BioTechniques, 40, 85–90 (2006). 26. Y. Gao, F. Lin, G. Hu, P. Sherman, and D. Li, Development of a novel electrokinetically-driven microfluidic immunoassay for detection of Helicobacter pylori, Analytica Chimica Acta, 543, 109–116 (2005).

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27. G. Hu, Y. Gao, P. Sherman, and D. Li, A Microfluidic chip for heterogeneous immunoassay using automatic electrokinetical control, Microfluidics and Nanofluidics, 1, 346–355 (2005). 28. Y. Gao, G. Hu, P. Sherman, and D. Li, An automatic electrokineticallycontrolled immunoassay lab-on-a-chip for simultaneous detection of multiple microbial antigens, Biomed Microdevices, 7, 301–312 (2005). 29. Y. Gao, P. Sherman, Y. Sun, and D. Li, A multiplexed high-throughput electrokinetically-controlled immunoassay for the detection of bacterial antibodies in human serum, Analytica Chimica Acta, 606, 98–107 (2008).

CHIP BASED ELECTROANALYTICAL SYSTEMS FOR MONITORING CELLULAR DYNAMICS A. HEISKANEN, M. DUFVA, AND J. EMNÉUS

Department of Micro- and Nanotechnology, Technical University of Denmark, Ørsteds Plads 345 East, DK-2800 Kgs. Lyngby, Denmark, [email protected]

Abstract. Electroanalytical methods are highly compatible with micro- and nano-machining technology and have the potential of invasive but “nondestructive” cell analysis. In combination with optical probes and imaging techniques, electroanalytical methods show great potential for the development of multi-analyte detection systems to monitor in real-time cellular dynamics.

1. Introduction In cell biology and pharmacology, the determination of cellular functions and responses to exogenous effectors is a general part of the scientific quest. However, assays that, for instance, determine the activity of an enzyme upon induction of gene expression are customarily conducted after the cells have been lysed, and the resulting cell extract or a further purified enzyme fraction is used for the assay [1]. Furthermore, high-throughput screening (HTS) of compound libraries in drug discovery has strongly relied on assays conducted using purified or isolated targets, i.e. enzymes, ion channels, signaling proteins as well as cell surface- and nuclear receptors [2]. The fundamental question is: How reliable and true are the obtained results that are based on an isolated fraction of the whole system, i.e. a cell, organ or organism? In a living cell, the different cellular functions and subcellular compartments, although to a certain degree autonomous, they are at the same time strongly dependent on feedback from each other. As examples can be mentioned the activity of enzymes that transfers electrons to or from different cellular metabolites, such as glucose, which is the main energy source of mammalian cells, and the activation of G protein coupled receptors (GPCRs) that mediate external signals upon binding of a ligand to the receptor, giving rise to an intracellular cascade of biochemical events, leading to the execution of a certain function. The significance of cell-based assays as a source of information that yields a more holistic view of the cellular dynamics, i.e. the interaction of S. Kakaç et al. (eds.), Microfluidics Based Microsystems: Fundamentals and Applications, DOI 10.1007/978-90-481-9029-4_19, © Springer Science + Business Media B.V. 2010

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biological functions in general and the intercompartmental biological effect of different compounds has been recognized in HTS of compound libraries in drug discovery. The advantages are associated with the involvement of the entire cellular environment as the modulator of the monitored responses whether these are primarily connected to the activation of GPCRs, ion channels or enzyme activity. If an assay involves binding of a ligand to a receptor (target), this takes place in the real biological environment of the target. Additionally, when the target is located in the intracellular environment, a cell-based assay also gives possibility to screen for secondary cellular events (multi-parameter monitoring) as well as bioavailability of the used test compounds [3]. Work featuring methods and techniques for assaying biological parameters in the context of intact cells comprise e.g. intracellular [4] and extracellular [5] monitoring of oxygen consumption, monitoring of enzyme activity and cofactor availability [6–9], cellular adhesion [10] as well as cellularly released secondary metabolites [11, 12] and G-protein coupled receptor (GPCR) activation [13]. Although cell-based assays have been strongly implemented in drug discovery, they are primarily in microtiter plate format, including applications for even 1,536 well-plates [14] and screening of compound libraries of 100,000 compounds [15]. Implementation of cell-based assays in HTS suffers, however, from problems caused by the microtiter plate format. These concern reliability of temperature and CO2 control in the incubator as well as increased evaporation and difficulties involved in liquid handling due to the large number of wells comprising an extremely small volume [15]. The emergence of perfusion based microfluidic cell culture chips (see Chapter “Perfusion Based Cell Culture Chips” of this book) with the inherent technological capability to undergo sufficient miniaturization and parallelization represents a new trend that can both alleviate the drawbacks of microtiter plate based assays and facilitate real-time monitoring of cellular dynamics instead of only end-point detection. 2. Detection of Cellular Dynamics 2.1. DETECTION TECHNIQUES

2.1.1. Fluorescence Detection As consequence of implementation of parallelization in microfluidic cell culture chips, detection of biologically relevant cellular parameters imposes further requirements on the development of the applied detection techniques. Using available motorized microscope stages, time-lapse fluorescence microscopy is a widely applied technique in monitoring cellular responses. Alternatively, fluorescent plate readers facilitate real-time monitoring in highly parallelized systems (readouts for 1,536 well microtiter plate format).

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Implementation of fluidic functions inside a plate reader is however not a straightforward task. For short-term detection, the chip depicted in Fig. 10f [16] in the Chapter “Perfusion Based Cell Culture Chips” of this book could be amenable for use with a plate reader since its function does not require any external pump. However, for long- term real-time monitoring, this system is not suitable due to the need for a CO2 incubator. An alternative approach could be based on a multichannel pump, suitable for integration with a polymeric microfluidic cell culture chip independent of a CO2 incubator. The pump shown in Fig. 10b [17] in the Chapter “Perfusion Based Cell Culture Chips” of this book could function as the basis for such an approach. Fluorescence based monitoring of dynamic cellular processes is not, however, a complete solution to the need of detection in cell culture systems. Long-term monitoring causes photobleaching of fluorophores and photodamage to the cells in the case of autofluorescence detection [18]. To alleviate the problem with photobleaching [19] and photodamage [20], twophoton excitation microscopy has emerged as a microscopic technique. However, the required instrumentation is expensive and the technique itself does not facilitate easy automation and high-throughput monitoring. Furthermore, fluorescence detection, in general, is not suitable for monitoring of all relevant parameters of cellular dynamics. For instance, monitoring of calcium triggered vesicular release (exocytosis) of cellular secondary metabolites, such as the neurotransmitter dopamine or hormone insulin, is not possible directly using fluorescence detection. Only indirect detection of the process has been demonstrated using, for instance, internal reflection fluorescence microscopy of co-exocytosed fluorescent dye upon loading of cellular vesicles [21]. 2.1.2. Electrochemical Detection In many cases, monitoring of cellular dynamics involves detection of molecules that are either released or taken up by the cells. Monitoring of such parameters comprises (i) nutrients and primary metabolites (e.g. glucose [22], lactate [23] and oxygen [5]), (ii) secondary metabolites, such as neurotransmitters (e.g. dopamine [12] and glutamate [11]) and hormones (e.g. insulin [24]), and (iii) compounds resulting from xenobiotic1 metabolism and physical stress (e.g. hydrogen peroxide and superoxide radical [25], glutathione conjugates [26] quinones [27] and quinols [28]). All the listed compounds are examples of species that can be detected electrochemically either directly as electroactive species or by using enzymes as the biorecognition element.

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In xenobiotic metabolism, foreign compounds, such as drugs and toxicants, are enzymatically detoxified.

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Figure 1 illustrates the detection scheme of such cellular factors: Extracellularly placed electrodes are used to detect compounds that are produced in cellular metabolism and released by the cells either based on active transport or diffusion through the plasma membrane. Analogously, compounds used by the cells in their metabolism are taken up from the extracellular environment and consequently the decrease in concentration is detected.

Figure 1. A schematic illustration of electrochemical monitoring of cellular dynamics. An extracellularly placed electrode is used to detect cellular release and uptake of molecules.

Traditionally, extracellular microelectrodes that have been used to detect, for instance, release of compounds have been placed adjacent to the cell body using a micromanipulator [29] or scanning electrochemical microscope (SECM) [27]. Such measurements are normally conducted using cells that form a part of a population in a culture vessel, such as a Petri dish. Although the published results, have contributed to a highly accurate and mechanistic description of the studied biological phenomena based on single-cell measurements, the approach to use micromanipulated microelectrodes has some severe drawbacks. Detection cannot be automated and throughput is limited. Furthermore, the required instrumentation and operational skills are beyond what normally are needed for electrochemical detection. A new approach has emerged that applies microchips having planar microelectrodes on a substrate, most commonly an oxidized surface of a silicon wafer (for fabricational aspects, see [30]), simultaneously functioning as the substrate, on which cells either sediment or grow. The approach to use chip based electroanalytical systems to monitor the dynamics of processes in living cells facilitate the possibility to integrate the detection systems to microfluidic cell culture chips. In virtue of the functional principle of such systems, cells can be cultured on the platform where detection takes place. Hence, the measurements can be conducted in an environment that has been tailor-made for proper adaptation to the requirements of the cultured cells. Furthermore, such miniaturized systems possess the capability to achieve operational automation and facilitate measurements

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on a small population of cells or even single cells. Aside from single-cell measurements, the miniaturization of systems, comprising a microfluidic cell culture chip with an integrated microchip for electrochemical detection, also enables utilization of small amounts of chemicals that are needed as cellular effectors to, for instance, trigger certain metabolic responses. This feature facilitates cell-based assays with a high degree of parallelization without extensive increase in the incurred expenses. Electrochemical measurements on cells are primarily conducted using impedimetric [10], potentiometric [31] and amperometric measurements [12]. In this chapter, amperometric measurements are described based on examples comprising monitoring of cellular redox environment and detection of exocytosis, i.e. Ca2+-triggered release of cellular secondary metabolites, e.g. the neurotransmitter dopamine [12]. In amperometric measurements, most commonly, a three-electrode configuration controlled by a potentiostat is applied: A microelectrode functioning as the working electrode (WE) is in direct contact with the cells the measurements are to be conducted on and has a certain poised potential, at which the detected chemical species is either oxidized2 or reduced. A reference electrode (RE) is used under potentiostatic control to adjust the applied potential of the WE with respect to the third electrode, the counter electrode (CE),3 which is the site of the electrochemical process complementary to the one taking place at the WE. If oxidation of a chemical species involving the donation of n electrons is detected at the WE, a corresponding number of electrons are accepted arbitrarily at the CE by any chemical species in the electrolyte that is used as the medium of measurements. Hence, the electrochemical processes taking place at the electrode–electrolyte interface of the WE and CE together with the potentiostat form a closed electrical circuit that facilitates movement of electrons that can be registered as a faradaic current. The faradaic current (I), according to Faraday’s law of electrolysis, is directly proportional to the number of moles of molecules oxidized or reduced (Eq. (1)):

I=

Q nFn x = t t

(1)

where Q is the total charge carried by the electrons that are accepted or donated, t is the time during which the current is recorded, n is the number

______

2 In amperometry, oxidation refers to donation of a number of electrons from a chemical species to an electrode and reduction refers to acceptance of a number of electrons by a chemical species from an electrode. 3 In electrochemical literature, counter electrode is oftentimes also called auxiliary electrode.

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of accepted or donated electrons, F is the Faraday constant (96,485 C mol–1) and nx is the number of moles of the chemical species oxidized or reduced. In amperometry, the applied potential at the WE is chosen to provide a sufficient driving force, overpotential, for the desired electrochemical process, i.e. oxidation or reduction. Each electroactive chemical species is characterized by a certain reduction potential (E°), at which the oxidized and reduced form of the species are in equilibrium.4 Since oxidation or reduction of different chemical species that are detected in biological systems is also pH dependent due to involvement of proton transfer, the formal potential (E°′) is used instead of reduction potential. The tabulated values of formal potential for different chemical species are usually valid at pH 7. The formal potential also implicitly comprises the contribution of activity coefficients. A sufficient overpotential for oxidation or reduction is obtained by poising the WE at a potential that is more positive or negative, respectively, than the formal potential of the detected species. This means that at the chosen potential, predominantly either oxidation or reduction takes place independent of whether both the oxidized and reduced component of the redox couple are present. For example, in a system containing the redox couple, ferrocyanide ([Fe(CN)6]4–)/ferricyanide ([Fe(CN)6]3–), which has the reduction potential 274 mV with respect to a Ag/AgCl5 RE [32], at an applied potential of 400 mV with respect to a Ag/AgCl RE, [Fe(CN)6]4– is oxidized whereas [Fe(CN)6]3– is not affected by the electrode process. Generally, the effect of an applied overpotential at a WE can be presented using an energy level diagram schematically depicting the energy levels of the electrons in the electrode material as well as the lowest unoccupied (LU) and highest occupied (HO) molecular orbital (MO). When the overpotential is sufficiently positive, to make the energy of electrons in the electrode material lower than that of the energy of the HOMO of the species to be oxidized, electrons can be donated to the electrode, resulting in oxidation (Fig. 2A). In the opposite case, a negative potential rendering the

______ 4

At equilibrium, the oxidized and reduced form of an electroactive species, collectively termed as redox couple, are reduced and oxidized, respectively, at an equal rate. 5 Most often, the tabulated values of formal potential are given with respect to the normal hydrogen electrode (NHE), which has the defined potential 0 V. However, in practise, a silver/silver chloride (Ag/AgCl) electrode or a plain metal surface (e.g. Au or Pt) is commonly used as a RE. An Ag/AgCl RE, having an internal electrolyte of saturated KCl, has a characteristic potential of 197 mV with respect to the NHE. A plain metal surface, on the other hand, does not have a characteristic potential that can be expressed in terms of NHE. Instead, its potential depends on the prevailing conditions, affected by the deposited species and the electrolyte. E.g., if a Au surface is used as an RE to adjust the potential of, for instance, another Au surface (WE), both the RE and WE are affected by the same conditions. The equilibrium potential between such electrodes is ideally 0 V and a poised potential is directly an overpotential with respect to the equilibrium potential.

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electrons in the electrode material with an energy higher than that of the energy of the LUMO of the species to be reduced, electrons can be donated by the electrode, resulting in reduction (Fig. 2B).

Figure 2. Energy diagrams schematically illustrating oxidation-reduction (redox) reactions. (A) An electrode material with a sufficiently positive potential can accept an electron from the highest occupied molecular orbital (HOMO) of species A, which is oxidized (A → A+ + e−). (B) An electrode material with a sufficiently negative potential can donate an electron to the lowest unoccupied molecular orbital (LUMO) of species B, which is reduced (B + e− → B−).

3. Monitoring of Cellular Redox Environment 3.1. CELLULAR REDOX ENVIRONMENT

3.1.1. Cellular Redox Couples Organisms obtain the necessary energy and building blocks for cellular functions, such as locomotion, contraction and biosynthesis, from digested food. The main constituents of food, carbohydrates, fats and proteins, are digested to the monomers making up the biopolymeric structures. Carbohydrates consist of different hexoses, such as glucose, fructose and galactose. Fats are esters of glycerol and fatty acids with different length of carbon skeleton. Proteins are formed of amino acids through amide

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linkages. The resulting hexoses, glycerol, fatty acids and amino acids are taken up by cells, where they undergo further degradation, i.e. catabolic processes. Partly, products of the catabolic processes are utilized for synthesis of new biomolecules needed for building new cellular material to maintain the cellular structures and sustain the needs of growth, i.e. anabolic processes. However, these processes require energy, which also comes from the catabolic processes. In order not to release the entire energy contents in one single process, which would be too exothermic for the cells to bear, the cells may store the energy in the form of catabolic intermediates, e.g. reduced cofactors nicotinamide adenine dinucleotide (NADH) and nicotinamide adenine dinucleotide phosphate (NADPH) as well as acetyl coenzyme A (Acetyl-CoA), the energy of which can be released in subsequent processes to synthesize, for instance, adenosine-5′-triphosphate (ATP) for energy requiring cellular processes. Collectively, NADH and NADPH as well as the corresponding oxidized forms, NAD+ and NADP+, respectively, are referred to as cellular redox couples. Examples of other redox couples are flavin adenine dinucleotide (FAD-FADH2) involved in metabolic processes, and glutathione (GSSG-GSH) involved in cellular detoxification processes to alleviate, for instance, oxidative stress. The general functional principle of cellular redox couples is to participate in enzymatic processes catalyzing oxidation or reduction of nutrients and other biomolecules. The oxidized form of a redox couple functions as an electron acceptor, whereas the reduced form functions as an electron donor. 3.1.2. Definition of Cellular Redox Environment Each of the cellular redox couples has a characteristic formal potential, the value of which is valid under equimolar composition of the oxidized and reduced form. However, the functions of living cells require a nonequimolar composition. For instance, in the case of the redox couple NADP+-NADPH, the ratio [NADP+]/[NADPH] 0), the particle is attracted to high intensity electric field regions. This is termed as positive dielectrophoresis (pDEP). Conversely, if the particle is less polarisable than the medium, ( Re ⎡⎣ f%CM ⎤⎦ < 0), the particle is repelled from high intensity field regions and negative dielectrophoresis (nDEP) occurs. Therefore the real part of the Clausius–Mossotti factor characterizes the frequency dependence of the DEP force, as demonstrated in Fig. 1. In practice, it is difficult to measure the DEP force due to the effects of Brownian motion and electrical field-induced fluid flow [3]. Instead, the DEP crossover frequency can be measured as a function of medium conductivity and provides sufficient information to determine the dielectric properties of the suspended particles. The DEP crossover frequency, fcross, is the transition frequency point where the DEP force switches from pDEP to nDEP or vice versa. According to Eq. (6), the crossover frequency is defined to be the frequency point where the real part of the Clausius– Mossotti factor equals zero: f cross =

1 2π

(σ m − σ p )(σ p + 2σ m ) (ε p − ε m )(ε p + 2ε m )

=

1

σm −σ p

2π

ε p − εm

f MW

(9)

where fMW is again the Maxwell-Wagner relaxation frequency, labeled in Fig. 1. In addition to measurements of crossover frequency, the DEP-induced particle velocity can be measured to characterize particles. The DEP induced particle velocity, uDEP, is directly proportional to the DEP force [4] according to:

u DEP =

⎞ FDEP ⎛ F + ⎜ u0 − DEP ⎟ e − t / tm 6π Rη ⎝ 6π Rη ⎠

(10)

where η is the viscosity of the medium and u0 is the initial velocity. The time constant tm is referred to as the momentum relaxation time and is: tm =

m 6π Rη

(11)

where m is the mass of the particle. For a typical cell the momentum relaxation time is of the order of tens of microseconds and can be ignored.

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Therefore in practice, a measurement of particle velocity is a direct measure of the force on that particle 2.3. TRAVELLING WAVE DIELECTROPHORESIS

Masuda et al. [5, 6] were the first to demonstrate that travelling electric fields, generated by sequentially phase-shifted AC voltages, can be used to induce translational motion of particles. Practically, for travelling wave dielectrophoresis (twDEP) to occur, the particle should experience nDEP and be levitated above the electrodes. In a travelling field it experiences a linear force propelling it along the electrode array. Fuhr et al. [7] presented a theoretical model to explain the behavior of microparticles in a travelling electric field generated with a linear array of electrodes. Huang et al. [8] used interdigitated electrodes of comb geometry (Fig. 4) to generate travelling electric fields, established by sequentially addressing the electrodes with a four-phase sinusoidal voltages (90° phase shift) and keeping directly opposing electrodes on either side of the channel phase-shifted from each other by 180°.

Figure 4. Diagram showing an interdigitated electrode array used to induce travelling wave dielectrophoresis. The cells move over the electrodes along the channel in the direction opposite to that of the travelling field. Cells on the left-hand (right-hand) side of the channel rotate in a clockwise (anti-clockwise) sense while moving.

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In electric fields with spatially varying phases, Eq. (6) can be expanded as:

( (

1 % 2 − 1 v Im [α% ] ∇ × Re ⎡E % % FDEP = v Re [α% ] ∇ E ⎣ ⎤⎦ × Im ⎡⎣E ⎤⎦ 4 2

))

(12)

For a spherical particle, Eq. (12) becomes:

( (

% 2 − 2πε R3 Im ⎡ f% ⎤ ∇× Re ⎡E % % FDEP = πε mR3 Re ⎣⎡ f%CM ⎦⎤ ∇ E m ⎣ ⎤⎦ × Im ⎡⎣E⎤⎦ ⎣ CM ⎦

)) (13)

The first term on the right is the DEP force. The second term on the right is the additional travelling wave dielectrophoretic force, which propels the particle moving along the electrode arrays. If there is no spatially varying phase, the imaginary part of the electric field is zero ( Im ⎡⎣E% ⎤⎦ = 0 ), which means there is no twDEP. Generally, in order to generate a twDEP force, the frequency of the excitation voltage and the conductivity of the medium should be chosen to satisfy two conditions: (i) the particle experiences nDEP so that it is levitated above the electrodes. (ii) the imaginary part of the Clausius–Mossotti factor is non-zero. As shown in Fig. 1, at low frequencies, the real part of the Clausius–Mossotti factor is positive, the imaginary part of the Clausius–Mossotti factor is zero except for the mid frequency range where twDEP is possible. 2.4. ELECTROROTATION

The action of an external electric field on a polarisable particle creates an induced dipole moment. The two ends of the dipole experience an equal and opposite force tending to align the dipole parallel to the field generating a torque and causing it to rotate. This phenomenon is called electrorotation (ROT). The direction and rate of rotation depends on the frequency and spatial configuration of the field and also the dielectric properties of the suspending medium and the particles. The phenomenon of ROT was explored in detail by Arnold and Zimmerman [9, 10]. ROT has been widely used in biotechnology, to measure the viability of cells and bacteria [11–14], biocide testing [15] and cell characterization [16–21]. The time-averaged torque on a particle is given by Jones [22]:

(

1 % * ⎤ = −v Im [α% ] Re ⎡E % % Γ ROT = Re ⎡p% × E ⎣ ⎤⎦ × Im ⎡⎣E ⎤⎦ ⎦ 2 ⎣

)

(14)

For a spherical particle, this becomes: %2 Γ ROT = −4πε m R3 Im ⎡⎣ f%CM ⎤⎦ E

(15)

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Equation (15) shows that the frequency-dependent property of the ROT torque depends on the imaginary part of the Clausius–Mossotti factor. The particle rotates with or against the electric field, depending on whether the imaginary part of the Clausius–Mossotti factor is negative or positive. If the charge relaxation time constant of the particle is smaller than that of the medium (τp = εp/σp < τm = εm/σm), the particle rotates with the field. If τm < τp, the particle rotates against the field. The torque is measured indirectly by analyzing the rotation rate (angular velocity) of the particle, given by Arnold and Zimmerman [10]: RROT (ω ) = −

ε m Im ⎡⎣ f%CM ⎤⎦ E% 2η

2

ξ

(16)

where RROT(ω) is the rotation rate and ξ is a scaling factor that accounts for the fact that neither the viscosity nor the electric field strength are precisely known. Again owing to the viscous nature of the system the momentum relaxation time is small resulting in a constant angular velocity that is proportional to the torque. Therefore the frequency spectra of both the DEP force and ROT torque provide information on the dielectric properties of biological particles in suspension. The relationship between DEP and ROT can be further examined using Argand diagrams [23, 24], where the real and imaginary parts of the Clausius–Mossotti factor are mapped onto the complex plane as a function of frequency. 2.5. MULTIPOLES

All the theories presented above are based on the dipole approximation. However, the dipole approximation can lead to significant inaccuracies for the case where the scale of the electric field non-uniformity is large compared to the size of the particle. For example, a particle at a field null will have no net induced dipole moment. Therefore the force on the particle will arise from induced higher-order moments, which are not considered in the dipole approximation. Multipolar theory has been developed by Jones [22, 25–27] and Washizu [28, 29] and Wang et al. [30]. Multipoles can be classified into the linear and general multipoles. For linear multipoles, as shown in Fig. 5a, the formation of a dipole can be considered as a monopole (a point charge) a certain distance away from another monopole of opposite sign. The quadrupole is formed by the superposition of an oppositely polarized dipole at a distance from the original dipole. The higher order multipole is formed in a similar method. The linear multipoles are applicable only when the electric field is axisymmetric, otherwise general multipoles

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should be used. For general multipoles, every order of multipole is composed of several dipoles. The moment of order n + 1 is formed by two closely spaced nth order moment of opposite polarity as shown in Fig. 5b.

Figure 5. Diagram showing the generation of multipoles (a) linear multipoles (b) general multipoles.

Calculations of the multipolar force and torque can be performed using the effective moment method [22]. Using the dyadic tensors, the nth order time-averaged multipolar DEP force F ( n ) DEP , and ROT torque Γ ( n ) ROT are given by Jones and Washizu [27]: F

Γ

(n)

(n)

ROT

⎡ ⎤⎤ 1 ⎢ 1 ⎡⎢ &&& ( n ) n n * ⎥ % = Re p% [⋅] ( ∇ ) E ⎥ 2 ⎢ n! ⎢ ⎥⎥ ⎦⎦ ⎣ ⎣

(17)

⎡ ⎤ ⎤ 1 ⎢ 1 ⎡⎢ &&& ( n ) n −1 n −1 *⎥ % ⎥ % = Re ×E p [⋅] ( ∇ ) ⎥ 2 ⎢ (n − 1)! ⎢ ⎥ ⎣ ⎦ ⎣ ⎦

(18)

DEP

&&&

For a spherical particle, the nth order of moment p% ( n ) and Clausius– Mossotti factor f% ( n ) are: CM

&&& 4πε m R 2 n +1n % ( n ) n −1 % %p ( n ) = f CM ( ∇ ) E (2n − 1)!!

(19)

492

H. MORGAN AND T. SUN (n) f%CM =

ε% p − ε%m nε% p + (n + 1)ε%m

(20)

According to Eq. (20), the multipolar DEP force and ROT torque on a particle can be determined as long as the electric field distribution in the system is known. 3. Particle Manipulation in Microsystems AC electrokinetic techniques, particularly DEP, have been used for the manipulation, separation, focusing, trapping and handling of latex spheres [31–34], viruses [35–39], bacteria [40–45] and cells [46–50]. Many different electrode geometries have been used to perform DEP. 3.1. CASTELLATED ELECTRODE ARRAY

The castellated electrode array was first used by Pethig’s group [40, 41] to dielectrophoretically collect particles. Similar configurations (e.g. sawtooth electrode array [36] and interleaved electrodes [47]) were used for separating biological particles [51–55]. Figure 6a, b shows a diagram of this type of electrode together with an electric field plot. Typical electrode dimensions are 10–100 μm width and gap. Note that the field is maximum at the electrode tips and minimum in the gaps between electrodes. Such an electrode array has been widely used to characterize the behavior of particles. Those experiencing pDEP collect on the tips, and those experiencing nDEP in the gaps. Figure 6c shows a diagram of this.

Figure 6. (a) Diagram showing the structure of castellated electrode array. (b) Numerical simulation showing the high and low electric field region within the electrode array. (c) Diagram showing the separation mechanism of colloidal particles using DEP in castellated electrode array.

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3.2. INTERDIGITATED ELECTRODE ARRAY

The interdigitated electrode array also generates field non-uniformities and is widely used for DEP and also twDEP. Figure 7 shows such an electrode showing the voltage sequence used for DEP. This design of electrode is often used in DEP separation systems, since it generates a DEP force that decays exponentially from the surface. Also twDEP can be generated in the same system using four signals with phase shifts of 90°, sequentially applied to the electrodes. This generates a travelling electric field with a spatially dependent phase.

Figure 7. Diagram showing an experimental system used for DEP or twDEP. The interdigitated electrode array is fabricated on a glass substrate and energized with different AC signals. For DEP, the electrodes are connected to voltages with 180° phase shifts. For twDEP, the electrodes are connected to a frequency generator with 90° phase shift. w is the electrode width, g is the electrode gap and h is the height of the channel.

A number of papers have derived analytical expressions for the electric field generated by this interdigitated electrode arrays. The methods include Green’s theorem [56], Green’s function [57, 58], half-plane Green’s function [59] and Fourier series [60, 61]. However, these analytical solutions all involve approximations. In both the Green’s theorem and Fourier series methods, it is assumed that the potential varies linearly with distance in the electrode gaps. In the method of Green’s function, the gradient of the electric field magnitude squared is influenced by the choice of a characteristic length scale. In the method of half-plane Green’s function, a linear approximation for the surface potential in the gaps between the electrodes is adopted. Moreover, the presence of the upper surface of the fluidic channels (the insulating lid in real devices), which imposes a Neumann condition on the solution of the potential, was not considered in Refs. [56–60]. In Ref. [61], this condition was analyzed using a closed form of Fourier series, but the solution approximates the potential distribution in the electrode gaps to a linear function. Other approaches, such as the charge density method [52]

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and finite element method [62] are accurate but computationally expensive. Recently, Sun et al. [63] used a Schwarz–Christoffel Mapping method to derive analytical solutions for the electric fields and the dielectrophoretic and travelling-wave dielectrophoretic forces for the interdigitated electrode arrays. The analytical solutions for the DEP and twDEP forces are related to the geometrical constant of the device: electrode length, gap distance and the channel height. Figure 8a shows that the DEP force (direction and magnitude) for the DEP interdigitated electrode array, demonstrating that while the DEP force vectors point towards the electrode edge. The maximum in the DEP force is at the electrode edge with four minima in each corner.

Figure 8. DEP force vectors and magnitude for an interdigitated electrode array. The electrodes are drawn in the figure. (a) The DEP force (direction and magnitude) for DEP. (b) The DEP force (direction and magnitude) in a twDEP array. (c) The twDEP force (direction and magnitude) in a twDEP array. (d) ROT component (magnitude) for twDEP (Sun et al. [63]).

Figure 8b shows the direction and the magnitude of the DEP force component for the twDEP array. The behaviour is similar to the DEP force in a DEP array. Above a certain height, the direction of the DEP force at every position points straight towards the electrode plane, with an exponentially decreasing magnitude. The DEP force magnitude plot clearly shows the maxima at the edges of the electrode. The minima in the centre of the

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electrodes and the gap can also be seen. Figure 8c shows the direction and the magnitude of the twDEP force component. Approaching the bottom, the vectors point in the opposite direction. In the region directly above the edges of the electrode, the vectors show a circular pattern. There are three twDEP force minima in the near field region. Along the surface of the electrode, the magnitude of twDEP force increases towards the edge of the electrode. However, it does not go to a maximum above the edge of the electrodes. Instead, it rapidly drops to a minimum over the electrode edge because the vectors are re-circulating in this region. Figures 8d shows the magnitude of the ROT torque in the twDEP array. The direction of the torque is in the third dimension (i.e. out of the page). The magnitude of the torque goes to a maximum at the edge of the electrode. 3.3. POLYNOMIAL ELECTRODES

The polynomial electrodes design has four electrodes with edges defined by a hyperbolic function in the centre and parallel edges out to an arbitrary distance. The theoretical principle of this electrode design has been described by Huang and Pethig [46]. The polynomial electrode can be used for trapping and characterization of biological particles [33, 37, 39] using either pDEP and nDEP, as shown in Fig. 9.

Figure 9. (a) Image showing pDEP of 557 nm diameter latex spheres on polynomial electrodes. (b) Image showing nDEP of 557 nm diameter latex spheres on polynomial electrodes (Green et al. [33]).

3.4. CONTINUOUS SEPARATION

A continuous DEP separation system was developed by Markx and Pethig [64]. Steric drag force produced by a gentle fluid flow in the chamber was used to separate cells by selectively lifting cells out of potential energy wells generated by the electric field. Holmes and Morgan [65] designed a continuous flowing DEP fractionation system, consisting of two separate arrays of interdigitated electrodes, as shown in Fig. 10a. The particles are

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first focused in the flow stream to a central plane of the flow channel by nDEP, and then attracted by pDEP to the separation electrodes (Fig. 10b).

Figure 10. (a) Schematic showing the continuous DEP separator. (b) Image showing separation of THP-1 cells (green) and PBMCs (red) (Holmes and Morgan [65]).

3.5. DEP FIELD-FLOW FRACTION SYSTEM

Field flow fraction (FFF) describes a method for separating particles based on combining a deterministic force with hydrodynamic separation. A typical configuration is shown in Fig. 11. The system consists of a channel with interdigitated microelectrodes patterned on the bottom substrate. Particles are introduced into the system and when the field is switched on they experience nDEP, moving to equilibrium positions which are defined according to the balance of dielectrophoresis (DEP) and gravity (buoyancy). Different types of particles move to different equilibrium positions in the

Figure 11. Diagram showing the principle of dielectrophoretic field-flow fractionation (DEP-FFF).

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system. Application of a laminar flow carries particles out of the device at a rate that depends on their original equilibrium position. Since different types of the particles are transported at different rates [66–69], a sample can be separated and fractionated along the channel. 3.6. INSULATOR-BASED DEP

Dielectrophoresis does not always have to be performed with conducting metal electrodes. For example, 3D insulating-post arrays [34, 44, 45] have been developed to trap and separate live and dead bacteria using DC voltages applied across the length of a microchannel. The insulating posts in the channel create obstructions in the pathways of the electric field producing non-uniformities in the electric field distribution in the channel, causing particle DEP, as shown in Fig. 12a. Here two different species of bacteria are dielectrophoretically trapped in two distinct regions (Fig. 12b).

Manifold

Reservoir opening Electric field lines being squeezed between the insulating posts

Vacuum line Reservoir

Region of lower field strength Negative dielectrophoresis

Microchannels containing insulating posts Electrode

post

Glass chip Outlet reservoir Inlet reservoir 10 µm height Electrode

Region of higher field strength Positive dielectrophoresis Flow direction

Flow direction

Figure 12. (a) Schematic showing the setup of the insulating-posts geometry and the principle of generating non-uniform electric field in the microchannel. (b) Image showing the separation of live (green) and dead (red) E. coli by creating 60 V/mm electric field (Lapizco-Encinas et al. [45]).

A continuous-flow dielectrophoretic spectrometer system has been developed based on insulating DEP techniques with three-dimensional geometries on an insulating substrate [70]. Different field gradients were generated by fabricating devices in polymers with constrictions in the channel depth to create a device that continuously separates particles with controls of transverse channel position. 3.7. SINGLE CELL TRAPPING

Single cell trapping is important in many applications of biotechnology, such as the study of cell-cell interaction, drug screening and diagnostics. Electric field cages that generate nDEP forces to trap single cells were

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introduced by Fuhr et al. [71] in the early of 1990s. Since then single cell trapping systems have been widely studied [72–81]. Müller et al. [72] used planar quadrupole electrode configuration to trap and concentrate micrometer and sub-micrometer particles. A 3-D microelectrode system [73] consisting of two layers of electrode structures was designed to focus, trap and separate cells and latex beads using nDEP. Schnelle et al. [75] fabricated an AC cage with octode electrode to trap cells against a fluid stream. Manaresi et al. [76] used 0.35 µm CMOS technology to fabricate a complex microelectrode array for manipulating a large number of individual cells.

Figure 13. Image showing the dynamic array cytometer consisting of single cell traps (Voldman et al. [78]).

Voldman and colleagues [77–82] developed multiple single cell DEP traps. Figure 13 is an example of an array of traps, made with sets of four electroplated gold electrodes arranged trapezoidally [78, 79]. The device is was used to obtain luminescence information of the trapped cells and also to sort them. An review of cell manipulation techniques using electrical forces has been published by Voldman [83]. Various electrode geometries such as the quadrupole and octopole electrode, nDEP microwells, point-and-lid geometry and ring-dot geometry are described and evaluated. Recently, a novel design of particle trap that uses nDEP in high conductivity physiological media was reported [84]. The single cell trap consists of a metal ring electrode and a surrounding ground plane, as shown in Fig. 14a. The ring electrodes creates a closed electric field cage in the centre (Fig. 14b). Figure 14c shows 15 μm diameter beads trapped against a fluid flow.

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Figure 14. (a) Diagram showing the structure of ring electrodes. The ring traps are fabricated from two Ti/Pt layers (yellow) with a benzocyclobutene dielectric layer (blue). (b) Numerical simulation showing DEP force vectors and electric field distribution in the ring trap. (c) Four 40 µm diameter ring traps from an array of 48 traps. Single beads are captured by nDEP (Thomas et al. [84]).

4. Scaling in AC Electrokinetic Microsystems Neglecting electrohydrodynamic forces, the two main forces that act on particles in addition to DEP are gravity and Brownian motion. As the size of the particle is reduced, so the effects of Brownian motion become greater. Therefore, to enable the dielectrophoretic manipulation of sub-micron particles using realistic voltages, the characteristic dimensions of the system must be reduced, to increase the electric field. However, a high strength electric field also produces a force on the suspending electrolyte, causing fluid flow [85]. Indeed, this motion may be a far greater limiting factor than Brownian motion. The force and velocity associated with Brownian motion have zero average. However the random displacement of the particle follows a Gaussian profile. To move an isolated particle in a deterministic manner during this period, the displacement due to the deterministic force should be greater than that due to the random (Brownian) motion. This consideration is meaningful only for single isolated particles. For a collection of particles, diffusion of the ensemble must be considered. Calculations of the typical displacements for particles can be made provided the electric field (and gradient) is known [86, 87]. The simplest

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geometry is a semi-infinite parallel plate structure, consisting of two coplanar rectangular electrodes with an infinitely small gap, as shown in Fig. 15a [85].

Figure 15. (a) Simple electrode geometry consisting of two parallel plate electrodes with a small gap used to calculate the typical particle displacements. (b) Particle displacement in one second versus particle radius for a particle of mass density 1,050 kg m−3. The characteristic length for used in this figure is r = 25 μm.

In this geometry, the field as a function of radial distance (r) is E = V/πr, where V is the amplitude of the applied voltage and r is the distance to the centre of the gap. The influence of Brownian motion, gravity and DEP on a single particle can be calculated for this electrode structure, and are summarized in Fig. 15b [85]. The plot shows the displacement of a particle during a time interval of one second as a function of particle radius, a. For a radius of 25 μm, at 5 V, it can be seen that the displacement due to Brownian motion is greater than that due to DEP if the particle is less than 0.4 μm diameter. Also, gravity is less important than DEP for any particle sizes, since both scales as a2. The deterministic manipulation of particles smaller than 0.4 μm can be achieved if the magnitude of the applied voltage is increased, or the characteristic length of the system r is reduced. The figure shows the effect of increasing the voltage by a factor of three, which increases the displacement due to DEP by one order of magnitude. Although Fig. 15b shows that it should be relatively easy to move small particles simply by increasing the electric field, this naïve assumption presumes that no other forces appear in the system. This is generally not the case, and the action of the electric field on the fluid must be considered. To summarize, the DEP force depends on the electric field gradient, which changes with the length scale of the electrodes; DEP is a short range effect. From the perspective of the design of microsystems for particle manipulation, different electrode shapes and sizes can be fabricated relatively easily. The forces scale in a complex manner with system dimensions, frequency, field, etc.

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5. Conclusions The behavior of particles and fluids on the microscale is determined by a number of forces. In AC field, the electrokinetic forces act on the induced dipole. Electrohydrodynamic forces are predominantly due to double layer charge or body forces due to gradients in conductivity and/or permittivity created by thermal gradients. In separation systems, buoyancy force can be significant (as in FFF) but often the magnitude of this force is much lower than the other forces for micron sized particles. The DEP force depends on the gradient of the energy density, which changes on the length scale of the electrodes and is a short range effect. The DEP force can be modulated by changing the frequency and electrical properties of the suspending medium. The electrokinetics forces scale in a complex manner with system dimensions, frequency, field etc. AC electrokinetic manipulation of particles and fluids is a powerful and flexible enabling technology which has many applications in microfluidic systems.

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MICROFLUIDIC IMPEDANCE CYTOMETRY: MEASURING SINGLE CELLS AT HIGH SPEED TAO SUN AND HYWEL MORGAN

Nano Research Group, School of Electronics and Computer Science, University of Southampton, SO17 1BJ, UK, [email protected]

Abstract. High throughput single cell microfluidic analysis platforms offer the ability to characterize large numbers of individual cells (or more generally particles) at high speed. Miniature flow cytometers offer new methods for the rapid analysis of single cells. Impedance analysis of single cells provides information on cell size (volume), membrane and cytoplasmic characteristics. The technology has developed rapidly and offers the prospects of new approaches for counting and differentiating cells with applications from basic research to point of care diagnostics.

1. Introduction Flow cytometry is a well established technique for counting, identifying and sorting cells [1, 2]. Modern commercial fluorescence-activated-cell-sorting (FACS) machines can analyze thousands of cells per second, but are generally expensive complex machines that are unsuited to handling small sample volumes. Lab-On-Chip (LOC) technologies [3–9], offer new approaches to cell assays, and new technologies are being developed for high speed cell manipulation. Individual cells can be identified on the basis of differences in size and dielectric properties using electrical techniques that are non-invasive and label-free. Characterization of the dielectric properties of biological cells is generally performed in two ways, with AC electrokinetics or impedance analysis. AC electrokinetic techniques are used to study of the behavior of particles (movement and/or rotation) and fluids subjected to an AC electric field. The electrical forces act on both the particles and the suspending fluid and have their origin in the charge and electric field distribution in the system. They are the basis of phenomena such as dielectrophoresis [10–14], travelling wave dielectrophoresis [15, 16], electrorotation [17, 18] and electroorientation [19].

S. Kakaç et al. (eds.), Microfluidics Based Microsystems: Fundamentals and Applications, DOI 10.1007/978-90-481-9029-4_24, © Springer Science + Business Media B.V. 2010

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Electrical impedance spectroscopy (EIS), measures the AC electrical properties of particles in suspension from which the dielectric parameters of the particles can be obtained. The earliest work on bio-impedance measurements can be traced back to the 1910s [20–22] that compared the low and high frequency conductivity of erythrocytes. The frequencydependence of the conductivity was measured (due to the cell membrane) and this paper was the first to estimate the conductivity of the interior of an erythrocyte. In 1924 and 1925, Fricke published a series of papers [23–25] that described the electrical conductivity and capacity of disperse systems using principles laid down by Maxwell [26]. Measurements of the capacitance of the suspending system [27–29] were used to estimate the capacitance and thickness of the cell membrane. Cole [30, 31] used Maxwell’s mixture equation to derive the complex impedance of a single shell cell in suspension. Schwan pioneered the field of cell impedance analysis [32, 33], and identified three major dielectric dispersions (α, β and γ) in biological cells. The dispersion occurring at the lowest frequency is the α-dispersion which is attributed to polarisation of the double layer around a colloidal particle. The β-dispersion occurs in the MHz regime and originates from charging of the capacitive cell membrane. It is the most widely measured and used to determine cell membrane capacitance. Schwan’s contributions to the dielectric measurements of biological material have been summarized by Foster [34]. 2. Theory Impedance is the ratio of the voltage across a system to the current passing through the system. It measures the dielectric properties (permittivity and conductivity) of the system. The dielectric behavior of colloidal particles in suspension is generally described by Maxwell’s mixture theory [26]. This relates the complex permittivity of the suspension to the complex permittivity of the particle, the suspending medium and the volume fraction. Based-on Maxwell’s mixture theory, shelled-models have been widely used to model the dielectric properties of particles in suspension [35–40]. A single shelled spherical model is shown in Fig. 1a. The complex permittivity of the mixture is ε%mix :

ε%mix = ε%m

1 + 2Φf%CM 1 − Φf%CM

with

ε% p − ε%m f%CM = ε% p + 2ε%m

(1)

where ε% = ε − jσ / ω is the complex permittivity, j2 = −1, ω the angular frequency, f%CM is the Clausius–Mossotti and Ф is the volume fraction. The subscripts p and m refer to particle and medium respectively.

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Figure 1. (a) Diagram of a single shelled spherical particle, representing a cell in suspension. (b) Plot showing the real and imaginary parts of the Clausius–Mossotti factor of the mixture, calculated for different conductivities of the medium. The following parameters for the medium and a cell were used: εo = 8.854 × 10−12 Fm−1, R = 3 × 10−6 m, d = 5 × 10−9 m, εm = 80 × εo, εmem = 5 × εo, σmem = 10−8 Sm−1, εi = 60 × εo, σi = 0.4 Sm−1.

The complex permittivity of the cell, ε% p is a function of the dielectric properties of membrane and cytoplasm, cell membrane ε%mem and internal properties ε%i , and cell (inner radius R and membrane thickness d) given by:

ε% p = ε%mem

⎛ ε%i − ε%mem ⎞ ⎟ ⎝ ε%i + 2ε%mem ⎠ with γ = R + d R ⎛ ε% − ε% ⎞ γ 3 − ⎜ i mem ⎟ ⎝ ε%i + 2ε%mem ⎠

γ 3 + 2⎜

(2)

The Clausius–Mossotti factor f%CM , characterizes the frequency-dependent effective dipole moment. Separating the real and imaginary part of the Clausius–Mossotti factor give a Debye relaxation of the form: ⎛ σ p − σ m ⎞ ⎛ ε p − εm ⎜ ⎟−⎜ ⎛ ε p − ε m ⎞ ⎜⎝ σ p + 2σ m ⎟⎠ ⎜⎝ ε p + 2ε m + Re ⎡⎣ f%CM ⎤⎦ = ⎜ 2 ⎜ ε p + 2ε m ⎟⎟ 1 + ω 2τ MW ⎝ ⎠

⎞ ⎟⎟ ⎠

(3)

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Im ⎡⎣ f%CM ⎤⎦ =

⎡⎛ ε p − ε m ⎢⎜⎜ ⎣⎢⎝ ε p + 2ε m

⎞ ⎛ σ p −σm ⎟⎟ − ⎜⎜ ⎠ ⎝ σ p + 2σ m 2 1 + ω 2τ MW

⎞⎤ ⎟⎟ ⎥ ωτ MW ⎠ ⎦⎥

(4)

with

τ MW =

ε p + 2ε m σ p + 2σ m

(5)

where Re[ ] and Im[ ] are the real and imaginary part of, respectively. In AC electrokinetics [12], the frequency dependence and the direction of the dielectrophoretic force are governed by the real part of the Clausius– Mossotti factor, whilst the electrorotation spectrum depends on the imaginary part of the Clausius–Mossotti factor. Figure 1b shows spectra of the real and imaginary parts of the Clausius–Mossotti factor of a cell for different suspending medium conductivities (see legends for details). In Eq. (5), τMW is referred to as the Maxwell-Wagner relaxation time constant. For single cells in suspension, the suspending system has two intrinsic relaxation frequencies. The first relaxation (time constant τ1), occurs at low frequencies and is due to Maxwell-Wagner polarisation of cell membrane-suspending medium interface. The second relaxation (time constant τ2) occurs at higher frequencies, and is due to polarisation between the suspending medium and the cell cytoplasm, when the cell membrane capacitance is effectively short-circuited. Figure 1b shows these two relaxations as the real and imaginary parts of the Clausius–Mossotti factor. For a cell the DEP component (real part) is always negative at low frequencies but at intermediate frequencies this varies with the conductivity of the suspending medium. Note that there are two ROT peaks (imaginary part of Clausius–Mossotti factor), each of which corresponds to the two relaxations. Characterization of the dielectric properties of single cells is often performed by analyzing the rotation spectra, in conjunction with measurements of the low frequency DEP cross-over point [11, 12]. Pauly and Schwan [41] described two characteristic relaxation time constants in terms of cell properties: ⎛ 1− Φ ⎞ 1 +⎜ σ i ⎝ 2 + Φ ⎟⎠ σ m τ 1 = RCmem ⎡ 1 ⎛ 1− Φ ⎞ 1 ⎤ 1 + RGmem ⎢ + ⎜ ⎟ ⎥ ⎣σ i ⎝ 2 + Φ ⎠ σ m ⎦ 1

(6a)

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τ2 =

ε i + 2ε m σ i + 2σ m

511

(6b)

Their results are based on three approximations: (i) The conductivity of the cell membrane was considered to be very small compared with the cytoplasm and the suspending medium conductivity (σmem