Mechanics of Bio-Sediment Transport 9783662611586, 3662611589

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Hongwei Fang · Lei Huang · Huiming Zhao · Wei Cheng · Yishan Chen · Mehdi Fazeli · Qianqian Shang

Mechanics of Bio-Sediment Transport

Mechanics of Bio-Sediment Transport

Hongwei Fang Lei Huang Huiming Zhao Wei Cheng Yishan Chen Mehdi Fazeli Qianqian Shang •

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Mechanics of Bio-Sediment Transport

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Hongwei Fang Department of Hydraulic Engineering Tsinghua University Beijing, China

Lei Huang Department of Hydraulic Engineering Tsinghua University Beijing, China

Huiming Zhao China Institute of Water Resources and Hydropower Research Beijing, China

Wei Cheng Beijing Engineering Corporation Ltd. PowerChina Beijing, China

Yishan Chen College of Water Resources and Environmental Engineering Zhejiang University of Water Resources and Electric Power Zhejiang, China

Mehdi Fazeli Department of Civil Engineering Yasouj University Yasuj, Iran

Qianqian Shang River and Harbor Engineering Department Nanjing Hydraulic Research Institute Nanjing, China

ISBN 978-3-662-61156-2 ISBN 978-3-662-61158-6 https://doi.org/10.1007/978-3-662-61158-6

(eBook)

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer-Verlag GmbH, DE, part of Springer Nature 2020 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer-Verlag GmbH, DE part of Springer Nature. The registered company address is: Heidelberger Platz 3, 14197 Berlin, Germany

Preface

The mechanics of sediment transport involves the study of sediment transport under the action of flow. It is an important part of the hydraulic science and is mainly related to the problems of engineering safety such as sediment deposition in reservoirs and the erosion of downstream river channels. The operation of a reservoir changes the flood process of natural rivers and the extremely low discharge in dry seasons, which mitigates potential water disasters into beneficial uses. In recent years, due to the large-scale development and application of water conservancy projects and the rapid economic development, the nutrients and pollutants in the water bodies have increased substantially, and the flow condition also deviates more and more from the natural state. The basic law of the coupled transport of these substances and sediment is the theory and method of environmental sediment. The research on environmental sediment mainly concerns the influence of sediment particles on chemical constituents to ensure the safety of water quality (see the monographs of D. M. DiToro and Hongwei Fang). Moreover, microorganisms such as bacteria, algae, and fungi adhere to the sediment particle surfaces to form biofilms. Generally, epilithic biofilm will form at bed surfaces where they are irradiated by the sun, and bacterial biofilms will form at bed surfaces at large water depths. On the one hand, biofilm growth changes the physical laws of sediment transport; on the other hand, it also affects the environmental and ecological processes in the water and at the bed surface. These changes should be the main components of eco-fluvial dynamics, and this book mainly discusses the effects of biofilm growth on sediment transport. There are several key issues in the study of biofilm-coated sediment (hereafter referred to as bio-sediment) transport. First, bio-sediment not only experiences chemical flocculation but also biological flocculation. The resultant particle size is much larger than that of individual original sediment particles, and the density and morphology also will greatly change. Second, the bed surface of bio-sediment is different from that of the original sediment, in the aspects of bedform and resistance

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Preface

characteristics. Correspondingly, the transport characteristics of suspended sediment and bed sediment will be changed. Therefore, this book considers the flocculation characteristics of bio-sediment, and the suspended load and bedload are classified following traditional fluvial dynamics to determine the sediment transport properties after biofilm growth. In this book, Chap. 1 describes the surface morphology, the heterogeneous surface charge distribution, and the adsorption/desorption characteristics of natural sediment particles (focusing on the research mainly completed by Dr. Lei Huang, Dr. Minghong Chen, and Dr. Zhihe Chen). Chapter 2 describes the change of surface morphology and density of sediment particles due to biofilm growth and also analyzes the microbial community in the bio-sediment (Dr. Huiming Zhao and Dr. Yishan Chen). Chapter 3 proposes a biomass dynamic model and discusses the bedform on the bio-sediment bed and the resistance to flow as well as the turbulence characteristics (Dr. Yishan Chen and Dr. Wei Cheng). Chapter 4 describes the bedload transport of bio-sediment, including the rheological properties, the incipient velocity, and the bedload transport rate (Dr. Huiming Zhao, Dr. Qianqian Shang, and Dr. Mehdi Fazeli). Chapter 5 describes the suspended load transport of bio-sediment, including the biological flocculation, the settling velocity, and the suspended load transport rate (Dr. Haojie Lai, Dr. Qianqian Shang, and Dr. Mehdi Fazeli). The sixth chapter discusses laboratory experiments of bio-sediment transport using a recirculating flume and also proposes mathematical models of bio-sediment transport based on the foregoing basic theories (Dr. Mehdi Fazeli, Dr. Huiming Zhao, Dr. Haojie Lai, and Dr. Wei Cheng). The whole book is written by Hongwei Fang and Lei Huang. About ten years of our study of bio-sediment transport is summarized. Every Ph.D. student, the aforementioned persons, under my guidance, gradually added their research into a theoretical framework, thus forming a systematic research work. I thank these students for their hard work and good cooperation with me. The study of bio-sediment transport is an interdisciplinary subject involving many basic theories and extensive applications. Now the relevant research is still in its infancy, and it is difficult to present a systematic and comprehensive introduction of the theoretical framework. Thus, there have been certain defects and shortcomings in the process of compiling this book, and your comments and suggestions are highly appreciated. Review comments by Steve Melching and suggestions by Danny Reible have led to an improved manuscript, although I bear the responsibility for any errors or shortcomings that remain. Beijing, China November 2019

Hongwei Fang

Preface

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References DiToro DM (2001) Sediment Flux Modeling. New York: Wiley-Interscience. Fang HW, Chen MH, Chen ZH (2009) Surface Characteristics and Model of Environmental Sediment. Beijing: Science Press. (In Chinese)

Contents

1 Surface Micro-morphology and Adsorption Properties of Sediment Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Surface Micro-morphology of Sediment Particles . . . . . . . . . . . 1.1.1 Description of Surface Micro-morphology . . . . . . . . . . . 1.1.2 Measurement of Surface Micro-morphology . . . . . . . . . 1.1.3 Mathematical Expression of Surface Micro-morphology . 1.2 Heterogeneous Surface Charge Distribution . . . . . . . . . . . . . . . 1.2.1 A Review of Surface Charge Properties . . . . . . . . . . . . 1.2.2 Measurement of the Surface Charge Distribution . . . . . . 1.2.3 Statistical Analysis of Surface Charge Distribution and Morphology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Adsorption on Sediment Particles . . . . . . . . . . . . . . . . . . . . . . 1.3.1 Adsorption Isotherms . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.2 Mechanistic Surface Complexation Model . . . . . . . . . . . 1.3.3 Interactions Between Sediment and Bacteria . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Basic Characteristics of Bio-sediment . . . . . . . . . . . . . 2.1 Morphology Characteristics of Bio-sediment . . . . . 2.1.1 A General Introduction to Biofilm Growth . 2.1.2 Biofilm Growth on Sediment Substratum . . 2.1.3 Morphology Characteristics of Bio-sediment 2.2 Basic Characteristics of Bio-sediment . . . . . . . . . . 2.2.1 Group Characteristics of Bio-sediment . . . . 2.2.2 Dry Bulk Density of Bio-sediment . . . . . . . 2.2.3 Bulk Density of Bio-sediment . . . . . . . . . . 2.3 Analysis of Biofilm Bacterial Communities . . . . . . 2.3.1 Experimental Design and Measurement . . . . 2.3.2 Diversity Indices . . . . . . . . . . . . . . . . . . . .

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1 1 1 5 15 36 36 39

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44 46 46 48 58 70

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81 81 82 86 92 109 110 119 123 124 125 129

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2.3.3 Taxonomic Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 131 2.3.4 Bacterial Groups with Significant Differences . . . . . . . . . . 144 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 . . . . . . . . . . . . . .

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153 153 154 157 159 170 170 173 183 191 192 194 204 204

4 Bedload Transport of Bio-sediment . . . . . . . . . . . . . . . . . 4.1 Rheological Properties of Bio-sediment . . . . . . . . . . . . 4.1.1 Introduction of Rheology . . . . . . . . . . . . . . . . . 4.1.2 Rheological Experiments . . . . . . . . . . . . . . . . . 4.1.3 Rheological Properties of Bio-sediment . . . . . . . 4.2 Incipient Motion of Bio-sediment . . . . . . . . . . . . . . . . 4.2.1 Incipient Motion of Noncohesive and Cohesive Sediment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2 Incipient Motion of Bio-sediment . . . . . . . . . . . 4.2.3 Derivation of Incipient Velocity Equations . . . . 4.3 Bedload Transport of Bio-sediment . . . . . . . . . . . . . . . 4.3.1 Theoretical Equation of Bedload Transport . . . . 4.3.2 Experiment on Bedload Transport . . . . . . . . . . . 4.3.3 Simulation of Bedload Transport . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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209 209 210 211 214 221

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222 227 234 248 251 255 260 266

5 Suspended Load Transport of Bio-sediment . . . . . . . . . . 5.1 Bioflocculation of Suspended Sediment . . . . . . . . . . . 5.1.1 Bioflocculation Dynamics . . . . . . . . . . . . . . . . 5.1.2 Influencing Factors for Bioflocculation . . . . . . 5.1.3 Bioflocculation Modeling . . . . . . . . . . . . . . . . 5.2 Settling Velocity of Bio-sediment . . . . . . . . . . . . . . . 5.2.1 Experimental Design for Bio-sediment Settling 5.2.2 Settling Properties of Bio-sediment . . . . . . . . . 5.2.3 Mechanism Analysis of Settling Motion . . . . .

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271 271 272 279 285 297 299 305 310

3 Biofilm Growth and the Impacts on Hydrodynamics . . 3.1 Mathematical Modeling of Biofilm Growth . . . . . . . 3.1.1 Common Models of Biofilm Growth . . . . . . . 3.1.2 Biomass Dynamics Model . . . . . . . . . . . . . . 3.1.3 Validation of Biomass Dynamics Model . . . . 3.2 Bedform and Resistance of Bio-sediment Bed . . . . . 3.2.1 Introduction of Bedforms . . . . . . . . . . . . . . . 3.2.2 Bedforms of Bio-sediment Bed . . . . . . . . . . . 3.2.3 Resistance of Bio-sediment Beds . . . . . . . . . 3.3 Effects of Biofilm on Turbulence Characteristics . . . 3.3.1 Experimental Setup and Procedure . . . . . . . . 3.3.2 Biofilm Effects on Turbulence Characteristics 3.3.3 Implications . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Contents

5.3 Suspended Load Transport of Bio-sediment . . . . . . . . . . . 5.3.1 Theoretical Equation of Suspended Load Transport 5.3.2 Experiment on Suspended Load Transport . . . . . . 5.3.3 Suspended Load Transport . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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317 318 318 320 322

6 Numerical Simulation of Bio-sediment Transport . . . . . . . . . . . 6.1 Experiment on Bio-sediment Transport . . . . . . . . . . . . . . . . 6.1.1 Biofilm Formation and Analysis . . . . . . . . . . . . . . . . 6.1.2 Erosion of Bio-sediment . . . . . . . . . . . . . . . . . . . . . . 6.1.3 Bio-sediment Transport . . . . . . . . . . . . . . . . . . . . . . 6.2 1D Mathematical Model of Bio-sediment Transport . . . . . . . 6.2.1 Model Equations and Principles . . . . . . . . . . . . . . . . 6.2.2 Results of 1D Bio-sediment Transport Model . . . . . . 6.3 3D Mathematical Model of Bio-sediment Transport . . . . . . . 6.3.1 Model Equations and Principles . . . . . . . . . . . . . . . . 6.3.2 Validation of 3D Bio-sediment Transport Model . . . . 6.4 Modeling Biofilm Development with Sediment Transport . . . 6.4.1 Biofilm Development Model . . . . . . . . . . . . . . . . . . 6.4.2 Biofilm Development in the Three Gorges Reservoir . 6.4.3 Biofilm Development in the Middle Reach of the Yangtze River . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Notation1

A AB Abwm Ai Ap Ar >Al–OH2+ >Al–OH2–RCOOH+ A0, {an}, {bn} As0, {asn}, {bsn} ah and bv a−i ax ' − i x ' ay ' − i y ' a' and b' a0 and m0 a1–a5 ap ar as B

Cross-sectional area (of particle) A coefficient representing the comprehensive effects of both aggregation and breakage on compaction Effective Hamaker constant for the system of bacteria, water, and mineral Interface area between two particles Surface area of particles
 Archimedes number, i.e. gD3f qf
q q=l2 Surface functional group of corundum Attached bacteria on the surface of corundum Fourier coefficients Normalized Fourier coefficients by the mean radius, Rmean, of sediment Distances of the vertical and horizontal forces to the rotation point for the rolling of particles Gray values for the neighboring grid cells in Fig. 1.10 First-order derivatives related to x for the neighboring grid cells in Fig. 1.10 First-order derivatives related to y for the neighboring grid cells in Fig. 1.10 a' = −ln a and b′ = −b in Eq. 2.20 Parameters in the equation of bio-sediment size Coefficients in Eqs. 4.24 and 4.25 Constant related to particle shape in Eq. 1.29 Reference level z = ar Calibration parameter in the formula of shear breakage frequency, si,s (Eq. 5.23) Biomass

1

The following symbols are used in this book.

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B0 Ba Bacc Bb Bi Bmean Bt Bw B(z) Bb(z) bi C C′ C0, C1, C2 CA CA′ CC CD CD0 CDf CL Cmax Cs Cw c c(s, t) cauto ccat cdet c′det cellsize D D* D0 D1 and D2 D50 Db Df

Notation

Minimal biomass Active part of biomass Biomass accumulation in the sediment layer Active bacterial density Inactive part of biomass Mean value of biomass along the vertical direction Total biomass in the Capdeville biofilm growth model (Eq. 3.4) River (flume) width Biomass at the vertical location z Active bacterial density at the vertical location z Concentration of ith biomass in the multi-species composite biofilm model (Eq. 3.5) Chézy coefficient Chézy coefficient related to bio-sediment roughness Capacitances of the corresponding layers for the electrical double layer (EDL) Adhesion coefficient CA′ = a5 CA where a5 is a coefficient Cohesive coefficient (=9.06  10−5/((qs − q) D2) Drag coefficient Drag coefficient of original sediment Drag coefficient of bio-sediment Lift coefficient (=η CD) Adsorption capacity, i.e. the maximum adsorption amount in Eq. 1.36 Adsorption amount per gram of sediment Aqueous concentration of adsorbate at equilibrium The total mass concentration Correlation function between the small image w(x, y) and the large image g(x, y) at the given position (s, t) Auto-detachment coefficient of biomass Catastrophic detachment coefficient of biomass Chronic detachment coefficient of biomass Bacterial detachment coefficient Grid spacing in Eqs. 1.13 and 1.14 Sediment particle diameter Dimensionless D, i.e. particle parameter Original sediment size Diameters of the interacting bacterial cell and particle (or the interacting particles) Median sediment size Deposition rate Floc/bio-sediment size

Notation

Di Dx d df dfi df,max E, F and G Eb ^D E Ex e FCi Ffp Fi Fs F F1 FA Fb FC FD Ff FG FGi Fi FL Fr Fy Fr Fku Fkw fcol ffp f f(r, t)

xv

Mean diameter of the sediment particles of size class i for the calculation of SVm in Eq. 2.12 Diameter for which x percent of the particles are finer, e.g. D25, D75, D80, D84, and D90 Pore size of sediment particles Fractal dimension Fractal dimension of class i Maximum fractal dimension Basic quantities of the first kind as the coefficients of the first basic form of the surface in Eq. 1.6 Entrainment rate Non-dimensional TKE dissipation rate (e) as scaled by h=U3 Diffusion coefficient Electron charge Conservative force representing the non-bonding potential and bonding forces that irreversibly connect particles Average information of Lagrangian particles Force exerted on each of the aggregated particles (i = 1, …, Na) Force exerted on the single particle Faraday’s constant (=96485.34 C/mol) Flocculation intensity Adhesive force Buoyancy force Cohesive force Drag force Frictional force Gravity force Gravity force per unit volume Forces acting on the cantilever of EFM Lift force Resistance force Floc strength pffiffiffiffiffi Froude number (=U= gh) Non-dimensional TKE flux in the longitudinal direction (=fku =U3 ) Non-dimensional TKE flux in the vertical direction (=fkw =U3 ) Inter-particle contact force Fluid–particle interaction force Friction coefficient Particle distribution function

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f(S), f(N), f(I), and f(T) f(x, y) fflood(Q) fku

Notation

Functions representing the effects of substrata, nutrients, illumination, and temperature on biofilm growth A continuous function Catastrophic detachment function for biofilm growth Turbulence kinetic energy flux (TKE flux) in the    longitudinal direction ¼ 0:5 u0 u0 u0 þ u0 w0 w0

fkw

Turbulence kinetic energy flux (TKE flux) in the vertical    direction ¼ 0:5 u0 w0 w0 þ w0 w0 w0

G Gp Gx

Turbulent shear rate Production of turbulent kinetic energy First-order derivative of the continuous function f(x, y) relative to x First-order derivative of the continuous function f(x, y) relative to y Lewis acid–base interaction energy Electrical double layer interaction energy Lifshitz–van der Waals attractive energy Total interaction energy Gravitational acceleration A function describing the gain or loss of biomass A large image of M  N for the PTV measurement (image matching) Mean value of g(x, y) in the overlying region with w(x, y) A function of erosion representing the influence of sediment erosion rate on the biofilm development Mean curvature of the surface Hole size (or threshold) that draws a clear distinction between the strong events outside the hole and the weak ones inside it Separation distance between the bacterial cell and sediment particle Minimum separation distance between two surfaces (=1.57 Å) Separation distance between the EFM tip and sample Water depth Atmospheric pressure measured by height of water column A function of the vertical location representing the linear distribution of biofilm development Illumination intensity Moment of inertia of the particle Ionic strength

Gy GAB GEL GLW GTot g gi g(x, y) gðx; yÞ ge(wzb) HM H

Hbm Hmin Hts h ha hb(z) I Im Is

Notation

it Jbi JSN j J JN K KB Kd KF KG KL KM Kn(x) KR KS Kapp Kint int Kint a1 and Ka2 KHnx and KHpx k k0, ki, and kj ka k a' kB kb k b' kD ke keff kI kinv,B kinv,Bb km kN

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Threshold of the pixel values for the black–white binarization Flux of ith biomass in the multi-species composite biofilm model (Eqs. 3.5 and 3.6) Flux of jth nutrient in the multi-species composite biofilm model (Eqs. 3.5 and 3.6) Bed slope Diffusion flux of nutrients at the biofilm–liquid interface Floc carrying capacity for hosting the biomass (=bK(L3 − V)) Boltzmann constant (=1.38  10−23 J/K) Partition coefficient representing the partitioning of adsorbates between the particulate and dissolved phases Freundlich adsorption constant Gaussian curvature of the surface Langmuir adsorption constant related to the affinity of adsorbent to the adsorbate Mass transfer coefficient Kirkwood function defined as Eq. 1.47 Mean value of the curvatures at each point of the cross section Half-saturation coefficient for mass transfer Apparent surface complexation constant Intrinsic surface complexation constant Intrinsic acidity constants Half-saturation constants for the absorption of nitrogen and phosphorus during microbial growth   Turbulent kinetic energy (TKE), i.e. 0:5 u0 2 þ v0 2 þ w0 2

Fitting coefficients in Eq. 4.4 Aggregation rate Dimensionless aggregation parameter Half-saturation coefficient of biomass for active bacteria growth Breakage rate Dimensionless breakage parameter Inverse half-saturation coefficient for sediment size Electrostatic constant (=8.9880  109 Nm2/C2) Effective force constant for the EFM cantilever Half-saturation coefficient for illumination Inverse half-saturation coefficient for biomass Inverse half-saturation coefficient for active bacterial density Coefficient in the expression of ubottom = kmU* Half-saturation coefficient for nutrients

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kp1 and kp2 ks ks ' ks″ k+s ksp k* L Li and Lj Lp Ls L, M, N l(i, j) M and N m mi and ai m1 − m4 m* mag(▽f) N N0 Nb NDLVO

NGRAY(i) Ni Nl Nm Np NSN

Notation

Principal curvatures (i.e. the maximum and minimum normal curvatures, respectively) Equivalent roughness height (=ks' + ks″ ) Roughness due to particles (i.e. skin friction) Roughness due to bedforms (i.e. form-drag friction) Dimensionless roughness height (=U*ks/v) Spring constant for the EFM cantilever representing the ability to resist elastic deformations Empirical coefficient in the expression of sediment carrying capacity, S* (Characteristic) floc size Sizes of interacting particles Primary particle size Non-equilibrium adaptation length for bedload transport Basic quantities of the second kind as the coefficients of the second basic form of the surface in Eq. 1.8 Element in the link matrix that reflects the relations of particles in adjacent images Number of rows and columns of the image pixels in Eq. 1.1 Mass of particles Coefficients in Tang’s (1963) equation of incipient velocity Constants in the expression of interface area between two particles (Eq. 4.22) Empirical exponent in the expression of sediment carrying capacity, S* Magnitude of the first-order derivative of the continuous function f(x, y) at the point (x, y) Nutrient concentration Positive pressure between particles Types of biomass in the multi-species composite biofilm model (Eqs. 3.5 and 3.6) Dimensionless parameter that characterizes the interaction energy for unfavorable deposition (=jAbwm =e0 er Wb Wm ) Number of pixels with a pixel value of i Number concentration of flocs of class i Number of particles positioned within a certain distance l from the original stationary particle Number of measurements Number of discrete point charges on the particle surface Types of nutrients in the multi-species composite biofilm model (Eqs. 3.5 and 3.6)

Notation

NH4, NO3, and PO4d n nF ni nM nR nsy, nl, and nse P P0 PD ^D P PM Pm n (cosh) p and q p0 and p1 p' p(i) Q Qc Qcl Qr q1 and q2 qa qb qbx qby qb* qi ql qs qsurf qsx qsy qtip ^q R R2 Ru

xix

Concentrations of ammonium nitrogen, nitrate nitrogen, and dissolved phosphate Number of the Fourier series (or number of terms of ki and kj in Eq. 4.4) Adsorption constant Number of the present ions per unit volume Manning coefficient Exponent in the rheological model Fitting term of sy, l, and se in Eqs. 4.5 and 4.6 Nitrogen pressure Saturated vapor pressure at liquid nitrogen temperature Pressure energy diffusion rate Non-dimensional PD as scaled by h=U3 Pressure in the momentum equation (Eq. 6.9) Associated Legendre function First-order derivatives of Z = Z(x, y) (i.e. p = ∂Z/∂x and q = ∂Z/∂y) Probability of class occurrence with pixel values of 0 − it and it + 1 − 255, respectively Pressure fluctuation Percentage of pixels with a pixel value of i Flow discharge Critical discharge for catastrophic detachment Quality factor of the cantilever Reaction quotient of surface adsorption Surface charges of the interacting bacterial cell and particle, respectively, in Eq. 1.53 Bedload transport rate at reference level z = ar Bedload transport rate Bedload in the x-direction Bedload in the y-direction Equilibrium bedload transport rate Discrete charge value at (rsi, hi, ui) Discharge per unit width of the tributary or lateral inflow Suspended load transport rate Surface charges of the sample for EFM measurement Suspended load in the x-direction Suspended load in the y-direction Surface charges of the tip for EFM measurement Maximum mass transfer rate Particle radius Coefficient of determination Universal gas constant (=8.31 J/(mol K))

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RBa RBi RBt Rb Rb' Re Re* Re*' Rmean R(h) Rs(h) Rs(h, u) Rs1(h, u) and Rs2(h, u) R–COOH0 r r, s, t rj (rp, h) (rs, h, u) S S* S2 Sa Sb Sbm Sb* SB Sf Sinlet Smax SN SNb

Notation

Growth rate of active biomass Ba in the Capdeville biofilm growth model Growth rate of inactive biomass Bi in the Capdeville biofilm growth model Growth rate of total biomass Bt in the Capdeville biofilm growth model Hydraulic radius Hydraulic radius related to the particle size Reynolds number Particle Reynolds number for bed sediment (=U*D/m) or for settling bio-sediment (=xf Df /m) Roughness Reynolds number (=U*ks/v) Mean radius of a sediment particle Periodic function of radius representing the closed curve of particle edge profile Normalized periodic function of radius by the mean radius, Rmean, of sediment in the polar coordinates Corresponding polar radius, Rs(h), at the latitude of u Calculated Rs(h, u) along the longitudinal and latitudinal directions, respectively Surface carboxyl group of bacteria Lattice site Second-order derivatives of Z = Z(x, y) (i.e. r = ∂2Z/∂x2; s = ∂2Z/∂x∂y; t = ∂2Z/∂y2) A function describing the gain or loss of nutrients Polar coordinate Spherical coordinate Sediment concentration Sediment carrying capacity Sediment concentration at the first grid point above the bed of z' = z2' Reference concentration at the reference level z = ar Volumetric concentration of sediment in the bed layer Maximum volumetric concentration of sediment in the bed layer Equilibrium sediment concentration of the bed layer Concentration of the biomass fraction (=X S) Friction slope Sediment concentration at the beginning of the flume Maximum sediment concentration along the flume Concentration of nutrients in the reaction–diffusion kinetic model (Eq. 3.1) Concentration of nutrients in the biofilm phase of the boundary layer

Notation

SNj SNl Soutlet SS SVm S(z) Si,H(^z) >S >SL− >SOH >SOM+ s si

si,s Ti Tcol Tfp T T* T0B

T0Bb

TD T^D TF TN Tp T^p Ts t tzb

xxi

Concentration of jth nutrient in the multi-species composite biofilm model (Eqs. 3.5 and 3.6) Concentration of nutrients in the liquid phase of the boundary layer Sediment concentration at the end of the flume Concentration of the sediment fraction (=(1−X)S) LimitingPconcentration of non-uniform particles (=0.92 − 0.2lg Δpi/Di) Vertical distribution of volumetric concentration of sediment Fractional contribution from the event Ei (i = 1, 2, 3, or 4) toward RSS production Surface atom of sediment Adsorbed anions on sediment surface Surface hydroxyl group of sediment Adsorbed metal cations on sediment surface Relative density of sediment (=qs/q) or bio-sediment (=qf/q) Breakage rate of particle class i Breakage rate of particle class i induced by fluid shear rate Total torque acting on the particle Torques resulting from the inter-particle contact force Torques resulting from the fluid–particle interaction force Temperature or absolute temperature

0  2 2 =Uc Transport stage parameter ¼ U2
Uc Reference temperature with the maximum specific growth rate of biomass (or optimal temperature for biofilm growth) Reference temperature with the maximum specific growth rate of active bacteria (or optimal temperature for active bacterial growth) Turbulent kinetic energy (TKE) diffusion rate Non-dimensional TD as scaled by h=U3 Period of a periodic function in the polar coordinate for Fourier analysis Non-spherical curvature of the surface Turbulent kinetic energy (TKE) production rate Non-dimensional Tp as scaled by h=U3 Sampling duration for the analysis of conditional RSS distributions Time Time corresponding to the bed surface of zb

xxii

Notation

Ua Uf Upi Us U Uc Uc,t

Unidirectional velocity of all the aggregated particles Fluid velocity Particle velocity (i represents the ith particle) Translational velocity of the single particle Average flow velocity of cross section Incipient velocity Incipient velocity of sediment with biofilm cultivation period of t Incipient velocity of sediment with biofilm cultivation period of t = 0 (i.e. no biofilm cultivation) Friction velocity (shear velocity) Shear velocity related to particles (bio-sediment roughness) Critical shear velocity Friction velocity derived from the energy slope Friction velocity derived from the distribution of pffiffiffiffiffiffiffiffiffiffi Reynolds shear stress (= s0 =q) Time-averaged flow velocity in the streamwise direction Effective velocity at reference level z = ar Bio-sediment velocity in the streamwise direction Bottom velocity (i.e. velocity at a distance of D from the bed) Reynolds-averaged velocity components in directions xi (i = 1, 2, 3) Maximum velocity (i.e. velocity at the water surface) A simplified set of particle velocities at a lattice node (i represents the direction of velocity vector) Bio-sediment velocity relative to the flow qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (= ðu
x_ Þ2 þ z_ 2 ) Turbulent velocity fluctuations in the longitudinal, lateral, and vertical directions Volume of floc or bio-sediment Volume of the biomass fraction in the floc/bio-sediment Pore volume of sediment particles Unavailable, optimal, and available pore volume of sediment particles Volume of particles Volume of the sediment fraction in the floc/bio-sediment Kinematic viscosity coefficient Ratio of the volumes of biofilm and sediment (=VB/VS) Viscous diffusion rate Eddy viscosity Einstein’s white noise term Weight of the biofilm part of a bio-sediment particle

Uc,t=0 U* U *' U*c U*s U*s u ua ub ubottom ui (i = 1, 2, 3) umax upi ur u', v', w' V VB Vg Vg1, Vg2, and Vg3 Vp VS v vBS vD vt Wi WB

Notation

xxiii

WS wb wbio wzb  w w(x, y)

Weight of the sediment part of a bio-sediment particle Bio-sediment velocity in the vertical direction Vertical penetration rate of biofilm Sediment erosion rate Mean value of w(x, y) A small image of J  K for the PTV measurement (image matching) Population of a variable Biofilm cell density Measured values Average value of all measured data A sample space of a variable Location of pixels (or coordinate of points) of the 2D gray matrix Z(x, y) Streamwise velocity of bio-sediment/biofloc Acceleration of bio-sediment/biofloc in the streamwise direction x-, y-coordinates of the center of mass of the sediment particle projection Simulated values Difference between the calculated surface potential and

X Xf Xi  X (X1, X2, X3,…Xn) x, y x_ €x xc , yc Yi Yj Z(x, y) Z Zij ZR ZR' z z0 zb zi z' z 2' z_ €z ^z D D/k ΔGad ΔGel

the initial guessed value, i.e. Yj ¼ W0
W0 ðR; h; uÞ 2D matrix describing the gray image of sediment Water level Pixel value of the 2D gray matrix, Z(x, y) Rouse number (=xf/(bjvU*)) Modified Rouse number (=ZR + 2.5(xf/U*)0.8(Sa/Sbm)0.4) Vertical distance Zero-velocity level or the roughness length Elevation of the bed surface Charge of the adsorbed positive/negative ions or valency of the present ions in the solution Distance from the bed surface, i.e. z - zb Distance of the first grid point from the bed surface Vertical velocity of bio-sediment/biofloc Acceleration of bio-sediment/biofloc in the vertical direction Scaled vertical distance (=z/h, or (z + Δzvb)/h) Bedform height Bedform steepness Gibbs free energy of surface adsorption reaction (ΔGad = ΔGint + ΔGel + RTlnQr) Electrostatic component of Gibbs free energy of surface adsorption reaction

xxiv

ΔGint ΔGAB adh ΔGLW adh Δpi DSDe DSEr Δt Δu Δz Dzb Dzvb D/0 ▽f ▽ 2f ▽p as a a' a1 a2 a3 abx and aby aD ai, j aL aL ' am am,n, bm,n b b1 − b3

Notation

Chemical (intrinsic) component of Gibbs free energy of surface adsorption reaction Acid–base (AB) component of the change in free energy Lifshitz–van der Waals (LW) component of the change in free energy (Lifshitz free energy of adhesion) Weight percentage of the sediment particles of size class i for the calculation of SVm in Eq. 2.12 Change of suspended sediment concentration in the deposition region (=Soutlet − Smax) Change of suspended sediment concentration in the erosion region (=Smax − Sinlet) Computational time step Relative velocity of flow with respect to the moving particle in the streamwise direction Net change of surface charge due to species exchange that define the adsorption reaction Bed deformation Depth of virtual bed from the bed surface Phase shift of the cantilever vibration for the surface charge measurement First-order derivative of the continuous function f(x, y) Second-order derivative of the continuous function f(x, y) Pressure gradient Significance level Restoring saturation coefficient Breakage probability due to collision Coefficient of the roughness due to particle (=3 as suggested by van Rijn (1982)) Velocity coefficient (=ua/ub) Volumetric shape factor (=p/6 for spheres) Directional cosines =pCDf qD2f =8 Sticking efficiency between the particle classes i and j Lift coefficient in Eq. 4.50 =aL qm0:5 D2f ð@u=@zÞ0:5 Added mass coefficient to the bio-sediment mass (assumed to be 0.5 by van Rijn (1984a)) Moments of surface charge distribution defined as Eqs. 1.48 and 1.49, respectively A factor for diffusion of suspended sediment (=1 + 2(xf/U*)2) Coefficients in the expression of adhesive force, CA'(t)

Notation

bBb bI bi, j bi,BM j bi,DSj FS bi,j bK bT C c cB ci,j cm cs cs ' cs-M' cSB cSB′ cSB-M′ cLW

c+ c− c_ d dB db dij and dj3 dL dmax e e0 eB eB' eB-M eb ee ef

xxv

Temperature dependence coefficient for active bacterial growth Illumination dependence coefficient for biofilm growth Collision frequency between the particle classes i and j Collision frequency due to Brownian motion Collision frequency due to differential settling Collision frequency due to fluid shear Proportionality coefficient Temperature dependence coefficient for biofilm growth Total surface charge of sediment Bulk density (specific weight) of water Bulk density of biofilm Breakage distribution function Constant in Eq. 1.48 (cm = 1 when m = 0; otherwise, cm = 1/2) Bulk density (specific weight) of sediment Dry bulk density of sediment Maximum dry bulk density of sediment Bulk density of bio-sediment Dry bulk density of bio-sediment Maximum dry bulk density of bio-sediment Lifshitz–van der Waals energy component of the surface LW LW tension, and cLW b , cm , and cw represent the value for bacteria, mineral, and water, respectively (or cLW and s cLW represent the value for the solid and liquid, l respectively) Electron acceptor parameter, and c+b , c+m, and c+w represent the value for bacteria, mineral, and water, respectively Electron donor parameter, and c−b , c−m, and c−w represent the value for bacteria, mineral, and water, respectively Steady (critical) strain rate in the rheological model Thickness of water molecules (=3  10−8 cm) Thickness of biofilm Thickness of bedload layer Kronecker delta Thickness of viscous sub-layer (=11.6v/U*) Maximum possible depth for biofilm growth Turbulent kinetic energy (TKE) dissipation rate Permittivity of a vacuum Volume ratio of biofilm to the total deposit = ln[(eB-M − eB)/eB] in Eq. 2.20 Maximum value of eB Porosity of the bottom sediment Permittivity of the electrolyte (aqueous medium) Fluid volume fraction

xxvi

em ep er f η ηd H Hc Hc0 HcC HcA h hl j jv jBS k kBS kb ki, H(t)

kw l lapp lB lBb lmax lp ls n q qb qb' qf qs

Notation

Scale for the measurement of surface area and volume of particles Permittivity of the particle Relative permittivity of water Biomass fraction of the floc volume (=VB/V) Flow parameter (=H/Hc) Value of η corresponding to the maximum bedform steepness, (D/k)max Shields number Critical/threshold Shields number Noncohesive term of the critical Shields number for bio-sediment Cohesive term of the critical Shields number for bio-sediment Adhesive term of the critical Shields number for bio-sediment Inclination of riverbed Contact angle of the measuring liquid with mineral or bacteria Inverse Debye length, and j−1 is the thickness of the electrical double layer (EDL) Von Kármán constant Ratio of the bulk densities of biofilm and sediment (=cB/cS) Bedform length Biofilm thickness ratio (=dB/D) Saltation length of sediment Detecting function in Eq. 3.32, i.e. ki, H(t) = 1 if the (u', w') pair is in quadrant i with ju0 w0 j  Hru rw , otherwise, ki, H(t) = 0 Correlation length of water molecules in the liquid (i.e. gyration radius) Dynamic viscosity coefficient Apparent viscosity of non-Newtonian fluids Biomass growth rate Maximum specific growth rate for active bacteria Maximum specific growth rate for biomass Mean value of the population, X Mean value of the sample space, (X1, X2, X3, …, Xn) Resisting moment per unit area due to the cohesion Density of water/fluid Density of biofilm Dry density of biofilm Density of bio-sediment/biofloc Density of sediment/primary particle (=2650 kg/m3)

Notation

r0 and r1 r0, rb, rd rc rF rKR rp rR rs ru

rw

r2L r2J sf s ^s s0 sc sDe sEr se sij sR sy U /ðtÞ /ðx; yÞ u v W0 W*0

xxvii

Standard deviation of the class with pixel values of 0 − it and it + 1 − 255, respectively Surface charge of each plane for the electrical double layer (EDL) Turbulent Schmidt number Sum of the force derivatives for all the forces, Fi, acting on the EFM cantilever Standard deviation of the curvatures at each point of the cross section Standard deviation of the population, X Standard deviation of the radius of the cross section Standard deviation of the sample space, (X1, X2, X3, …, Xn) Turbulence intensity in the longitudinal direction pffiffiffiffiffiffi (= u0 2 ) Relative turbulence intensity in the longitudinal direction pffiffiffiffiffiffiffi Turbulence intensity in the vertical direction (= w0 2 ) Relative turbulence intensity in the vertical direction Within-class variance Between-class variance Stress tensor Reynolds shear stress (=
qu0 w0 ) Scaled Reynolds shear stress (=s/s0) Bed shear stress (=qU2* = cRbSf) Incipient/critical shear stress Bed shear stresses in the deposition region Bed shear stresses in the erosion region Stable shear stress in the rheological model Turbulent shear stress calculated with the k-e turbulence model Shear stress in the rheological model Yield stress in the rheological model A function of particle size in Sha’s (1965) equation of settling velocity Function represents the parameters sy ðtÞ, lðtÞ, or se ðtÞ in Eq. 4.4 Direction of the first-order derivative of the continuous function f(x, y) at the point (x, y), i.e. arctan(Gy/Gx) sorting coefficient (=(D75/D25)0.5) Einstein correction factor as a function of ks/dL Electrostatic potential of the surface relative to the bulk solution Initial guessed value of surface potential relative to the bulk solution

xxviii

W0 ðR; h; uÞ W0 ðR; h; uÞ W 0, W b , W d Wb and Wm wi Xs X Xa Xi(f) xpi x x0 xF xf xi and xj

Notation

Distribution of the (calculated) surface potential Average value of the (calculated) surface potential, W0(R,h,u) Surface potential of each plane for the electrical double layer (EDL) Surface potentials of the bacterial cell and mineral, respectively Constraint forces that remain the distances within the aggregate unchanged Rotational velocity of the single particle Biomass fraction of the sediment concentration A function of settling velocity in Sha’s (1965) equation of settling velocity Particle collision operator Angular velocity of the particles (i represents the ith particle) Settling velocity Settling velocity of original sediment Frequency of the Fourier series Settling velocity of bio-sediment/biofloc Settling velocities of interacting particles

Chapter 1

Surface Micro-morphology and Adsorption Properties of Sediment Particles

Biofilm growth on sediment is affected by the surface properties of sediment particles. Generally, sediment particles possess complex surface morphology, pores of various scales, and heterogenous surface charge distribution, which impact the adsorption of nutrients (pollutants) and attachment of bacteria on sediment, and further influence biofilm growth (Fang et al. 2009). Thus, this chapter first introduces the surface micro-morphology and charge distribution of sediment particles and their adsorption properties. That is, Sect. 1.1 describes the measurement and mathematical expression of surface micro-morphology; Sect. 1.2 presents the measurement and statistical analysis of the surface charge distribution; the adsorption properties and interactions between sediment and bacteria are discussed in Sect. 1.3. These concepts are the basis of the following chapters that explore biofilm growth and bio-sediment transport.

1.1 1.1.1

Surface Micro-morphology of Sediment Particles Description of Surface Micro-morphology

The detailed characterization of sediment morphology is dependent on what one wants to learn, as different variables and indexes are required for different research objectives, and this characterization also is limited by the available instruments and methods. The diversification and refinement of characterization methods promote thorough studies of sediment morphology and increase understanding of smaller-scale problems. This sub-section gives a description of the characterization of surface morphology.

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer-Verlag GmbH, DE, part of Springer Nature 2020 H. Fang et al., Mechanics of Bio-Sediment Transport, https://doi.org/10.1007/978-3-662-61158-6_1

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1 Surface Micro-morphology and Adsorption …

2

1.1.1.1

Traditional Description Method

The study of sediment transport is based on the theory of Newtonian mechanics, which mainly considers the physical and macroscopic effects such as gravity, currents, waves, and wind. When describing the motion of an individual sediment particle, the sediment particle is generalized into a mass point or a geometry of a specific shape to characterize the behavior of actual particles. Therefore, the geometric properties of individual sediment particles mostly are described by one or two parameters. For example, the sediment particle size usually is characterized by its diameter. Because of the large range of sediment size, there are special definitions of particle diameter and the corresponding measurement methods, as listed in Table 1.1, and the definitions and calculation of nominal diameter, sieving diameter, and settling diameter commonly are used. Moreover, the geometric features of sediment particles are generally described by roundness, sphericity, overall shape, and shape factor. Wentworth (1919) first proposed the concept of roundness to describe the sharpness of the edges and angles of particles, but roundness is difficult to apply to the projection of three-dimensional objects. Wadell (1932) improved the calculation of roundness and first defined sphericity as the ratio of the nominal diameter and the diameter of a circumsphere. The sphericity of this definition does not reflect the dynamics of particles in a fluid; Folk and Ward (1957) further proposed the concept of maximum projection sphericity, i.e. the ratio of the diameter of a sphere with the projected area the same as the minimum projected area of the particle and the nominal diameter. Similar to Table 1.1 Concept and definition of particle size (Wang et al. 2002) Physical quantities

Measuring method

Definition of particle size

Size of pebbles or gravel

Visualization, caliper, or gauge

Size of particle projection

Ruler or micrometer

Size of the transverse section of fine particles Minimum area of transverse section Mass

Measuring in enlarged slice images with the foregoing methods Sieving analysis

Length, width, and thickness; and their arithmetic, geometric, or logarithmic mean values Nominal projection diameter (the diameter of a circle with the same area as the projection) Slice diameter (the diameter of a circle with the same area as the slice)

Volume

Volume meter

Settling velocity

Settling cylinder, centrifuge, or sedimentation balance

Balance

Sieving diameter (the minimum screen aperture that the particle can pass) Diameter of a sphere with the same density and mass as the particle Nominal diameter (the diameter of a sphere with the same volume as the particle) Settling diameter (the diameter of a sphere with the same density and settling velocity as the particle)

1.1 Surface Micro-morphology of Sediment Particles

3

the maximum projection sphericity, shape factor also is used to characterize the relation among the three axes of particles, representing the deviation of particles from standard shapes (Wettimuny and Penumadu 2004). These methods of describing sediment particles are simply defined and have been widely used in traditional studies of sediment dynamics. However, they are subjected to greater limitations in the studies of sediment surface processes.

1.1.1.2

Fractal Dimension

Since the fractal theory was first put forward by Mandelbrot (1982), it has been widely applied to the study of complex geometry in nature, such as coastlines, river systems, terrain landforms, rock fractures, and even molecular structures. Pfeifer and Avnir (1983) found that many surfaces have self-similarity and self-affinity, i.e. fractal surfaces. Thus, fractal theory also is used to describe particles, such as rock, soil, protein, floc, and catalyst particles. The fractal method can describe not only the shape, but also the surface roughness and pore characteristics of particles, and there are different definitions of important particle features, such as the Hausdorff dimension, correlation dimension, information dimension, and capacity dimension (Xie 1991; Zhang 1995). There also are many methods to determine the fractal dimension, mainly the methods of yardstick (Mandelbrot 1982), gas adsorption (Avnir et al. 1984; Neimark 1990a; Yin 1991), thermodynamics (Neimark 1990b; Neimark and Unger 1993), mercury intrusion (Fu et al. 2001), small-angle X-ray diffraction (Tang et al. 2003), nuclear magnetic resonance (Kalumbu et al. 1996), and scanning electron microscopy (image method) (Chakraborti et al. 2000). Fractal theory provides a powerful tool for describing the anisotropy of particles. In the past, it was mainly used to describe soil (Perfect and Kay 1995; Rice et al. 1999; Sokolowska and Sokolowski 1999; Dathe et al. 2001), activated carbon (Huang et al. 2000; Wang et al. 2006a), silica gel (Zhao 2003; Sheng et al. 2005), and mineral rock (Liu et al. 2005). Relatively few studies have been conducted on the application of fractal theory to sediment morphology. Chao et al. (1997) studied the surface fractal characteristics of sediment particles through the adsorption of emulsified oil and concluded a surface fractal dimension of 2.33. Li et al. (2003) studied the fractal surface of sediment by adsorption of adsorbate with different cross sections and modified the application of the Langmuir and Freundlich adsorption isotherms to fractal surfaces. Wang et al. (2005a) investigated the influence of temperature on fractal dimension using the nitrogen adsorption method. Wang et al. (2006b) found that the surfaces of sediment particles usually have multi-fractal properties under scales from nanometers to microns through image analysis, and there are some differences in the fractal dimension at different scales. It is believed that the fractal dimension obtained by image analysis is a description in a purely geometric sense for the surface roughness. In addition, there are also studies that applied fractal theory to the shape of sediment flocs (de Boer 1997; de Boer and Stone 1999; de Boer et al. 2000; Stone and Krishnappen 2005; Hong and Yang 2006).

1 Surface Micro-morphology and Adsorption …

4

The fractal method provides a method for describing sediment particles, which is more elaborate than traditional methods and can reflect more information on particle shape and surface structure, but there are still some limitations. For the same fractal dimension, the shape or surface structure of sediment particles can be significantly different, and the corresponding mechanical and chemical properties may also greatly differ. Thus, the fractal dimension cannot be used alone to describe the relation between particle morphology and other surface processes. Moreover, the surface fractal dimension based on image analysis is a description of surface roughness in a geometric sense which might be affected by the gray field. In contrast, the fractal dimension calculated by the methods of gas adsorption and yardstick is a measurement of a particle’s surface-filling capacity, i.e. a higher accuracy.

1.1.1.3

Image Method

Fine sediment particles generally are of micron or millimeter size, and it is difficult to observe the surface morphology by eye. The rapid development of microscopic observation, image processing, and intelligence provides a convenient approach for morphologic study of fine particles. The commonly used microscopic equipment includes: scanning electron microscope (SEM) (Berkel and Beckett 1996), transmission electron microscope (TEM) (Hochella et al. 1999), atomic force microscope (AFM) (Buzio et al. 2003), environmental scanning electron microscope (ESEM) (Donald 2003; Zhao et al. 2011), energy-dispersive X-ray spectrometer (EDS) (Palumbo et al. 2001), and X-ray diffraction (XRD) (House and Denison 2002). The sample requirements are different for these different microscopic equipments, and the corresponding purposes of measurements also are very different. Many scholars have made substantial effort on how to study the morphology and material properties of particles after acquiring images. For example, Chandan et al. (2004) described the texture, angularity, and shape of aggregates used in expressway construction through wavelet analysis, gradient operation, and shape factor and sphericity, respectively, and studied the relation between particle shape and aggregate properties. Wettimuny and Penumadu (2004) and Al-Rousan et al. (2007) described the shape of aggregates using the Fourier series method and defined the shape and roughness parameters to reflect different physical characteristics. Wang et al. (1982) analyzed SEM images of quartz using a statistical method and classified the shape, angularity, and texture into several groups through empirical parameters. Durian et al. (2006, 2007) studied the relation between the shape of broken rock and its transport process under experimental and natural conditions using the distribution of profile curvatures. In these studies, the grayscale gradient and Fourier series are effective methods for the study of sediment particle morphology. Three-dimensional (3D) surface reconstruction based on the image method is an extension of particle morphology study. To reconstruct a 3D surface, images obtained from different light directions (ordinary optical imaging) or different

1.1 Surface Micro-morphology of Sediment Particles

5

electron incident angles (SEM imaging) are generally needed to compute the surface information. For example, Li et al. (2007) used the photometric stereo method for the 3D surface reconstruction of black melon seeds so as to identify the warpage of melon seeds. Zhu et al. (1997) and Liu et al. (2004) measured the morphology of a metal section using the SEM stereo imaging technology and reconstructed its 3D morphology. For the 3D surface reconstruction of sediment particles, because the angle that the SEM platform can rotate is small and particle surface has no obvious feature for location, there is great difficulty in matching points, making it difficult to reconstruct the surface with multi-angle images.

1.1.2

Measurement of Surface Micro-morphology

The previous sub-section introduced the description methods of particle surface morphology, including the traditional description methods (e.g. particle size, roundness, and sphericity), fractal dimension, and image methods resulting from the development of microscopic observation. In this sub-section, the surface morphology of sediment particles is observed using image methods, mainly by SEM. Meanwhile, the gas adsorption method is applied to analyze the pore size distribution on the sediment surface through the Barrett–Joyner–Halenda (BJH) theory.

1.1.2.1

Experimental Instruments

(1) High-resolution microscopes As previously stated, fine sediment is of micron and millimeter size, and it is difficult to observe the surface morphology by eye. Due to the rapid development of ultrahigh vacuum, thin film preparation, photoelectric microscopy, electrical measurement, and computer technology, a lot of surface analysis methods and instruments have been developed. In this section, the high-resolution microscopes for morphology observation used in this book are summarized and briefly introduced. 1) Principles of measurements The main instrument for microscopic observation is the SEM, which can precisely observe the microstructure and ultra-microstructure of sample surfaces. A SEM also is capable of doing element detection on sample surfaces with the addition of a variety of ancillary equipment (e.g. EDS). It scans the sample surface point by point with a narrowly focused electron beam, which interacts with the sample to produce various physical signals. These signals are then received, amplified, and converted into modulated signals by the detector and finally displayed on the screen to reflect the properties of the sample surface. The SEM has the characteristics of large depth of field, strong stereoscopic image, great amplification range, continuous adjustment, high resolution, large sample room, and simple sample preparation. The most

6

1 Surface Micro-morphology and Adsorption …

commonly used signals by a SEM are the secondary electron and backscattered electron signals. The former is used to represent the surface morphology, and the latter represents the atomic number contrast. A SEM is composed of an electron optical system, scanning system, signal detection and amplification system, image display and recording system, vacuum system, and power supply and control system. The requirement of a high vacuum environment limits the application of conventional SEMs (Gan et al. 2003), especially for environmental samples due to the high water content and poor conductivity. The sample preparation for SEM observation, i.e. the treatments of dehydration, drying, and electric conduction, would cause the shrinkage and destruction of observed samples. The ESEM is a new type of SEM for observing the surface microstructure and ultra-microstructure in a wet or partially hydrated state, and has been increasingly applied in the fields of environmental, microbiological, and material sciences. There are two key technologies that minimize the sample damage (Tang and Tai 2001). One is the multistage diaphragm pressure technology applied to form a gradient vacuum, and the pressure of the sample room can be maintained up to 2660 Pa water vapor pressure with adjustable temperature and relative humidity. The other is the gaseous secondary electron detector that the ionization of gas molecules by secondary electrons could magnify the weak secondary electron signal of environmental samples, and the produced positive ions could eliminate the charge accumulation on the sample surfaces. There are no requirements of extensive manipulation, fixation, dehydration, air or critical point drying, and metal coating for sample observation that a high vacuum SEM would require. Thus, environmental samples could be directly observed by an ESEM to obtain the true microscopic images. In addition to the environmental scanning mode, an ESEM also has a high vacuum scanning mode under which they become an ordinary high vacuum SEM. A scanning probe microscope (SPM) is a kind of microscope that characterizes the surface properties of samples by detecting the interaction forces between the tip and samples (such as the inter-atomic repulsion, friction, van der Waals, magnetic, and electrostatic forces), including atomic force microscope (AFM), lateral force microscope (LFM), magnetic force microscope (MFM), and electrostatic force microscope (EFM) (Bai et al. 2000). A SPM scans the sample surface using an elastic micro-cantilever (with a fixed end and a tip at the other end) which usually is made of silicon or silicon nitride with a length of 100–500 lm and a thickness of 0.5–5 lm. The deformation of the micro-cantilever is monitored with a laser system to obtain the surface properties of samples. There are three working modes for a SPM according to the scanning modes of the tip on sample surfaces, i.e. contact mode, non-contact mode, and tapping mode. The tapping mode not only maintains the high resolution of contact mode, but also does not destroy the sample similar to the non-contact mode. Particularly, an AFM characterizes the surface morphology of samples by detecting the van der Waals force, which has a high resolution of atomic level. It provides the real information of surface morphology that is convenient for further analysis, while a SEM only provides a two-dimensional gray image (i.e. relative values of surface morphology). An AFM can be applied in both

1.1 Surface Micro-morphology of Sediment Particles

7

air and liquid environments without special treatment of the samples, so it has been widely used in the fields of semiconductors, nanomaterials, biology, chemistry, and medicine. In addition, an EFM characterizes the surface charge properties of samples by detecting the electrostatic force. As the electrostatic force is inversely proportional to the square of distance, i.e. a long-range force, the working distance between the probe and samples can be relatively far (usually 100 nm). A metal film-coated tip usually is used by an EFM, and in most cases, it is necessary to apply voltages on the tip or samples to obtain a high-quality image. Confocal laser scanning microscopy (CLSM) characterizes the samples with the confocal theory and uses laser as the light source (Chen et al. 2007). Firstly, the samples are stained by fluorescent probes to mark its subcellular structure or molecule. Then, a UV–visible laser is used to excite the fluorescent materials to obtain fluorescence images of samples. Different structures or components have different fluorescent probes (Xi et al. 1996). A CLSM can conduct optical sectional scanning and maintain the wet hydrated state of biological samples, thus providing a feasible method to study the spatial architecture of environmental samples. In this book, SEM is mainly used for the morphology observation of original sediment, an EFM is applied for the measurement of surface charge distribution, and an ESEM and a CLSM are mainly used for the observation of biofilm-coated sediment. The SEMs used in this section and the corresponding sample preparation are first introduced. 2) Experimental instruments and sample preparation Three of the SEMs used in the examples discussed in this book are produced by Japan Electronics Corporation (JEOL), i.e. models JSM-6301F, S-4500, and S-5500. The resolutions of these three SEMs are different, and the corresponding requirements of sample preparation also are different. A high vacuum degree of the sample room and a good conductivity of the sample are required to observe the surface morphology using a SEM. As a sediment sample is non-conductive, a coating apparatus is used in the sample preparation for a clear image, including the gold coater and carbon coater. If only the surface morphology is observed, the sample surface can be coated with gold film due to its stronger conductive property so that a clearer morphology image can be obtained. If the surface elements also are observed, the sample should be coated with carbon film for a weaker interference with the detection of other elements. The methods for sample preparation of JSM-6301F and S-4500 SEMs are almost the same, with only a slight difference in the shape of sample stage, i.e. a disk with a radius of about 1.5 cm for JSM-6301F and a 4
2 cm rectangular plate for S-4500. As a sediment sample is granular material, it needs to be firmly stuck onto the sample stage by special double-sided adhesive or glue, and appropriate appliances are used to press properly to ensure complete adhesion of the samples for good conductivity. The particles should be slightly dispersed for convenient observation. Then, the sample is placed into the coating apparatus and subjected to vacuum pumping and coating with gold or carbon film, after which it is ready for SEM observation.

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1 Surface Micro-morphology and Adsorption …

The S-5500 is an ultrahigh-resolution SEM (with a magnification of 60– 2,000,000 times, and its secondary electron resolution is 0.4 nm (30 kV) and 1.6 nm (1.0 kV)) with higher requirements for sample preparation. The sample stage is a chamfer box of 1.5
0.5
0.4 cm, and it is required that the thickness of the sample on the stage should be smaller than 2 mm. A mixture of sediment and phenolic resin is put into a mosaic machine, melting under a high temperature of 140 °C for 15 min. Then, the sample is recooled at room temperature (the sediment particles are embedded in the resin) and manufactured into cylindrical workpieces. The workpieces are ground and polished for a smooth fracture, and then cut into small pieces of 3
3
2 mm. After cleaned by ultrasonic methods and dried, the sample can be glued on the sample stage and sent for film coating. In the examples discussed here, the specific SEM is selected according to the experimental purpose and desired measurement accuracy. (2) Physicochemical adsorption analyzer The gas adsorption method generally is used to measure the pore size distribution and specific surface area of samples. Here, nitrogen is selected as the adsorbate. At liquid nitrogen temperatures, the amount of nitrogen adsorbed on the solid surface is dependent on the relative pressure of nitrogen P/P0, where P is the nitrogen pressure and P0 is the saturated vapor pressure at liquid nitrogen temperature. The relation between the adsorption amount and relative pressure conforms to the Brunauer–Emmett–Teller (BET) equation (Brunauer et al. 1938) at a P/P0 range of 0.05–0.35, which is the theoretical basis for the determination of specific surface area by the gas adsorption method. Meanwhile, capillary condensation occurs when P/P0 > 0.4, i.e. nitrogen condensates in the micropore, based on which the pore volume and pore size distribution can be determined by adsorption experiment and the Barrett–Joyner–Halenda (BJH) theory (Barrett et al. 1951). Condensation can be observed at a lower P/P0 for a smaller capillary pore, and a higher P/P0 is required for condensation for a larger capillary pore. Thus, the adsorption amount increases sharply with the relative pressure due to the occurrence of capillary condensation, and it achieves the maximum value when all the pores are filled with liquid adsorbate (i.e. P/P0  1.0). Instead, if considering the desorption process, the condensate in larger pores is desorbed first when lowering the relative pressure, followed by desorption in smaller pores. Therefore, there is a relation between the pore size and the relative pressure that condensation or desorption from condensate occurs. An Autosorb-1-C surface area and pore size analyzer (Quantachrome Instruments, USA) is used in this book, and the measurement range of surface area is 0.0005–5000 m2/g and that of pore size is 0.35–500 nm. Sediment samples are added into a sample tube and then degassed. A certain amount of nitrogen is pumped into the tube at 77.3 K using a quantitative gas pump, and the pressure is measured with a precise pressure sensor after achieving equilibrium. So, the volume of adsorbed nitrogen could be calculated through the change of relative pressure. A series of adsorbed nitrogen can be obtained by adding a known amount of nitrogen repeatedly; i.e. a nitrogen adsorption isotherm is obtained. Subsequently,

1.1 Surface Micro-morphology of Sediment Particles

9

nitrogen is gradually removed from the tube after reaching the saturation gas pressure to derive a nitrogen isotherm of desorption. Then, the surface area and pore size distribution can be computed directly from the isotherms using the BET and BJH theories based on the characteristics of pore structure (Fang et al. 2008).

1.1.2.2

Micro-morphology of Sediment Particles

In this sub-section, the procedures for evaluating the micro-morphology of sediment samples are illustrated based on sediment samples from some of the major rivers in China. Sediment was collected from the Yangtze River (i.e. Cuntan, Yichang, Hankou, and Datong), Yellow River (i.e. Sanmenxia, Xiaolangdi, Huayuankou, and Gaocun), and Yongding River (i.e. the river course of the Yongding River and Guanting Reservoir), which are located in the southwestern, central, and northern parts of China, as shown in Fig. 1.1. These particles exhibit much different sizes and degrees of pollution. The median size increases from south to north, and the degree of pollution changes in a similar manner. Some sediment particles were directly sampled from the bottom of rivers or reservoirs, and some were collected by filtering the muddy water from the river course. All these sediment samples were ventilation dried in an oven under the condition of 30 °C after air-drying.

Fig. 1.1 Sampling sites in the major rivers of China

10

1 Surface Micro-morphology and Adsorption …

(1) Pretreatment of samples Sediment samples from natural rivers or reservoirs often are coated with complex organic compounds and adsorb nitrogen, phosphorus, and heavy metals, which need to be “washed” to reduce the effects of contaminants on experimental results. The process of washing is as follows (Wang et al. 1982; Gleyzes et al. 2002): 1) Put the sediment samples into a conical flask, add deionized water and hydrogen peroxide solution, and stir for adequate reaction. Bubbles will be produced during the reaction, which releases a lot of heat and gas with a pungent odor. Wash repeatedly with deionized water and discard the supernatant, when no bubbles and heat are released (i.e. sufficient reaction). 2) Add concentrated hydrochloric acid into the conical flask, and stir until the reaction is sufficient (a large amount of bubbles and heat release will also be observed); then, wash repeatedly with deionized water and discard the supernatant. 3) Repeat these steps to ensure that the reaction is sufficient and sediment particles are clean. Filter the cleaned sediment, and dry them in an oven. The purpose of cleaning sediment samples is to remove the attached materials and achieve a state of no pollution, while the major components and structures of particles are not destroyed. (2) Micro-morphology of natural and cleaned sediments Natural sediment: As stated by Krinsley and Doornkamp (1973) and Vilks and Wang (1981), almost all the studied sediment particles have rather irregular outlines showing primary glacial features. Due to the long-distance transport, many exposed particle surfaces have current marks superimposed on glacial features. Angular edges are rounded due to mechanical abrasion. Surface dissolution and silica coating during surface physicochemical processes produce pits, pores, and deposits. Thus, the assemblage characteristics could reflect the physical, chemical, and biological reactions that sediment particles have experienced, which is primarily related to the depositional environment. Figure 1.2a, b shows the SEM images of sediment samples from the Yichang station on the Yangtze River, which are relatively coarser corresponding to lower magnifications. The shapes of these particles are irregular and different from any simple Euclidean geometry. The detailed features are prominent, with the surface covered by flocculent materials forming compact pore structures, especially for particles A and C. There are also relatively flat regions on the particle surfaces that may be formed by mineral joints. Fine particles can be observed attaching to the concave or flat regions, such as the surfaces of particles B and D. Figure 1.2c, d shows the SEM images of sediment samples from the Huayuankou station on the Yellow River, which are obviously different from those in the Yangtze River. The overall abrasion degree is higher with a greater roundness, and there are abundant materials attached to the surface (see Fig. 1.2c). Figure 1.2d shows the locally enlarged image of particle F, where the main binding

1.1 Surface Micro-morphology of Sediment Particles

(a) Particle A, B (×400) - Yichang

(b) Particle C, D (×200) - Yichang

(c) Particle E (×1500) - Huayuankou

(d) Particle F (×7000) - Huayuankou

(e) Particle G (×8000) - Guanting

(f) Particle H (×10000) - Guanting

11

Fig. 1.2 SEM images of sediment samples from a–b Yichang station on the Yangtze River, c– d Huayuankou station on the Yellow River, and e–f Guanting Reservoir on the Yongding River

sites of these attached particles can be clearly seen. Almost no flat regions exist on the particle surfaces. Figure 1.2e, f shows the SEM images of sediment samples from the Guanting Reservoir on the Yongding River. The pollution of the Yongding River is more serious with a higher content of organic matter, thus resulting in a heavier pollution and a more complex micro-morphology of sediment

12

1 Surface Micro-morphology and Adsorption …

particles. These particles are generally coated by a layer of clastic materials with the original sediment almost indiscernible, and the coatings result in an irregular particle surface with many gullies and pores of different sizes, which change the physical and chemical properties of the particles. Mineral particles (mainly clay minerals) are the core skeleton of natural sediment particles. Organic matter and hydrous metal oxides are bonded to the mineral surfaces (Tang et al. 2000; Liu et al. 2006). The surface morphology of natural sediment particles is dependent on the sediment characteristics and surrounding environment, mainly reflected in the content of clay minerals, the specific surface area, and the degree of water pollution. In different basins, the factors influencing morphology are different, so the micro-morphology of sediment particles presents typical regional characteristics. (1) Clay minerals are the main component of fine sediment, which determine the particle size, morphology, and adsorption capacity. Illite, smectite (mainly montmorillonite), kaolinite, and chlorite are the dominant clay minerals of river sediment particles throughout the world (Irion 1991), among which the adsorption capacity and cation exchange capacity of montmorillonite are the strongest. As the content of montmorillonite decreases from north to south in China (Tang et al. 2000), the adsorption capacity of sediment particles from northern rivers is stronger. As shown in Fig. 1.2, there are more materials adsorbed on the surface of natural sediment in the Yongding River than those in the Yangtze River and Yellow River. (2) Specific surface area is a reflection of the comprehensive characteristics of sediment particles. A larger specific surface area corresponds to a higher surface energy and more complexation adsorption sites. The average specific surface areas of sediment (0 >0 Convex >0 0 Ridge ¼0 0 and a convex point when HM < 0. 2) If KG < 0, i.e. kp1 and kp2 have opposite signs, and the two curves in the main directions bend along opposite sides, then it is a hyperbolic point. The shape of the surface at the hyperbolic point is similar to a hyperbolic paraboloid, and the corresponding morphology is a saddle. 3) If KG = 0 while HM 6¼ 0, i.e. one of the two curves in the main directions bends forward or backward along the normal vector, and the other curve is in the asymptotic direction, then it is a parabolic point. Specifically, it is a groove point when HM > 0 and a ridge point when HM < 0. 4) If KG = 0 and HM = 0, i.e. the principal curvature kp1 = kp2 = 0, then it is a flat point. The Gaussian and mean curvatures are a reflection of the local surface shape in different directions, which represent the local surface structure and morphology that influence the physicochemical properties of sediment. Further, non-spherical curvature, TN, is introduced, which is a function of the Gaussian and mean curvatures and describes the proximity of local surface morphology to a sphere. The non-spherical curvature, TN, is defined as TN ¼

 1 kp1  kp2 ¼ 2

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 K HM G

ð1:12Þ

1.1 Surface Micro-morphology of Sediment Particles

21

Fig. 1.10 Template analysis window and the calculation flowchart for surface curvature (Chen et al. 2013)

Here, the third-order inverse distance squared weight difference method is applied for curvature calculation (Tang et al. 2005). For each grid point, a template analysis window composed of the point and its eight neighboring points can be determined, as shown in Fig. 1.10. The variables p and q in Eqs. 1.10 and 1.11, i.e. the first-order derivatives of the surface Z = Z(x, y) in the x- and y-directions, respectively, are calculated using the Sobel operator as previously introduced. p¼

@Z ða þ 2d þ gÞ  ðc þ 2f þ iÞ ¼ @x 8cellsize

ð1:13Þ

q¼

@Z ða þ 2b þ cÞ  ðg þ 2h þ iÞ ¼ @y 8cellsize

ð1:14Þ

where cellsize is the grid spacing and a − i are the gray values for the neighboring grid cells shown in Fig. 1.10. Two matrices of p and q values are obtained through Eqs. 1.13 and 1.14, based on which the second-order derivatives r, s, and t of the surface Z = Z(x, y) can be derived through another difference calculation, i.e.  0    ax þ 2dx0 þ g0x  c0x þ 2fx0 þ i0x @2Z r¼ 2 ¼ @x 8cellsize

ð1:15Þ

1 Surface Micro-morphology and Adsorption …

22

 0    ax þ 2b0x þ c0x  g0x þ 2h0x þ i0x @2Z ¼ s¼ @x@y 8cellsize     0 0 0 0 0 0 2 a þ 2b þ c þ 2h þ i  g y y y y y y @ Z t¼ 2 ¼ @y 8cellsize

ð1:16Þ

ð1:17Þ

where ax′ − ix′ are the calculated first-order derivatives relative to x for the neighboring grid cells according to Eq. 1.13 and ay′ − iy′ are the calculated first-order derivatives relative to y according to Eq. 1.14; see Fig. 1.10. Substituting Eqs. 1.13–1.17 into Eqs. 1.10–1.12, the Gaussian, mean, and non-spherical curvatures can be obtained for each point.

1.1.3.3

Projection of Sediment Particles

In addition, the outlines of individual particles can also be extracted from the SEM images for the analysis of micro-morphology (i.e. the projection of sediment particles). According to the principles of SEM, the gray matrix does not indicate the actual heights of the particle surface, while the outline of each individual particle provides the actual roughness of the particle. The sediment particle shape can be represented by a plane projection contour, i.e. a closed curve in the 2D plane. A more complex curve indicates a more complex shape of sediment. There usually is a background around the sediment particle in the SEM image. Thus, the particle must first be distinguished from the background using methods such as the Canny, Sobel, and Laplacian operators (Su and Wang 2005), to outline its edge for further analysis (see Fig. 1.11). The common methods of shape description include Fourier shape analysis, wavelet descriptor, Freeman chain code, parametric equations, and spline functions (Thomas et al. 1995; Ehrlich and Weinberg 1970), among which Fourier analysis has been widely used due to better shape retention, stability, and reliability. The following is a brief introduction of the Fourier analysis method applied to describe particle contours. (1) Introduction to Fourier analysis A gray matrix, Z(x, y), is obtained by digitizing a SEM image, and the coordinate system is shown in Fig. 1.12. Assuming that the particle is homogeneous, the center of mass of the sediment particle projection, (xc, yc), then is obtained according to the coordinates of all points on the edge profile. 8
SOH) on the sediment particle surfaces, where >S represents the surface atoms and OH represents hydroxide. The amphoteric dissociation of surface hydroxyl, >SOH, is expressed as H þ

H þ

þH

þH

[ SOH2þ þ [ SOH þ [ SO

ð1:31Þ

where H+ represents the hydrogen ions. As the surface of sediment particle is negatively charged, the equilibrium in Eq. 1.31 shifts toward the left side under the acidic conditions (i.e. a lower pH value). The adsorbed H+ would neutralize the surface charge of the sediment particles, resulting in a smaller absolute value of the zeta potential. In contrast, the equilibrium in Eq. 1.31 shifts toward the right side with a higher pH value. The hydroxyl anion, OH−, in solutions would increase the amount of negative surface charge, which then increases the EDL thickness resulting in a greater zeta potential. Thus, the absolute value of the zeta potential increases with increasing pH value. However, the cations calcium (Ca2+) and magnesium (Mg2+) will precipitate on the particle surface when the pH is too high, instead resulting in a rapid reduction of the zeta potential and even a charge reversal. Studies of sediment collected from the Pearl River estuary confirmed that the absolute value of the zeta potential increases first and then decreases with the increasing pH value (Qiu and Zhang 1994). Similar conclusions also were obtained by other researchers (Cai et al. 1988; Liu 1990; Guo et al. 2004). The adsorption of trace metal ions slightly influences the zeta potential of sediment particles, except for Ca2+ and Mg2+ ions which will precipitate on the particle surface as previously stated (Hunter and Liss 1982; Wang 1991). It is important to consider the effects of Ca2+ and Mg2+ ions due to their high concentrations in natural waters. In addition, the adsorption of organic matter significantly influences the zeta potential of sediment particles (Neihof and Loeb 1974; Hunter and Liss 1982; Zhang et al. 1990), i.e. a layer of organic film forms on the particle surface after the adsorption of organic matter, thus affecting the surface charge and leading to a more uniform distribution. Accordingly, the zeta potential of sediment particles becomes similar to each other which were originally very different.

1 Surface Micro-morphology and Adsorption …

38

1.2.1.3

Surface Charge Distribution

The electrostatic and electrokinetic properties of sediment particles reflect the average surface charge characteristics. To better understand the mechanisms of interactions among sediment, pollutants, and microorganisms, e.g. the distribution of pollutants at the sediment/water interface, it is necessary to study the local surface charge distribution on the particle surfaces. Colloid chemistry generally assumes that the surface charge is uniformly distributed, which is convenient for theoretical derivation and analytical solutions. Natural sediment particles, however, possess especially complex surface morphology and pores of various scales, and they are also assemblages of minerals such as quartz, feldspar, and iron/aluminum oxide. All these features lead to a heterogenous surface charge distribution. For instance, there are primarily two different views on the surface charge distribution of kaolinite. One view assumes that the basal plane surfaces are negatively charged with positive edges (van Olphen 1963), as shown in Fig. 1.21a. As kaolinite is a 1:1 sheet silicate, the second view assumes a dual basal plane surface model; i.e. the basal plane surfaces of a silicon–oxygen tetrahedron and aluminum–oxygen octahedron are negatively and positively charged, respectively, while the particle edges take a net negative or positive charge (Carty 1999; Yang et al. 2001); see Fig. 1.21b. Although these two views have not reached a consensus on the surface charge distribution of kaolinite, they both support the fact that the surface charge of kaolinite is heterogeneously distributed. A large amount of research has been done on the measurement of surface charge distribution. In the early studies, the surface charge distribution mostly was indirectly measured (Jacobs et al. 1997; Zhang et al. 2001). For instance, Feick and Velegol (2000) measured the average value and standard deviation of the zeta potential using translational electrophoresis and electrophoretic rotation, respectively, to indicate the charge non-uniformity on colloidal particles. Subsequently, Velegol and Thwar (2001) developed a closed-form analytical model to estimate the effects of non-uniform surface charge distribution on the mean force between spherical colloidal particles. Taboada-Serrano et al. (2005) measured the surface charge heterogeneity of a silica plate via AFM through measuring a 2D array of force versus distance curves in electrolyte solutions with different ionic strengths and pH values. Yin and Drelich (2008) further measured the force versus distance

Fig. 1.21 Concept diagrams of surface charge distribution of kaolinite. a Edge–basal plane surface model and b dual basal plane surface model (Huang et al. 2012a)

1.2 Heterogeneous Surface Charge Distribution

39

curves at different locations of a multi-phase volcanic rock, especially across the boundary between adjacent phases, to characterize the mineral-induced heterogeneous distribution of surface charge. Similar research was also done at the bitumen– water interface (Drelich et al. 2007). Compared with AFM, EFM is more convenient to characterize the surface charge characteristics due to the direct detection of electrostatic forces between the tip and samples (Martin et al. 1988). EFM is mostly applied to surface charge measurement of thin film materials, such as the polyimide film (Han 1999) and chitosan film (Yang and Tang 2005). Zhao et al. (2007a) generated surface charge by rubbing the polyimide film surface with a conductive probe and then characterized the surface charge using EFM. Results showed that the frictional speed of the probe and the applied voltage greatly influence the polarity, density, and distribution of surface charge. There are also some studies focusing on the surface charge distribution measurement of granular samples, e.g. polystyrene latex particles (Tan et al. 2005), but the direct measurement of surface charge distribution on sediment particles has not been reported. In the next section, the surface morphology and charge distribution of quartz sands are measured as an example using EFM (Huang et al. 2012b).

1.2.2

Measurement of the Surface Charge Distribution

Quartz is the main component of natural sediment. According to mineral composition analysis, it accounts for 31–73% of the sediment components in the Yangtze River (Huang et al. 2012b). Meanwhile, the surface of quartz sand is smoother than that of natural sediment, which is easier for experimental observations. Thus, quartz sand is selected as an example in this section for the measurement of the surface charge distribution.

1.2.2.1

Measurement Principle

The surface charge properties are measured using EFM by directly detecting electrostatic forces between the tip and samples. A MESP probe is used for the measurement that is coated with a layer of conductive metal film, and a known voltage is applied to the probe to obtain high-quality images. First, the sample surface is scanned point by point using the tapping mode, and the detailed information on surface morphology is recorded. To avoid the impacts of surface morphology on the signals of surface charge, the probe is moved back to the original position and elevated 50 nm vertically after the morphological characteristics are recorded. Then, the closed-loop feedback system is turned off and an open-loop scanning is done in accordance with the recorded surface morphology. This is the lift mode function of EFM, which can effectively eliminate the impact of surface morphology on charge measurement (Dianoux et al. 2003; Zhao et al. 2007b). Both

1 Surface Micro-morphology and Adsorption …

40

Fig. 1.22 Principle of the electrostatic force microscope (a) and the lift mode (b)

surface morphology and charge distribution at the nanometer scale are obtained after the measurements; see Fig. 1.22. A phase image is obtained through the surface charge measurement. The phase image shows the phase angle shift (hereafter referred to as the phase shift) between the piezoelectric actuator driving signal and actual cantilever oscillation (Terris et al. 1990; Zhao et al. 2007a). The tip–sample interactions change the vibrational characteristics of the cantilever causing a resonance phase shift, which is then presented on the screen through the signal acquisition and processing system. Magonov et al. (1997) analyzed the effect of tip–sample interactions on cantilever vibration by introducing an effective force constant, keff = ksp + rF, where ksp is the spring constant representing the ability to resist elastic deformations and rF represents the sum of the force derivatives for all the forces, Fi, acting on the cantilever. Here, only the electrostatic force, F = −keqtipqsurf/H2ts, is considered resulting in: rF ¼

X @Fi 2ke qtip qsurf ¼ @Hts Hts3

ð1:32Þ

where ke is the electrostatic constant (=8.9880
109 N m2/C2), Hts represents the separation distance between the tip and sample, which is set as a constant for the lift mode, qtip and qsurf are the surface charge of the tip and sample, respectively, and qtip is a constant once the applied bias voltage is given. Then, the phase shift of the cantilever vibration, D/0 , can be expressed as D/0 

Qcl rF Qcl 2ke qtip qsurf ¼  / qsurf ksp ksp Hts3

ð1:33Þ

where Qcl is the quality factor of the cantilever, which is influenced by the resonant frequency and damping factor reflecting the resonant properties of the cantilever. Equation 1.33 indicates that the phase shift, D/0 , is proportional to the local surface charge of the sample, qsurf, so the phase image provides a map of the charge distribution on the sample surface. The absolute value of the phase shift represents the density of the surface charge; i.e. a greater phase shift indicates a greater surface

1.2 Heterogeneous Surface Charge Distribution

41

charge density. Meanwhile, the phase shift is positive when the electrostatic force acting on the tip is repulsive while it is negative when the force is attractive. Thus, the relation between the signs of the phase shift and surface charge depends on the applied voltage. The phase shift has the same sign as the surface charge when qtip is positive; i.e. a positive phase shift corresponds to a positive surface charge. In contrast, the sign of the phase shift is opposite to that of the surface charge when qtip is negative, i.e. a positive phase shift corresponds to a negative surface charge.

1.2.2.2

Surface Charge Distribution

Quartz sand with a size range of 0.3–0.5 mm was collected from natural rivers and used as an example for the measurement of surface charge distribution. To image the surface morphology and charge distribution, quartz sand particles were randomly selected with a tweezer and stuck onto metal sample plates with double-sided adhesive. The whole process should be as fast as possible to reduce the contamination of samples. The experiments were done using the EFM mode of a DI 3100 atomic force microscope (Veeco Bruker, USA) in the Department of Physics at Tsinghua University. A large number of samples were prepared, and at least three different positions were chosen for observation of each sample. The selection of positions should be random, but also the researcher should try to ensure the representativeness of each position. Figure 1.23 shows the results of an EFM measurement, with a scanning range of 10
10 lm and a scanning array of 256
256 pixels. The interval between two adjacent scanning points is about 39 nm, providing a detailed description of surface morphology and charge distribution of quartz sand. Figure 1.23a shows the surface morphology, and the brightness represents the elevation; i.e. the bright and dark regions imply high and low elevations, respectively. It is observed that the surface elevation difference is within 100 nm. The corresponding phase image is shown in Fig. 1.23b, and the brightness represents the phase shift. The bright region represents a positive phase shift, implying a repulsive electrostatic force acting on the tip; the dark region represents a negative phase shift, i.e. an attractive electrostatic force. The sign of phase shift characterizes the sign of surface charge, and the magnitude of phase shift can determine the strength of surface charge. The observed phase shift is within 3°. Figure 1.23b is obtained when a bias voltage of +5 V is applied on the conductive tip. As the bright region corresponds to a positive phase shift, i.e. a repulsive force acting on the tip, the charge distribution in these regions should be positive, and there are stronger positive charges in the brighter regions. In contrast, the dark region corresponds to a negative phase shift, i.e. an attractive force, so there should be negative charge distribution, and the darker region implies a stronger negative charge. Compared with the image of surface morphology (Fig. 1.23a), surface charge distribution has a strong correlation with the morphology, and the region with more complex morphology exhibits a greater surface

42

1 Surface Micro-morphology and Adsorption …

Fig. 1.23 a Surface morphology and b phase image of quartz sand (with a bias voltage of +5 V applied on the conductive tip) (Huang et al. 2012b)

charge density. When a bias voltage of −5 V is applied, similar conclusions can be drawn as for the bias voltage of +5 V. To reflect the statistical properties of the surface charge distribution, the frequency histograms of the phase shift with a bias voltage of +5 V and −5 V are plotted in Fig. 1.24, which shows that the phase shift of quartz sand follows a normal distribution. Under the bias voltage of +5 V, the mean phase shift is negative (−0.020°), indicating an attractive force and thus negatively charged for the overall performance. Under the bias voltage of −5 V, the mean phase shift is positive (+0.008°), indicating a repulsive force and also negatively charged for the

Fig. 1.24 Frequency histograms of phase shift on the surface of quartz sand with a bias voltage of a +5 V and b −5 V applied on the conductive tip (note std = standard deviation) (Huang et al. 2012b)

1.2 Heterogeneous Surface Charge Distribution

43

overall performance, which confirms the conclusion obtained under the bias voltage of +5 V. The normal distribution illustrates that both positively and negatively charged regions exist on the quartz sand surface, with an overall performance of a weak negative charge. Two cross sections on the quartz sand surface were randomly chosen for further analysis; see the blue lines in Fig. 1.23. Figure 1.25 shows the surface morphology of these two cross sections, and the corresponding phase images reflecting the surface charge distribution are shown in Fig. 1.26. During the scanning process in the lift mode, the probe is elevated 50 nm vertically and a bias voltage of −5, 0, and +5 V is sequentially applied. When there is no bias voltage applied (0 V), only weak information on the surface charge distribution can be detected, and the phase shift fluctuates within a small region around the zero value. When a bias voltage of −5 V is applied, the tip–sample interaction is attractive when the probe sweeps through positively charged regions, i.e. negative phase shifts corresponding to concave parts of the curve. When the probe sweeps through negatively charged regions, the tip–sample interaction is repulsive, which results in positive phase shifts corresponding to convex parts (Terris et al. 1990). Similarly, when a bias voltage of +5 V is applied, the positively charged regions correspond to convex parts of the curve while the negatively charged regions correspond to concave parts. As shown in Fig. 1.26, the concave and convex parts of the curve under the voltage of −5 V correspond to the convex and concave parts of the curve under the voltage of +5 V, respectively. So, similar results of surface charge distribution for these cross sections can be acquired under the bias voltage of −5 V and +5 V. Comparing Fig. 1.25 with Fig. 1.26, it can also be seen that surface charge distribution has a strong correlation with the morphology. The regions with more complex morphology exhibit greater phase shifts, corresponding to a greater surface charge density.

Fig. 1.25 Surface morphology of the cross sections shown in Fig. 1.23 (i.e. the blue lines)

1 Surface Micro-morphology and Adsorption …

44

Fig. 1.26 Phase shifts of the cross sections in Fig. 1.23 for different applied bias voltages (Huang et al. 2012b)

1.2.3

Statistical Analysis of Surface Charge Distribution and Morphology

As previously described, the surface charge distribution has a strong correlation with the morphology. So, a statistical analysis is further done to characterize the relations between the surface charge distribution and micro-morphology. As listed in Table 1.2, the particle surface can be classified into concave, convex, groove, ridge, flat, and saddle parts by Gaussian curvature, KG, and mean curvature, HM. Table 1.8 sorts out the microstructures of two groups of quartz sands corresponding to the surface charge distribution. The results show that the positive and negative charge mostly concentrate on the saddle, convex, and concave parts of the surface with percentages of 53.26, 22.80, and 22.03%, respectively. Electrostatic interaction is a major factor for adsorption. The regions with a concentrated charge distribution include more active adsorption sites and may adsorb pollutants more easily. Therefore, it can be expected that greater adsorption would occur in the saddle, convex, and concave parts than in the groove, ridge, and flat parts. Chen (2008) once measured the distribution of adsorbed phosphorus (P) on the sediment surface. Spectrum analysis with an EDS illustrated that most Table 1.8 Relations between the surface charge distribution and micro-morphology (Huang et al. 2012b) Group 1# 2# Total

Number % Number % Number %

Saddle

Convex

Concave

Groove

Ridge

Flat

Total

31,886 54.91 33,959 52.53 65,845 53.26

13,229 22.78 14,955 23.13 28,184 22.80

12,745 21.95 14,485 22.40 27,230 22.03

106 0.18 119 0.18 225 0.18

104 0.18 133 0.21 237 0.19

906 1.56 1000 1.55 1906 1.54

58,070 100 64,651 100 123,627 100

1.2 Heterogeneous Surface Charge Distribution

45

adsorbed P is distributed in the saddle, convex, and concave parts with percentages of 57.50, 20.80, and 21.60%, respectively, while less is distributed in the groove, ridge, and flat parts. This is consistent with the locations of concentrated charge on the particle surface. Moreover, the relation between the surface charge distribution and non-spherical curvature, TN, is further quantitatively analyzed, as shown in Fig. 1.27. The non-spherical curvature, TN, as defined in Eq. 1.12, is zero for the surface of a smooth sphere, and a greater TN implies more complex surface morphology (Chen 2008). In Fig. 1.27, the x-axis represents non-spherical curvature using logarithmic coordinates, and it is normalized by the maximum value of TN to eliminate the impact of particle size. The y-axis represents the phase shift that characterizes the magnitude of surface charge. As the data in Fig. 1.27 are obtained under a bias voltage of +5 V, the positive and negative phase shifts imply positive and negative surface charges, respectively. It can be found that the surface is negatively charged when 0.05 < TN < 0.5, and it reaches the extreme (lowest) value near TN = 0.2. When 0 < TN < 0.05, the surface is positively charged. The smaller the non-spherical curvature is, the greater the surface charge, and the surface charge gradually tends to a constant value. When 0.5 < TN < 1, the surface also is positively charged. However, the greater the non-spherical curvature is, the greater the surface charge, with a relatively higher growth speed. The solid line is the best-fit result with the phase shift D/0 expressed as: D/0 ¼ 0:20 þ 0:27e15:06TN  0:38e1:80TN

ð1:34Þ

Equation 1.34 reflects the impact of surface morphology on charge distribution. Combining with the calculation of non-spherical curvature, the charge distribution on particle surfaces can be estimated using Eq. 1.34. Figure 1.28 shows the comparisons between the measured and calculated surface charge distributions of the cross sections in Fig. 1.23. The dots are the measured surface charge with the applied voltage of +5 V, which is directly obtained from the phase image, and the dotted lines represent the calculated values using

Fig. 1.27 Relations between surface charge distribution and non-spherical curvature normalized by the maximum TN (with a bias voltage of +5 V) (Huang et al. 2012b)

1 Surface Micro-morphology and Adsorption …

46

Fig. 1.28 Comparisons between the measured and calculated surface charge distributions of quartz sand particles with an applied voltage of +5 V (Huang et al. 2014)

Eq. 1.34. The solid lines represent the corresponding morphology of these two cross sections. It can be observed that the variations of the calculated surface charge are generally in agreement with those of measured values, indicating that Eq. 1.34 can reasonably simulate the surface charge distribution on particle surfaces.

1.3

Adsorption on Sediment Particles

As described in the previous sections, sediment particles have especially complex surface morphology, pore sizes of various scales, and non-uniform surface charge distribution. These characteristics affect the adsorption of nutrients/pollutants by sediment, and the attachment of microorganisms (e.g. bacteria) on particle surfaces, i.e. the important limiting factors for biofilm growth. Therefore, it is necessary to further explore the adsorption characteristics of sediment particles based on the reasonable characterization of their surface properties. In this section, the adsorption of nutrients, pollutants, and microorganisms by sediment is introduced from the view of adsorption models.

1.3.1

Adsorption Isotherms

Adsorption is the accumulation of substances at the interfaces, e.g. the solid/liquid interface (Brandt et al. 1993). Adsorption isotherms describe the relation between the adsorption amount and the aqueous equilibrium concentration at a given temperature, and different adsorption isotherms can be obtained for different combinations of adsorbents and adsorbates. The common adsorption isotherms include the Henry, Langmuir, and Freundlich isotherms of monolayer adsorption, as well as

1.3 Adsorption on Sediment Particles

47

the BET isotherm of multilayer adsorption. These isotherms are generally derived for solid–gas systems and then applied to the solid–liquid systems. As the adsorption in solid–liquid systems is mostly chemical adsorption, i.e. monolayer adsorption, the Henry, Langmuir, and Freundlich isotherms are introduced in this sub-section.

1.3.1.1

Henry Isotherm

For the Henry isotherm, it is assumed that the adsorption amount is proportional to the aqueous equilibrium concentration (Kondo et al. 2001), i.e. Cs ¼ Kd Cw

ð1:35Þ

where Cs is the adsorption amount per gram of sediment and Cw is the aqueous concentration of adsorbate at equilibrium. The parameter Kd is an adsorption constant, representing the partitioning of adsorbates between the particulate and dissolved phases, also known as the partition coefficient. The concept of a partition coefficient is simple and can easily be incorporated into the water quality models, so it was widely applied in early studies. However, the value of Kd will be significantly affected by the physicochemical conditions of the solution, and it may differ over several orders of magnitude in different systems, resulting in great difficulty in making a reasonable parameter choice in practical applications. Meanwhile, Kd is an empirical constant that lacks basic theoretical derivation and physical meaning. The Henry isotherm is generally applicable to adsorption in an extremely dilute solution.

1.3.1.2

Langmuir Isotherm

Langmuir (1918) proposed an isotherm of monolayer adsorption, as shown in Eq. 1.36, based on the assumptions such as that the adsorbent surface is homogeneous, all the adsorption sites are equivalent, monolayer coverage only, and there is no interaction between adsorbate molecules on adjacent sites. The Langmuir isotherm can be derived from both kinetic and thermodynamic methods. The former considers that the rate of adsorption equals that of desorption at equilibrium, and the latter considers that the chemical potential of molecules in the solution equals that of adsorbed molecules. Cs ¼ Cmax

KL Cw 1 þ KL Cw

ð1:36Þ

where Cmax is the maximum possible amount of adsorption, i.e. adsorption capacity, and KL is a constant related to the affinity of adsorbent to the adsorbate.

1 Surface Micro-morphology and Adsorption …

48

The Langmuir isotherm has been widely used in aqueous chemistry due to its clear physical meaning. For example, Wang et al. (2009) found that the maximum P adsorption amounts by sediment from Cuntan, Xiaojiang, Daning, and Xiangxi in the Yangtze River basin are 402, 358, 165, and 150 mg/kg, respectively. It has also been reported that the P adsorption capacity of sediment from the lakes in the middle and lower reaches of the Yangtze River is 128–833 mg/kg (Wang et al. 2005b).

1.3.1.3

Freundlich Isotherm

The Langmuir isotherm also deviates significantly from experimental results in many cases, primarily because it fails to account for the surface heterogeneity of adsorbent. Heterogeneous surfaces generally have multiple types of available adsorption sites. The Freundlich (1909) isotherm, an empirical formula, is the most important multi-site adsorption isotherm for heterogeneous surfaces, expressed as Cs ¼ KF ðCw Þ1=nF

ð1:37Þ

where KF and nF are the adsorption constants. As shown in Eq. 1.37, the Freundlich isotherm does not satisfy Henry’s law when Cw tends to zero. Meanwhile, the adsorption amount tends to infinity when Cw approaches infinity, which is inconsistent with real conditions (Kondo et al. 2001). So, the Freundlich isotherm is more applicable for adsorption with moderate bulk concentrations. Both the Langmuir and Freundlich isotherms have been widely used in the study of adsorption on sediment particles; however, there are still no conclusions on which one is better for application. In practice, the appropriate isotherm can be chosen according to the specific adsorption system.

1.3.2

Mechanistic Surface Complexation Model

The adsorption isotherm is generally used to describe the adsorption phenomena after the partition coefficient. There is a certain theoretical basis for the derivation of the adsorption isotherm, i.e. a semiempirical model, and it can be used to simulate the adsorption results. However, a detailed description of the adsorption mechanism is still lacking. Meanwhile, the values of model parameters also depend on the aqueous chemistry conditions, and the adsorption isotherm cannot effectively characterize the effects of specific adsorption, pH, and ionic strength on the adsorption process. Thus, the obtained isotherm of a specific solid–liquid system is difficult to apply in other water bodies (Tang et al. 2000). In this sub-section, the mechanistic surface complexation model will be further introduced.

1.3 Adsorption on Sediment Particles

1.3.2.1

49

Surface Complexation Model

The mechanistic surface complexation model, which describes surface adsorption phenomena as complexation reactions between the surface functional groups and the ions in the solution, has been widely applied to the study of the adsorption process since it was first proposed in the early 1970s (Stumm et al. 1970). For example, Catts and Langmuir (1986) studied the adsorption characteristics of copper (Cu), lead (Pb), and zinc (Zn) by manganese oxide (d-MnO2); Dzombak and Morel (1990) comprehensively studied the adsorption of hydrous ferric oxide; the effects of pH and ionic strength on the adsorption properties of different oxides were studied by Robertson and Leckie (1997). The surface complexation model has also gradually been applied to natural sediment, which is an assemblage of various minerals with more complex surface properties. Wen et al. (1998) regarded the sediment as a whole and studied the adsorption characteristics of Cu and cadmium (Cd) using the concept of average surface functional groups. Davis et al. (1998) analyzed the Zn adsorption by sediment using a component additivity approach, simultaneously considering the roles of different mineral compositions. Similarly, Dong et al. (2012) studied the adsorption of uranium (VI) (U (VI)) on sediment particles. There are various types of hydroxyl groups and other charged species present on the surface of sediment particles (Davis and Kent 1990). These surface hydroxyl groups can be protonated or deprotonated, as well as exchange with the ligands in the solution, as shown in Eqs. 1.38–1.41. Surface protonation: [ SOH þ H þ ¼ [ SOH2þ [ SOH ¼ [ SO þ H þ

ð1:38Þ

int Ka1

ð1:39Þ

int Ka2

Ligand exchange: [ SOH þ M2 þ ¼ [ SOM þ þ H þ [ SOH þ L2 ¼ [ SL þ OH

K int K int

ð1:40Þ ð1:41Þ

where >SOM+ and >SL− represent the adsorbed metal cations and anions, int int respectively, Kint is the intrinsic a1 and Ka2 are the intrinsic acidity constants, and K surface complexation constant. These intrinsic constants should be further corrected with an electrostatic factor to reflect the effects of the charge at the solid/liquid interface. The surface complexation model describes surface adsorption as chemical reactions between these charged surface groups and ions; i.e. the particle surface is treated as a kind of polyelectrolyte with many charged functional groups, and a complex equilibrium method is used to study the binding of H+, OH−, and contaminant ions on the particle surface. Thus, the surface complexation model is

1 Surface Micro-morphology and Adsorption …

50

capable of reflecting the adsorption characteristics of sediment under different aqueous chemistry conditions. The surface complexation reactions are expressed by the mass action and mass balance equations. Although the mathematical details vary somewhat, there are two common attributes shared by various surface complexation models (Tadanier and Eick 2002), i.e. (1) The Gibbs free energy of the surface adsorption reaction (ΔGad) is partitioned into the chemical (intrinsic) and electrostatic components in Eq. 1.42, and the electrostatic component is an important aspect of the surface complexation model to differentiate from the complexation equilibrium in the solution. DGad ¼ DGint þ DGel þ Ru T ln Qr

ð1:42Þ

where the intrinsic component ΔGint reflects the chemical energy change due to the reaction between the adsorbed ion and surface functional group, whereas the electrostatic component ΔGel represents the energy required to move the ion from bulk solution to the surface which has an electrostatic potential, W0, relative to the bulk solution. The third term on the right-hand side of Eq. 1.42 represents the dependence of the adsorption free energy on the system composition, in which Qr is the reaction quotient, Ru is the universal gas constant, i.e. 8.31 J/(mol K), and T is the absolute temperature. The intrinsic contribution of the free energy of adsorption is given as DGint ¼ Ru T ln K int

ð1:43Þ

and the electrostatic contribution is given by DGel ¼ DzFW0

ð1:44Þ

where Δz is the net change of surface charge due to species exchange that defines the adsorption reaction and F is Faraday’s constant (=96485.34 C/mol). Substituting Eqs. 1.43–1.44 into Eq. 1.42, and invoking the equilibrium condition that ΔGad = 0, it can be found that

K

app

¼ Qr ¼ K

int

DzFW0 exp  Ru T

ð1:45Þ

where Kapp is the apparent surface complexation constant. The exponential term in Eq. 1.45 is the Boltzmann factor, i.e. an electrostatic correction factor, which mathematically describes the influence of surface potential on the ion adsorption by charged surfaces. (2) An EDL adjacent to the surface with adsorbed ions placed in one or more discrete electrostatic planes is considered, in which the electrical potential of each plane is related to its charge by an electrostatic model. The constant capacitance model (CCM), diffuse layer model (DLM), and triple-layer model

1.3 Adsorption on Sediment Particles

51

(TLM) are the most common surface complexation models that have been extensively applied to describe the surface adsorption (Stumm et al. 1970; Schindler and Gamsjäger 1972; Yates et al. 1974). The relations between the surface potential of each plane (W0, Wb, and Wd) and its charge (r0, rb, and rd) are listed in Table 1.9, where the meanings of the subscripts 0, b, and d refer to Fig. 1.29 (i.e. the particle surface, inner- and outer-Herlmholtz layers, respectively), and C0, C1, and C2 are the capacitances of the corresponding layers. Is is the ionic strength of the solution, and zi is the charge of the adsorbed positive/ negative ions. It is worth noting that these EDL structures all assume that the particle is a symmetrical sphere with a smooth surface and a uniform charge distribution, and then the quantitative relations between the surface potential and charge are established. However, the surface charge is generally heterogeneously distributed for natural sediment, as described in the previous sections. The complex surface characteristics, such as the crystal structure, mineral composition, and surface roughness, always result in heterogeneities of surface charge distribution. Davis and Kent (1990) concluded that how to properly determine the EDL structure of natural sediment is a great challenge to apply the surface complexation model to natural systems. Thus, the surface complexation model should be further improved to consider the heterogeneous distribution of surface charge for natural sediment.

1.3.2.2

Modified Surface Complexation Model

The surface morphology and charge distribution of sediment particles have been previously observed by EFM, and a statistical relation between these two variables has been obtained; see Eq. 1.34. Thus, the surface charge distribution can be estimated by calculating the non-spherical curvature, TN, and subsequently the distribution of surface potential is derived using the formula of surface potential around charged particles. Then, the surface complexation constants can be further modified for a more reasonable correction of the electrostatic factor considering the non-uniform charge distribution (Huang et al. 2014). The formula for calculating the potential around heterogeneously charged particles is as follows (Kirkwood 1934; Sader and Lenhoff 1998): wðrs ; h; uÞ ¼

1 X n  X n¼0 m¼0

am;n cos mu þ bm;n sin mu



 Kn ðjrs Þ R n þ 1 jðr RÞ m e s Pn ðcos hÞ Kn ðjRÞ rs

ð1:46Þ where R is the particle radius, j is the inverse Debye length, (rs, h, u) represents the position in the spherical coordinate system, Pm n (cosh) is the associated Legendre function, and Kn(x) is the Kirkwood function expressed as

Diffuse layer model r0 ¼ 0:1174Is1=2 sinhðzi FW0 =Ru T Þ

Constant capacitance model r 0 ¼ C 0 W0

Surface complexation models

Relations between the surface potential and the charge

Table 1.9 Relations between the surface potential of each plane and its charge

rd ¼ 0:1174Is1=2 sinhðzi FWd =Ru T Þ

W0  Wb ¼ r0 =C1   Wb  Wd ¼ r0 þ rb =C2

Triple-layer model

52 1 Surface Micro-morphology and Adsorption …

1.3 Adsorption on Sediment Particles

53

Fig. 1.29 Structure of the electrical double layer

Kn ðxÞ ¼

n X 2s n!ð2n  sÞ!xs s¼0

ð1:47Þ

s!ð2nÞ!ðn  sÞ!

In addition, the coefficients am,n and bm,n are the moments of the surface charge distribution. For a particle with Np discrete point charges, i.e. a charge value of qi at (rsi, hi, ui), the coefficients am,n and bm,n can be calculated as: am;n ¼

P Np 1 ðn  mÞ! i¼1 qi ðrsi =RÞn Pm n ðcos hi Þ cosim/i h   K ð jR Þ nþ1 4pee R ðn þ mÞ!  n 1  ep =ee c Kn ðjRÞ

bm;n ¼

1 ðn  mÞ! 2pee R ðn þ mÞ!

2n þ 1

ð1:48Þ

m

P Np

n m i¼1 qi ðrsi =RÞ Pn ðcos hi Þ sin m/i   Kn þ 1 ðjRÞ n Kn ðjRÞ  2n þ 1 1  ep =ee

ð1:49Þ

where ep and ee are the permittivities of the particle and the electrolyte, respectively. When m = 0, cm = 1; otherwise, cm = 1/2. Equations 1.46–1.49 show how to calculate the potential around non-uniformly charged particles, and the distribution of surface potential W0(R, h, u) can be obtained by defining rs = R. Then, the relation among the surface morphology, charge distribution, and potential is established. Given the information on surface morphology, the distributions of surface charge and surface potential can be sequentially calculated. The mathematical sediment particle introduced in Sect. 1.1.3.4 is of a statistical sense, which characterizes the surface morphology of sediment particles using mathematical equations. Thus, the distributions of surface charge and potential are reproduced on mathematical sediment particles to ensure representativeness. Figure 1.30 shows the top view of the reproduced surface charge and potential distributions for the mathematical sediment particle in Fig. 1.18 with a radius of

1 Surface Micro-morphology and Adsorption …

54

Fig. 1.30 Top view of the distributions of surface charge (left) and potential (right) on a mathematical sediment particle (Huang et al. 2014)

10 lm, i.e. similar to the median size of sediment particles in the Yangtze River, and the total surface charge is approximately 7.3
10−13 C. The relations between the surface charge and potential of a statistical sense are then established, which are especially different from the assumed EDL structures of traditional surface complexation models as listed in Table 1.9. The distribution of pollutants at the solid/liquid interface is obtained by iteratively solving the mass action and mass balance equations. With initial guessed values of each term, such as the surface potential, W*0, the total surface charge, C, can be derived according to the various reactions in the system including the surface protonation and ligand exchange (see Eqs. 1.38–1.41), i.e. C¼F



 [ SOH2þ þ f [ SOM þ g  f [ SO g  f [ SL g

ð1:50Þ

Then, the total surface charge, C, is assigned to the surface of the mathematical sediment particle through Eq. 1.34, i.e. the statistical relation between surface charge distribution and morphology. Subsequently, the distribution of surface potential, W0(R, h, u), is obtained using Eqs. 1.46–1.49, and the convergence criterion of the electrostatic correction factor is Yj ¼ w0  w0 ðR; h; uÞ ¼ 0

ð1:51Þ

where W0 ðR; h; uÞ represents the average value of W0(R, h, u) and Yj estimates the difference between the calculated surface potential and the initial guessed value.

1.3.2.3

Validation of the Modified Surface Complexation Model

In this sub-section, data from titration and adsorption experiments were used for the model validation. Bolt (1957) did a surface titration experiment of quartz sands under different sodium chloride (NaCl) concentrations, i.e. 0.1, 0.01, and 0.001 mol/L, and the variation of surface charge density with pH is shown in

1.3 Adsorption on Sediment Particles

55

Fig. 1.31 Variation of surface charge density with pH for quartz sands under different NaCl concentrations. a 0.1 mol/L, b 0.01 mol/L, and c 0.001 mol/L. The data are from Bolt (1957) (Huang et al. 2014)

Fig. 1.31. The surface charge density decreases gradually with the increasing pH, and the isoelectric point (IEP) is about 4.5. The change rate of surface charge density varies at different NaCl concentrations; i.e. a higher ion concentration corresponds to a greater change rate. The CCM, DLM, and modified surface complexation model are used to fit the measured data, and the model parameters are listed in Table 1.10. In Fig. 1.31, the dots represent the measured data, and the solid, dashed, and dot-dashed lines represent the fitting results of the modified surface complexation model, CCM, and DLM, respectively. All these models can reproduce the experimental results, but the modified surface complexation model has relatively better performance, due to the consideration of the non-uniform surface charge distribution which is more consistent with the properties of natural sediment. Figure 1.32 shows the results of P equilibrium adsorption by sediment particles from the Yongding River, which was measured under a pH range of 6–7 and a background electrolyte concentration of 0.1 mol/L sodium nitrate (NaNO3) (Fang et al. 2013). The adsorption amount increases linearly at a low P equilibrium concentration, and then the increase rate gradually decreases with further increases in P concentration. Finally, the adsorption amount approaches the maximum value, i.e. the P adsorption capacity of approximately 0.35–0.40 mg/g. The fitting results

1 Surface Micro-morphology and Adsorption …

56

Table 1.10 Fitted parameters of surface complexation models for the titration experiment of Bolt (1957) (Huang et al. 2014) Surface complexation models

NaCl concentration (mol/L)

logKint a1

0.1 −1 0.01 −2 0.001 −2.75 0.1 −1.5 DLMa 0.01 −1.2 0.001 −1 Modified model 0.1 −1.5 0.01 −2.4 0.001 −3.3 a The parameters refer to Sverjensky and Sahai (1996) CCMa

logKint a2

Surface site density (sites/nm2)

C0 (F/m2)

−8 −9 −9.75 −8.5 −8.2 −8 −7.5 −8.4 −9.3

10

1

10

–

10

–

Fig. 1.32 Comparisons between the simulated and measured P equilibrium adsorptions (Huang et al. 2014)

of the CCM, DLM, and modified surface complexation model also are plotted in Fig. 1.32. The same surface acidity constants as the values in Table 1.10 are used, int i.e. log Kint a1 = −1.5 and log Ka2 = −7.5, and the other fitted model parameters are listed in Table 1.11. It can also be found that the modified model considering the non-uniform charge distribution on particle surfaces can better simulate the P equilibrium adsorption. Benyahya and Garnier (1999) studied the adsorption of trace metals including Cd, Zn, cobalt (Co), and manganese (Mn) by quartz sands with the pH range of 4– 9, as shown in Fig. 1.33. The applied concentration of quartz sands was 1 g/L, and a NaNO3 solution of 0.05 mol/L was used as the background electrolyte. Meanwhile, the initial concentrations of these trace metals were: Mn = 10 nmol/L, Co = 10 nmol/L, Zn = 50 nmol/L, and Cd = 10 nmol/L. As shown in Fig. 1.33, the adsorption of trace metals on quartz sand surfaces increases with the increasing

1.3 Adsorption on Sediment Particles

57

Table 1.11 Fitted parameters of surface complexation models for the P equilibrium adsorption by Fang et al. (2013) (Huang et al. 2014) Surface complexation models

logKint 1

logKint 2

logKint 3

Surface site density (sites/nm2)

C0 (F/m2)

CCM DLM Modified model

30.72 29.00 30.72

24.91 24.91 22.91

19.65 19.65 19.01

1 – –

þ ¼ [ SH2 PO4 þ H2 O [ SOH þ PO3 4 þ 3H

2.35 2.35 2.35 logKint 1

þ [ SOH þ PO3 ¼ [ SHPO 4 þ 2H 4 þ H2 O

logKint 2

þ

logKint þH ¼ þ H2 O 3 − 2− Note >SH2PO4, >SHPO4 , and >SPO4 represent the adsorbed phosphate anions [ SOH þ PO3 4

[ SPO2 4

Fig. 1.33 Adsorption of Cd, Zn, Co, and Mn by quartz sands (Huang et al. 2014)

pH value. The adsorption amount is especially small when pH is less than 6, which mainly originates from cation exchange. Then, the adsorption amount increases rapidly when pH is greater than 6, and the pH values corresponding to the maximum adsorption of these four trace metals follow: Zn < Cd < Co < Mn. The experimental results were fitted to the modified surface complexation model, and the model parameters are listed in Table 1.12. It can be found that the modified model can reasonably simulate the adsorption properties of these trace metals by quartz sands. Subramaniam et al. (2003) studied the adsorption of Cu by quartz sands of different sediment concentrations, as shown in Fig. 1.34. The concentration of quartz sands was set as 0.25, 1, and 2 g/L, and the initial concentration of Cu was 1.6
10−4 mol/L. Meanwhile, a NaNO3 solution of 0.001 mol/L was used as the background electrolyte, and the surface site density was about 5.0 sites/nm2. In Fig. 1.34, the lines represent the fitting results of the modified surface complexation model, where the utilized surface acidity constants and the surface complexation int int constant are log Kint = 1.39. The results show a1 = −1.5, log Ka2 = −7.5, and log K

1 Surface Micro-morphology and Adsorption …

58

Table 1.12 Fitted parameters of the modified surface complexation model for the adsorption of Cd, Zn, Co, and Mn (Huang et al. 2014)

a

Trace metals

logKint

logKint a1

logKint a2

Surface site density (sites/nm2)

Cd Zn Co Mn

−5.57 −3.73 −6.31 −6.35

−1.5

−7.5

2.35

logKint [ SOH þ M2 þ ¼ [ SOM þ þ H þ a 2+ M represents the metal cations, i.e. Cd, Zn, Co, and Mn

Fig. 1.34 Adsorption of Cu by quartz sands under different sediment concentrations (Huang et al. 2014)

that the adsorption of Cu is affected by the concentration of adsorbent, which can be reliably simulated using the modified surface complexation model. Overall, the modified surface complexation model is closer to the adsorption characteristics of natural sediment and can better simulate the adsorption of nutrients/pollutants on sediment surfaces.

1.3.3

Interactions Between Sediment and Bacteria

Bacteria are ubiquitous in aqueous environments (Whitman et al. 1998; Wu et al. 2012). Sediment provides excellent substratum for bacterial colonization, and the majority of bacteria are attached to the exposed sediment surfaces in natural systems (Beveridge et al. 1997; Hong et al. 2014). Accordingly, the secretion of metabolic products (e.g. extracellular polymeric substances, EPSs) causes the formation and growth of biofilm on the sediment surfaces (Wingender et al. 1999; Flemming and Wingender 2010). Thus, biofilm is a complex matrix of living microorganisms and their metabolic products, and the bacterial attachment on the sediment surface is the prerequisite for biofilm growth. The interactions between

1.3 Adsorption on Sediment Particles

59

Fig. 1.35 Schematics of the bacterial adhesion process (Hori and Matsumoto 2010). a Reversible adsorption by electrostatic and van der Waals forces or cell surface hydrophobicity, and b irreversible firm attachment by extracellular bridging polymers

sediment and bacteria will influence the geochemistry and microbiology processes such as biofilm formation, mineral weathering, and biodegradation of organic pollutants (Chenu and Stotzky 2002), thus further strongly affecting the sediment transport and sediment-associated contaminant transport (Headley et al. 1998; Tolhurst et al. 2008; Shang et al. 2014). In this sub-section, the interactions between sediment and bacteria will be further introduced. Bacterial attachment to the particle surfaces represents an initial step in bacterial colonization and biofilm formation (Forsythe et al. 1998; Ams et al. 2004). Similar to most natural surfaces, the cell surfaces are usually negatively charged probably exhibiting varying degrees of hydrophobicity (Krasowska and Sigler 2014). Bacteria can become loosely associated with the particle surfaces through a reversible adsorption mediated by electrostatic and van der Waals forces or by cell surface hydrophobicity. An irreversible firm attachment may later occur usually mediated by the extracellular bridging polymers (Marshall et al. 1971; van Loosdrecht et al. 1990; Dhand et al. 2009), see Fig. 1.35, so biofilm formation will enhance the bacteria adhesion to particle surfaces. Initial adhesion of bacteria can be regarded as an abiotic physicochemical process (Bos et al. 1999; Hermansson 1999), which is greatly influenced by various factors such as pH (Farahat et al. 2009; Borkowski et al. 2015), ionic strength (Redman et al. 2004; Liu et al. 2013), mineral composition (Salerno et al. 2004; Rong et al. 2008), bacteria species (Li and Logan 2004; Morrow et al. 2005), and organic matter (Parent and Velegol 2004; Foppen et al. 2008; Park and Kim 2009). Generally, the bacterial adhesion decreases with the increasing pH, and a higher ionic strength results in a greater bacterial adhesion due to the compression of EDL. The effects of substrate mineralogy on bacterial adhesion might be interpreted as a charge effect, i.e. beyond a simple surface area dependence. For example, there will be lower adsorption of bacteria by quartz sands due to their similar negative charge, comparing with the adsorption by the oppositely charged calcite or ferric (Fe) oxyhydroxide-coated quartz. The bacterial adhesion varies among different bacterial species, mainly affected by the cell wall structures. The significant suppressive effects of low molecular weight organic ligands on bacterial adhesion have

60

1 Surface Micro-morphology and Adsorption …

also been observed, which are ascribed to both the increased negative charges by adsorbed ligands and the competition of ligands for binding sites. Bacterial adhesion to mineral surfaces has been examined extensively through experimental studies, which highlight the importance of both physical and chemical influences on bacterial mobility (Roberts et al. 2006; Farahat et al. 2010; Wu et al. 2012; Zhao et al. 2014). However, it is impossible to do exhaustive experiments on all types of bacterial species and mineral surfaces of environmental or geological interest. Therefore, it is important to design experiments that will enable the extrapolation and interpolation of experimental results to a more general and complex setting. Particularly, numerical models are especially required to describe the partition of bacteria at the solid/liquid interface, which is the foundation for further studies on biofilm growth, and the resultant effects on sediment and contaminant transport. The bacterial adsorption to particle surfaces can be described by not only the adsorption isotherms (Mills et al. 1994), but also the Derjaguin– Landau–Verwey–Overbeek (DLVO) theory (Hermansson 1999) and chemical equilibrium models (Yee et al. 2000).

1.3.3.1

Adsorption Isotherm for Bacterial Adhesion

Adsorption isotherms have been used to determine the partition of bacteria at solid/ liquid interfaces, but this approach also is empirical, and hence, the adsorption isotherms must be measured for each condition of interest (Yee et al. 2000). Bacterial adsorption yields equilibrium, linear, adsorption isotherms that vary with the bacterial species and solution chemistry (Mills et al. 1994). (1) Linear adsorption (Henry isotherm) The bulk partitioning approach is commonly used to describe bacterial adsorption onto mineral/sediment surfaces (e.g. Lindqvist and Bengtsson 1991; Zhang and Olson 2012). It is assumed that the adsorbed cells increase linearly with the bacterial concentration, as indicated by Eq. 1.35. Mills et al. (1994) studied the adsorption of groundwater bacteria by quartz sands at different ionic strengths, and the partition coefficient, Kd, ranges from 0.55 to 6.11 mL/g, with the greatest adsorption observed at the highest ionic strength due to the compression of the EDL. As the thickness of the EDL is inversely proportional to the square root of ionic strength, a linear relation between Kd and the square root of ionic strength has been obtained (R2 = 0.95–0.99). Although a high ionic strength results in greater bacterial adhesion, it is worth noting that the effect of ionic strength appears to gradually reach a plateau, i.e. a smaller increment of adsorption for additional salt added to the bulk solution. Zhang and Olson (2012) studied the effect of heavy metals on the attachment of Escherichia coli (E. coli) in soils and found that the addition of heavy metals reduces the negative charge of bacterial surfaces, which reduces the repulsive forces between bacteria and soil surfaces and then enhances bacterial attachment to soil surfaces. Cai et al. (2013) studied the adsorption of E. coli O157:H7 by the montmorillonite, kaolinite, and

1.3 Adsorption on Sediment Particles

61

goethite and found that the Kd values are in the sequence of goethite > kaolinite > montmorillonite at the same ionic strength. As the dominant bacterial adsorption reaction changes as a function of experimental conditions, the linear partition coefficient, Kd, varies significantly with pH, ionic strength, mineral composition, and bacterial species (Fein 2000). Thus, the determined partition coefficient is system specific and cannot be directly extrapolated to adsorption under other experimental conditions. (2) Adsorption isotherms Langmuir and Freundlich equations are the most generally applied adsorption isotherms, with the expressions presented in Eqs. 1.36 and 1.37, respectively. For the equilibrium adsorption isotherms, the steepness of the isotherms and the maximum equilibrium adsorption are distinct functions of the solution conditions and/or mineral types. The steepness of the isotherm is related to the affinity of bacteria to the substrate, and the adsorption capacity reflects the binding site density of the substrate (Tan and Chen 2012). Mills et al. (1994) observed a threshold of 6.93
108 cells/g for Fe(III)-coated sand using the Langmuir isotherm. Meanwhile, the adsorption in mixtures of quartz and Fe(III)-coated sand was successfully predicted by a simple additive model, and even a small amount of Fe(III)-coated sand in the mixture would significantly influence the extent of adsorption. The adhesion of E. coli to nano-Fe/aluminum (Al) oxides (Al2O3 and Fe2O3, respectively) was studied by Liu et al. (2013). The maximum adhesion to c-Al2O3 and a-Fe2O3 was 3212.9 and 219.5 mg/g, respectively, and the KL value for c-Al2O3 (i.e. 357.2 mL/mg) also was greater than that for a-Fe2O3 (i.e. 81.9 mL/mg). Thus, c-Al2O3 had a greater adhesion capacity due to the higher positive charge and also a higher adhesion strength for E. coli than aFe2O3. The adhesion of E. coli and Bacillus subtilis (B. subtilis) on amorphous Fe and Al hydroxides was further studied by Liu et al. (2015). The maximum Al(OH)3 adhesion capacities were estimated to be 2689.6 and 2358.7 mg/g for E. coli and B. subtilis, respectively, and the maximum Fe(OH)3 adhesion capacities of the two bacteria were 750.5 and 893.6 mg/g. The main reason for the relative lack of data on bacteria adsorption on clay minerals is the difficulty in the separation of bacteria in suspension from that adsorbed on clay minerals, due to the similar sizes of bacteria and clay minerals. Jiang et al. (2007) studied the adsorption of Pseudomonas putida (P. putida) on clay minerals (i.e. montmorillonite and kaolinite) and iron oxide (goethite), which conformed to the Langmuir equation. The maximum adsorption of P. putida on minerals occurred within the initial few hours, and the adsorption amount follows: goethite > kaolinite > montmorillonite, i.e. 4.8
1010, 4.1
1010, and 3.2
1010 cells/g, respectively. Vasiliadou et al. (2011) studied the attachment of P. putida onto differently structured kaolinite minerals, including the well (KGa-1) and poorly (KGa-2) crystallized kaolinite. Results indicated that KGa-2 presented a higher affinity and attachment capacity than KGa-1, showing that structural disorder can influence the attachment capacity of clay mineral particles. The adsorption of P. putida on different size fractions of soil particles, including the clay, silt, and

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62

sand fractions, was studied by Wu et al. (2012). The maximum amount of P. putida adsorbed by the clay fraction was 4.3 and 62.3 times as great as that by silt and sand fractions, respectively. The affinity of bacteria to soil particles followed the sequence of silt > clay > fine sand > coarse sand, indicating that the bacteria were apt to adhere to silt at the initial attachment, while the surface area of silt fractions may limit their capacity for bacterial adsorption. Zhao et al. (2014) studied the adhesion of bacterial pathogens to soil colloidal particles considering the influences of cell type and natural organic matter (NOM), and the results were fitted to the Freundlich equation. The KF values of Streptococcus suis (S. suis) SC05 adhesion to soil colloids were 4.1–8.1 times as large as those of E. coli WH09. Pathogen adhesion to NOM-stripped colloid (210.6–856.1 mL/g) was far greater than those to NOM-present colloid (31.3– 252.6 mL/g), which suggests that NOM inhibits bacterial adhesion probably by covering the active sites, changing the surface charge, and increasing the steric hindrance between bacteria and soil fractions. The adsorption isotherms, such as the Langmuir and Freundlich equations, are simple to apply without requiring a detailed understanding of the surface properties or the involved adsorption mechanisms. These models can be successfully applied in describing the adsorption processes if the conditions can be directly simulated in the laboratory. However, similar to the partition coefficient, the parameters of Langmuir and Freundlich models might vary as a function of the solution chemistry and system compositions by orders of magnitude. Thus, they are also only applicable to the conditions at which they are determined, and cannot be easily extended to other conditions (Fein 2000).

1.3.3.2

DLVO and Extended DLVO Theory

Bacterial adhesion begins with long-range, non-specific interactions between the bacterial cells and substrate, i.e. an unstable attachment, and the adsorbed bacterial cells can be removed from surfaces at this stage by fluid shear. Once the bacterial cells are in close proximity to a surface, short-range and specific interactions can be established, which are stable and able to glue the bacterial cells to the surface. These two processes are collectively referred to as initial adhesion, which depends upon the physical and chemical properties of bacterial cells, substratum surfaces, and the intervening medium (Chen and Zhu 2005). (1) DLVO theory The bacteria are about 0.5–2.0 lm in size, i.e. similar to the size of colloidal particles. Therefore, the bacteria can be treated as colloids so that the bacterial adhesion is described by the DLVO theory (Marshall et al. 1971), with the changes in free energy between the charged cell and solid surface evaluated as a function of the separation distance (Bos et al. 1999; Sharma and Rao 2002). The classical DLVO theory, as described by Derjaguin and Landau (1941) and Verwey and Overbeek (1948), is the first successful attempt to quantitatively describe the

1.3 Adsorption on Sediment Particles

63

colloidal stability interactions. The total interaction energy (GTot) is defined as the summation of electrical double-layer interaction energy, GEL, and Lifshitz–van der Waals attractive energy, GLW, i.e. GTot ¼ GEL þ GLW

ð1:52Þ

Electrical double-layer interaction energy, GEL: Electrostatic (EL) forces arise due to the EDL interactions between the particle and cell surfaces, which originate from the Coulomb interaction between charged molecules. The EL forces can be either attractive or repulsive depending on the chemical structure, suspending medium chemistry, and surface potential. The EDL interaction energy, GEL, between the bacterial cell and mineral particle can be expressed by the following equation for a sphere–sphere system: EL

G

  pee D1 D2 q21 þ q22 ¼ 2ðD1 þ D2 Þ  2q1 q2 1 þ expðjHbm Þ þ ln 1  exp 2jH
2 ln ð Þ f g bm q1 þ q22 1  expðjHbm Þ

ð1:53Þ

where ee is the permittivity of the electrolyte (aqueous medium), D1 and D2 represent the diameters of the bacterial cell and particle, respectively, and q1 and q2 are their corresponding surface charges. Moreover, Hbm is the separation distance between the bacterial cell and mineral particle, and j−1 is the thickness of EDL expressed as:  j¼

e2 X izi ni ee KB T

1=2 ð1:54Þ

where e denotes the electron charge, KB is the Boltzmann constant (=1.38
10−23 J/K), T is the absolute temperature, zi is the valency of the present ions, and ni is the number of ions per unit volume. Assuming D2 D1 , Eq. 1.53 is reduced to G

EL

    pee D1 q21 þ q22 2q1 q2 1 þ expðjHbm Þ
2 þ ln 1  exp 2jH ¼ ln ð Þ f g bm 2 q1 þ q22 1  expðjHbm Þ ð1:55Þ

Lifshitz–van der Waals interaction energy, GLW: Lifshitz–van der Waals (LW) attractive forces are the attraction force between condensed-phase molecules or surfaces, including dispersion, induction, and orientation Lifshitz–van der Waals forces (Farahat et al. 2010). For a sphere–sphere system, the Lifshitz–van der Waals attractive energy, GLW, is expressed as:

1 Surface Micro-morphology and Adsorption …

64

GLW ¼

D1 D2 Abwm 12Hbm ðD1 þ D2 Þ

ð1:56Þ

Considering that the radius of a mineral particle is larger than that of bacterial cell, i.e. D2 D1 , Eq. 1.56 is reduced to GLW ¼

D1 Abwm 12Hbm

ð1:57Þ

where Abwm is the effective Hamaker constant for the system of bacteria, water, and mineral, i.e. 2 DGLW Abwm ¼ 12pHmin adh

ð1:58Þ

where Hmin is the minimum separation distance between two surfaces (=1.57 Å) and ΔGLW adh is the Lifshitz free energy of adhesion, i.e. the LW component of the change in free energy, and can be evaluated as: DGLW adh ¼ 2

qffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffi cLW cLW cLW cLW w m  w b 

ð1:59Þ

where cLW is the Lifshitz–van der Waals energy component of the surface tension and the subscripts b, m, and w stand for the bacteria, mineral, and water, respectively. The magnitude of the total interaction energy and the associated separation distance determines how strong and reversible the adhesion is (Ozkan and Berberoglu 2013). A negative GTot indicates attractive interaction between the surfaces, and a positive value indicates repulsive interaction. The van der Waals attractive force is dominant in the vicinity of a surface, while the EDL interaction becomes dominant at a distance away from the surface, because the van der Waals force decreases sharply with distance (Hori and Matsumoto 2010). Accordingly, a typical total interaction energy profile contains a deep primary attractive well at a very small separation distance, an energy barrier, and a smaller secondary attractive region at a larger separation distance, as shown in Fig. 1.36. The deposition in the primary well is considered to be irreversible due to the large energy barrier, whereas the deposition in the secondary minimum is reversible under constant chemical conditions (Zhang and Olson 2012). Bacterial adsorption onto negatively charged surfaces has been observed by many researchers, although a sizable electrostatic energy barrier is obtained by the DLVO calculation; i.e. the adsorption is likely occurring in the secondary energy minimum (van Loosdrecht et al. 1989; Cai et al. 2013). Redman et al. (2004) studied the adhesion and transport of E. coli in porous media of quartz sediment grains at different ionic strengths. Results show that the depth of the secondary

1.3 Adsorption on Sediment Particles

65

Fig. 1.36 A typical total interaction energy profile between two interacting surfaces including the primary and secondary minimums, and the energy barrier

Fig. 1.37 Effects of ionic strength on the total interaction energy between the bacterial cell and particle surface (Hori and Matsumoto 2010)

energy minimum increases with the ionic strength of pore water (see Fig. 1.37), and an increase in the ionic strength results in an increase in the bacterial attachment. In contrast, a decrease in the ionic strength thereby eliminates the secondary energy minimum, resulting in a release of the majority of previously adsorbed bacteria, indicating that these cells are deposited reversibly in the secondary minimum. The DLVO theory can reasonably model the change in potential energy with the changing ionic strength by accounting for the differences of EDL thickness associated with each surface (Yee et al. 2000).

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1 Surface Micro-morphology and Adsorption …

S. suis SC05 and E. coli WH09 also are found to weakly adhere in the shallow secondary energy minimum by Zhao et al. (2014), and a negative correlation between the bacterial adsorption amount and the energy barrier height was obtained (R2 = 0.727, p < 0.01), which clearly confirms the major role of DLVO-type forces. The depth of the secondary energy minimum and the height of the energy barrier depend on a number of factors, including the surface potentials of both the bacterial cell and mineral (denoted as Wb and Wm, respectively), the range of the electrostatic interactions characterized by the inverse Debye length j, and the van der Waals interactions characterized by the Hamaker constant, Abwm. Elimelech (1992) formulated a dimensionless parameter NDLVO that incorporates these factors and characterizes the interaction energy for unfavorable deposition, i.e. NDLVO ¼

jAbwm e0 er W b W m

ð1:60Þ

where e0 is the permittivity of a vacuum and er is the relative permittivity of water. The correlation between the bacterial cell attachment efficiency and NDLVO fits a power law with a slope close to unity, and the excellent agreement strongly suggests that the electrostatic and van der Waals components are the dominant forces affecting the interactions between the bacterial cells and particles. It is worth noting that the application of the DLVO theory to bacteria–mineral systems requires knowledge of the Hamaker interaction parameter, surface potential, and surface energy of bacteria, which must be measured for each system of interest (Yee et al. 2000). As previously stated, the DLVO theory can successfully estimate the effects of ionic strength on bacterial adsorption, but it cannot estimate the extent of adsorption if the mechanism changes as a function of pH, fluid composition, bacteria: mineral ratio, and mineralogy. Thus, it is difficult to estimate the adsorption processes over a wide range of conditions without a similarly wide range of experimental measurements (Fein 2000). (2) Extended DLVO theory In the classical DLVO theory, both the substratum and colloidal particle surfaces are assumed to be chemically inert, which is not valid for the conditions where hydrogen bonding, and hydrophobic and steric interactions are involved in the adhesion mechanism. van Oss et al. (1986) suggested an extension of the DLVO theory where the Lewis acid–base interaction (AB, likely relevant to the hydrophobic and hydrophilic conditions) is added, based on the electron-donating and electron-accepting interactions between the polar moieties in aqueous solution (Farahat et al. 2009). Then, the total interaction energy is expressed in Eq. 1.61, where GAB is the Lewis acid–base interaction energy which describes the attractive hydrophobic interactions and repulsive hydration effects.

1.3 Adsorption on Sediment Particles

67

GTot ¼ GEL þ GLW þ GAB

ð1:61Þ

Lewis acid–base interaction energy, GAB: The Lewis acid–base interaction energy, GAB, for a particle–cell system (i.e. a sphere–sphere system) can be expressed as:   ½ðH H Þ=k  1 min bm w GAB ¼ pDkw DGAB adh e 2

ð1:62Þ

where D is the diameter of the solid particle and kw is the correlation length of water molecules in the liquid, which is also known as the gyration radius. For hydrophilic interactions, kw is equal to 6 Å; while it ranges from 1 to 2 Å for hydrophobic interactions, because the water molecule has a larger gyration radius around hydrophobic surfaces (Ozkan and Berberoglu 2013). The parameter Hmin is the minimum separation distance between two surfaces (=1.57 Å), and Hbm is the separation distance. ΔGAB adh is the AB component of the change in free energy, which can be calculated from the Lifshitz–van der Waals acid–base approach, i.e. qffiffiffiffiffiffiffi

qffiffiffiffiffiffiffi

pffiffiffiffiffiffiffi pffiffiffiffiffi pffiffiffiffiffi pffiffiffiffiffiffiffi pffiffiffiffiffi pffiffiffiffiffi þ  2 þ  c c  c  c cbþ  cmþ c m w b b  cw b pffiffiffiffiffiffiffi pffiffiffiffiffiffiffipffiffiffiffiffi pffiffiffiffiffi  c 2 cmþ  cwþ m  cw

DGAB adh ¼ 2

ð1:63Þ where c+ and c− refer to the electron acceptor and electron donor parameters, respectively, and the subscripts b, m, and w also represent the bacteria, mineral, and water, respectively. To derive these parameters, the contact angles of three different liquids (including water, formamide, and 1-bromonaphthalene) on the solid phase (mineral or bacteria) are measured. Then, the parameters can be calculated by applying Young’s (1805) equation: 1 ð1 þ cos hl Þcl ¼ 2

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffi þ LW þ csþ c cLW c s cl s cl l þ

ð1:64Þ

where hl is the contact angle of the measuring liquid with the mineral or bacteria and cLW is the Lifshitz–van der Waals component of the surface tension, with the subscripts s and l referring to the solid (mineral or bacteria) and liquid, respectively. + − In addition, cl, cLW l , cl , and cl have the following relation þ2 cl ¼ cLW l

qffiffiffiffiffiffiffiffiffiffiffi clþ c l

ð1:65Þ

The distance dependence of the acid–base interaction also is relatively short-ranged, and calculations have shown that a distance of less than 5 nm between the interacting surfaces is required before the acid–base interaction

68

1 Surface Micro-morphology and Adsorption …

becomes operative (Farahat et al. 2009). The acid–base interactions are 10–100 times stronger than the Lifshitz–van der Waals interactions, and electrostatic forces at close contact (Hong et al. 2014; van Oss 1989). Li and Logan (2004) measured the bacterial adhesion to metal oxide-coated or metal oxide-uncoated glass surfaces, to understand the relative contribution of surface charge and hydrophobicity on bacterial adhesion. An increased hydrophobicity of the surface is observed due to metal oxide coatings, which consistently increase the bacterial adhesion compared to uncoated glass surfaces; surface charge appears to exert less direct influence on bacterial adhesion. The adhesion of E. coli onto quartz, hematite, and corundum was studied by Farahat et al. (2009) using the extended DLVO theory, with the essential parameters experimentally determined including Hamaker constants and acid–base components. Results show that the primary contribution to the total energy comes from the electrostatic energy, GEL, followed by the Lewis acid–base energy, GAB, and the Lifshitz–van der Waals energy, GLW. Farahat et al. (2010) also studied the adhesion of Ferroplasma acidiphilum (F. acidiphilum) onto pyrite, and it was observed that the pyrite loses its hydrophobic nature and becomes hydrophilic after bacterial adhesion. Ozkan and Berberoglu (2013) reported the cell–substratum interactions of a diverse group of microalgae based on the extended DLVO approach and concluded that the acid–base interactions are the dominant mechanism of the interaction for microalgae. Hong et al. (2014) investigated the adhesion of B. subtilis on kaolinite, montmorillonite, and goethite over a wide range of ionic strength and pH value. The extended DLVO theory reliably predicts the adhesion trend with ionic strength and that under basic pH, but fails to explain the adhesion at low pH, which possibly results from the chemical interactions between EPS on the cell surface and goethite. Although the physicochemical approach based on electrostatic, van der Waals, and acid–base interactions provides important models of bacterial adhesion, it has a limited capacity to provide a complete understanding of the complex adhesion process of bacterial cells (Hori and Matsumoto 2010). In the DLVO theory, the bacterial cells, with structurally and chemically heterogeneous surfaces, are often described from the view of overall cellular properties; but these heterogeneities probably provide locally favorable regions for bacterial adhesion which cannot be predicted by the model (Redman et al. 2004). Meanwhile, the DLVO theory does not account for the biological interactions such as chemotaxis (Jerez 2001), metabolic activity of bacteria (Tan and Chen 2012), and the excretion of EPS by bacteria (Sand and Gehrke 2006). Hori and Matsumoto (2010) described the complexity of bacterial adhesion and presented the surface structures of bacterial cells for a better understanding of the corresponding molecular mechanism, due to their important roles at the nanometer scale.

1.3.3.3

Chemical Equilibrium Model

The bacterial cell walls contain a variety of surface organic functional groups, such as carboxyl, hydroxyl, phosphate, and amino groups, which display electrostatic,

1.3 Adsorption on Sediment Particles

69

chemical, and hydrophobic affinities for mineral surfaces (Fein 2000). The bacterial adsorption onto mineral surfaces appears to be a reversible process in most cases (van Loosdrecht et al. 1989), suggesting that chemical equilibrium models can successfully account for the interactions (Yee et al. 2000; Ams et al. 2004). Surface complexation models describe the adsorption processes as chemical reactions between the functional groups and the ions in solution (also see Sect. 1.3.2), which can account for the changes of surface and aqueous speciation as a function of pH and solution composition (Davis and Kent 1990; Stumm and Morgan 1996). The application of surface complexation models to bacterial adhesion would enable a quantitative extrapolation of experimental results to more general and complex settings, thus providing a powerful means for estimating the bacterial adsorption onto minerals over a wide range of aqueous conditions. Yee et al. (2000) studied the adsorption of B. subtilis by positively charged corundum (a-Al2O3) and negatively charged quartz, considering the effects of pH and ionic strength. The results indicate that bacterial adsorption onto mineral surfaces is a completely reversible process, and equilibrium can be reached in less than 1 h. The adsorption process is controlled by the hydrophobicity of bacteria, i.e. the inability of bacteria to hydrate, thus remaining suspended in the water column. The bacterial cell walls are neutrally charged at low pH and become increasingly negatively charged with increasing pH due to the successive deprotonation of organic functional groups, i.e. RCOOH0 , RCOO þ H þ

ð1:66Þ

where R denotes the bacteria to which the functional group (e.g. surface carboxyl group –COOH) is attached. The corresponding negative log acidity constant is 4.82 ± 0.14. Thus, the bacteria are dominantly hydrophobic under low pH conditions, with an increasingly hydrophilic component with increasing pH. The adsorption of B. subtilis onto positively charged corundum is successfully modeled using Eq. 1.67, with a log stability constant value of 13.0 ± 1.1, and the extent of bacterial adsorption increases with decreasing pH, increasing bacteria: mineral ratio, and decreasing ionic strength. [ AlOH2þ þ RCOOH0 , [ AlOH2  RCOOH þ

ð1:67Þ

where >Al–OH2+ represents the surface functional group of corundum and >Al– OH2–RCOOH+ is the attached bacteria. Further, the role of electrostatic interactions in the initial adsorption is demonstrated by comparing bacterial adsorption onto Al2O3 with that onto silicon dioxide (SiO2), and it is found that the surface charge of the mineral plays a significant role in the bacteria–mineral interactions. Thus, bacterial adsorption onto mineral surfaces is driven by hydrophobicity, and the electrostatic interactions also play an important role. The chemical equilibrium model, which considers both the hydrophobicity and electrostatic interactions between the bacteria and mineral, can account for the effects of solution chemistry and surface speciation on the adsorption behavior.

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1 Surface Micro-morphology and Adsorption …

Similarly, Ams et al. (2004) studied the adsorption of B. subtilis (gram-positive) and Pseudomonas mendocina (P. mendocina, gram-negative) onto Fe-oxyhydroxide-coated and Fe-oxyhydroxide-uncoated quartz sands. It was observed that B. subtilis was adsorbed by Fe-coated quartz to a greater extent than P. mendocina, probably due to their different electrostatic properties and cell wall structures. The adsorption behavior appears to be controlled by the overall surface charge of both the bacteria and mineral, and there are significant differences in the equilibrium constants of adsorption reactions among the bacterial species (Jiang et al. 2007). Moreover, the enhancement of bacterial adsorption by Fe oxyhydroxide coatings was also observed in the previous studies (Mills et al. 1994; Li and Logan 2004), indicating that the electrostatic interactions between bacterial and mineral surfaces exert a controlling influence on the adsorption behavior. The metabolizing cells produce a variety of exopolymers to form biofilms that would aid the attachment of bacteria under non-favorable electrostatic conditions (Forsythe et al. 1998). However, it is unlikely that the bacterial adsorption onto mineral surfaces is controlled strictly by site-to-site interactions (Fein 2000); thus, the use of a site-specific model to account for the bacterial adsorption onto mineral surfaces represents a semiempirical approach. Nevertheless, surface complexation models offer an approach of explicitly relating the adsorption behavior to the speciation of both surfaces, which accounts for the changes of surface and aqueous speciation as a function of environmental variables. In particular, the equilibrium constants which describe the extent of adsorption are invariant with respect to the parameters which affect partition coefficients and the parameters of adsorption isotherms, making it possible to extrapolate the experimental results to more complex systems (Fein 2000).

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Chapter 2

Basic Characteristics of Bio-sediment

Biofilms are ubiquitous in natural environments. The attachment of bacteria and the secretion of metabolic products induce biofilm formation and growth on sediment surfaces, which will change the basic properties of sediment particles such as the surface morphology, and physicochemical (e.g. bulk density) and biological (e.g. bacterial community) characteristics of biofilm-coated sediment (hereafter referred to as bio-sediment). These changes will further affect the sediment transport properties including the bedload and suspended load transport through influencing the bed resistance, incipient, and settling velocities, etc. Thus, the basic characteristics of bio-sediment are first introduced in this chapter which are the foundation for the further studies of bio-sediment transport. Specifically, Sect. 2.1 describes the morphology characteristics of bio-sediment; Sect. 2.2 presents the group characteristics and density; and Sect. 2.3 discusses the biofilm bacterial communities.

2.1

Morphology Characteristics of Bio-sediment

Chapter 1 has introduced the surface micromorphology of sediment particles through microscopic observation and concluded that sediment particles have complex surface morphology and pores of various scales. Meanwhile, the methods for mathematically characterizing sediment profiles and surface micromorphology were proposed, based on which a “mathematical sediment” research platform was established. In this section, the question of how will the surface morphology of sediment particles change after biofilm growth is answered (Zhao 2010). A general introduction of biofilm growth is first presented, followed by a description of experiments of biofilm growth, and then the morphology of bio-sediment is characterized.

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer-Verlag GmbH, DE, part of Springer Nature 2020 H. Fang et al., Mechanics of Bio-Sediment Transport, https://doi.org/10.1007/978-3-662-61158-6_2

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2 Basic Characteristics of Bio-sediment

A General Introduction to Biofilm Growth

(1) Basic concepts of biofilms Biofilm growth is widespread in the natural environment, see Fig. 2.1a, and can be observed on solid surfaces of natural environments such as rivers, lakes, pipeline systems, and artificial environments such as ship instruments and medical equipment (Headley et al. 1998). There are different understandings of biofilm growth in different fields. For instance, biofilms are crucial to ecosystem functioning and have an excellent ability to degrade and transform pollutants. Biofilms are also used to solve a huge problem in the treatment of wastewater. However, biofilms also have negative effects in man-made systems (e.g. drinking water distribution systems) including biofouling and microbial-induced corrosion (Mora-Gómez et al. 2016). Biofilms play an important role in engineering treatments. Conventional research has mostly focused on environmental science in which biofilms are widely used in wastewater treatment (Wang et al. 1999), e.g. to remove, adsorb, and identify organic pollutants in technologies such as activated sludge and biofilm processes (Moreau et al. 1994; van der Kooij et al. 1995). In the medical field, the chronic infection caused by biofilm bacteria has been explored by studying their infection and resistance mechanisms. For drinking water distribution systems, the interactions between biofilms and water quality are studied to reduce the corrosion of pipes and improve water quality (Hallam et al. 2001). Meanwhile, biofilms have been found ubiquitously distributed in aqueous ecosystems (Gerbersdorf et al. 2009), which can be formed on sand, sediment, rocks, cobbles, wood and leaves, and the surface of submerged plants, thus also playing an important role in the natural water environment. Throughout the biological world, bacteria thrive predominantly in surface-attached, matrix-enclosed, multi-cellular communities or biofilms, as opposed to isolated planktonic cells; some studies have reported that bacteria

Fig. 2.1 a Biofilm growth in different environments (modified from Hall-Stoodley et al. 2004; Vreeburg and Boxall 2007); and b schematic diagram of biofilm growth (modified from Center for Biofilm Engineering at Montana State University) (Note EPS extracellular polymeric substances)

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83

attached to aquatic surfaces are often 1,000–10,000 times greater in number than planktonic bacteria (Donlan 2002). As described in Sect. 1.3.3, most microorganisms in natural waters are initially attached to the solid substrates by physicochemical forces such as van der Waals force, electrostatic force, and hydrophobic force (Jiang et al. 2007), which are affected by environmental factors and the properties of substrates (Yee et al. 2000; Jia et al. 2011) and microorganisms (Jia et al. 2008; Vilinska and Rao 2008). Then, the adhesion of microorganisms to the substrates is further enhanced by the secretion of metabolic products (e.g. extracellular polymeric substances, EPS) and the flagella, etc. Biofilm is the term used for cells within a matrix of EPS that are secreted by microorganisms (Fang et al. 2012). Wetzel (1983) first described biofilms as an assemblage of bacteria, algae, fungi, and protozoa within a protective matrix of EPS and detritus, which colonize submerged surfaces in lakes and rivers. Marshall (1984) also stated that biofilms are a collection of microorganisms and their extracellular products bound to a solid (living or inanimate) surface (termed as substratum). The formation of biofilms is an ancient and integral component of the prokaryotic life cycle and is a key factor for survival in diverse environments. The proclivity of microorganisms to adhere to solid surfaces and form biofilms in so many environments is undoubtedly related to the selective advantage that surface association offers, and biofilm formation represents a protected mode for cells to survive in hostile environments and also disperse to colonize new niches (Hall-Stoodley et al. 2004). Biofilms are a population of cells that are concentrated at the solid–liquid interface and typically surrounded by the EPS matrix, which are structurally and dynamically complex biological systems. EPS is an important component of biofilms, and the content of EPS is about 50–90% of the total organic matter in biofilms (More et al. 2014), with the functions of adhesion, aggregation of bacterial cells, retention of water, protective barrier, sorption of organic compounds and inorganic ions, enzymatic activity, nutrient source, etc. (Flemming and Wingender 2010). EPS is comprised of protein, polysaccharide, extracellular DNA, lipids, particulate material, and detritus (Marvasi et al. 2010; More et al. 2014), among which protein and polysaccharide account for 75–90% of the total EPS. The chemical composition and structure of EPS are affected by microbial species, biological activity, and environmental factors, for example, the genotype, carbon-to-nitrogen ratio, pH value, temperature, and hydrodynamic conditions all influence the secretion of EPS (Durmaz and Sanin 2001; Ye et al. 2011). EPS as a type of supporting material enables a variety of microorganisms to be fixed in specific locations in the biofilm for a long period, forming a microbial symbiosis with diverse functions and cooperations (Zhang and Wu 2007). These microorganisms gather together to form a complex and stable ecological system (Fuchs et al. 1996), providing a relatively stable environment for the existence, growth, and transformation of microorganisms (Decho 2000). (2) Processes of biofilm growth Previous studies have shown a linked structural development with protein expression in Pseudomonas biofilms (Sauer et al. 2002), thereby demonstrating that

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biofilms can have regulated “life-cycles.” Generally, biofilm formation follows the processes of microbial attachment, growth, and detachment (Costerton et al. 1987; Stoodley et al. 2002), see Fig. 2.1b. The first stage is generally identified by a loose or transient association of bacteria to the surface followed by robust adhesion, which is significantly influenced by the surface properties of substrata (Gerbersdorf and Wieprecht 2015). The second stage involves the aggregation of cells into micro-colonies and subsequent growth and maturation. During this period, the bacteria gradually grow and reproduce accompanied by EPS secretion to form biofilms with diffusive porous structures (Lehtola et al. 2004). The third stage is characterized by a return to transient motility where biofilm cells are sloughed or shed (Hall-Stoodley et al. 2004), i.e. detachment caused by external perturbations such as increased fluid shear, by internal biofilm processes such as endogenous enzymatic degradation, or by the release of EPS or surface-binding proteins. Both active dispersal strategy (motility-driven) and passive dispersal strategy (shear-mediated) can be identified. (3) Influencing factors Although there are great diversities in the details of biofilm development among various species, there are also commonalities. Biofilm development is the results of interactions between bacteria and the environment, which is modulated by the bacterial properties (mainly the bacterial species), environmental medium conditions (e.g. the type of substrata, light, temperature, and the availability of nutrients), and dynamic conditions (such as flow velocity, shear stress, and turbulence intensity), which determine the biofilm composition and structure and, in consequence, its metabolism and functions (Uehlinger et al. 1996). A large number of experiments have been done to describe biofilm growth, especially in the field of wastewater treatment. The nature of substrata is the most important factor for biofilm development. Percival et al. (1998) presented a biofilm development over 12 months on stainless steel with different roughness (grades 304 and 316), and it was observed that the viable cell and total cell count on matt stainless steel remained significantly higher than that on smooth stainless steel after 4 months and 8 months of biofilm development, but at month 12, the viable cell counts were not significantly different. Many studies have shown that the size, roughness, pore structure, and specific surface area of particles are important factors affecting biofilm formation (Fox et al. 1990; Heijnen et al. 1992). Further, microorganisms can more easily attach to particles with coarse size, porous structure, and large specific surface area, which are all beneficial to biofilm formation. Hydrodynamic conditions also are important to biofilm formation, and the structure of the formed biofilm varies with the flow condition. Hall-Stoodley et al. (2004) concluded that biofilms growing in fast-moving, high-shear flows tend to form filamentous streamers and ripple structures, while in quiescent or low-shear environments, biofilms tend to form circular structures, such as “mushrooms” or mounds that are similar to those of stromatolites. Paul et al. (2012) developed biofilms on rectangular polyethylene plates under various shear stresses (0.1–13 Pa) and concluded that the thickness and mass of biofilms decreased with the increasing

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shear stress whereas the density increased, i.e. the application of shear stress to the biofilms resulted in both detachment and compression. Hunt and Parry (1998) assessed the effects of substratum roughness and river flow rate on the development of biofilms and found that a combination of roughness and high flow rate can greatly increase the biomass. Moreover, Rao et al. (1997) characterized the biofilm growth in naturally lit (photic) as well as dark (aphotic) environments on perspex panels, and both the biofilm thickness and volume in the photic environment are greater than that in the aphotic environment. Villanueva et al. (2011) reported a faster biofilm formation at a higher temperature, and Liu (1997) also found a faster growth of the nitrifying biofilm at a higher influent ammonium-N concentration. The structure of biofilms also changes with nutrient conditions (Stoodley et al. 1998). (4) Biofilm growth on sediment Natural sediment has extremely complex surface morphology (Fang et al. 2008; 2009; Chen et al. 2013a), which can easily adsorb nutrients and pollutants. Thus, sediment provides excellent substratum for bacterial colonization especially in contaminated waters (Wang et al. 2012), and the secretion of EPS causes the formation and growth of biofilms on the sediment surfaces (Flemming and Wingender 2010). Biofilm growth can influence the sediment properties, e.g. size gradation, morphology, and density, by binding fine-grained sediment, changing water content and enhancing the organic content, resulting in a significant change of sediment transport processes such as incipient sediment motion and sediment settling (Tolhurst et al. 2008; Shang et al. 2014), further affecting sediment-associated contaminant transport and habitat change (Headley et al. 1998; Fang et al. 2015; Gerbersdorf and Wieprecht 2015). So, the characteristics of bio-sediment transport and its environment effects will be quite different from that of sediment without biofilms. In recent decades, the frequency and severity of large-scale human disturbances have significantly increased globally. Especially, a large number of reservoirs have been constructed which have substantially changed the hydrological processes of natural rivers, causing profound and irreversible changes to river system functions (Yang et al. 2008; Liu et al. 2013). For instance, the sediment delivery ratio of the Three Gorges Reservoir (TGR) was estimated to be 24.2% from June 2003 to December 2015 (CWRC 2015), and more than half of the phosphorus load was intercepted by deposition in the reservoir (Huang et al. 2015). Factors such as low velocity flow, sediment deposition, and water pollution in the reservoir provide a favorable condition for biofilm growth on the bed (Costerton et al. 1987; Stone et al. 2011), i.e. the accumulation of sediment and nutrients at the bed surface further stimulates bacteria attachment and biofilm growth (Hall-Stoodley et al. 2004; Zhao et al. 2011). Thus, investigating the changes of sediment properties and processes with biofilm growth is important to understand natural sediment dynamics. Investigation of biofilms is increasingly reported in the literature. The studies of biofilm effects on sediment in estuary and coastal areas are mainly focused on the erosion characteristics, such as the change of the critical shear stress, erosion rate,

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and sediment stability (Grant and Gust 1987; Paterson 1989; Stal 2003; Amos et al. 2004; de Brouwer et al. 2005; Tolhurst et al. 2008). The research on biofilm effects on deposition is mainly done in the field of wastewater treatment as the settling velocity of biofilm-carrying particles is an important parameter for evaluating the efficiency of a bio-fluidized bed (Nicolella et al. 1999). Overall, most of the previous studies used artificial materials as the substrata for biofilm cultivation (Rao et al. 1997; Percival et al. 1998; Paul et al. 2012), such as stainless steel, polyethylene, and perspex panels, while few studies concerned biofilm growth on natural sediment particles. The studies of biofilm growth on sediment mostly focus on coarse sediment, e.g. gravel, cobbles, and rocks, which are significantly different from the cohesive sediment deposits (Graba et al. 2010). Fine sediment is conducive to bacterial attachment and accumulation of nutrients due to the greater specific surface area (Fang et al. 2015), which is probably beneficial to biofilm growth resulting in more biofilms formed on fine sediment than coarse sediment. Thus, sediment (especially fine sediment) provides excellent substratum for biofilm growth, which would, in turn, affect the properties of sediment, and systematic studies should be further done.

2.1.2

Biofilm Growth on Sediment Substratum

As previously stated, it is urgent to study the biofilm growth on natural sediment particles (especially fine sediment) and investigate the changes of sediment properties after biofilm growth, which is important for the further study of bio-sediment transport. At present, biofilm studies are generally done in natural waters through field sampling and analytical analysis. Biofilm growth is a complicated process that is influenced by various environmental and hydraulic conditions. Some errors may be introduced by directly sampling from natural environments, as it is difficult to make an extraction of bio-sediment without changing or disturbing its original status. Meanwhile, it also is difficult to observe the entire process of biofilm growth under natural conditions. So, it is necessary to do laboratory experiments with biofilm growth on sediment particles under certain environmental conditions, which may provide a foundation for further bio-sediment studies.

2.1.2.1

Description of Biofilm Cultivation

In this subsection, the methods for biofilm cultivation under laboratory conditions are preliminarily described, such as the experimental water and the added nutrients. Surface sediment samples from the Guanting Reservoir near Beijing, China, were used as an example for biofilm growth (refer to Sect. 1.1.2.2), with the SEM images of natural and cleaned sediment particles shown in Figs. 1.2 and 1.4, respectively. Figure 2.2 shows the corresponding X-ray diffraction energy spectrum, where the horizontal axis refers to the measured diffraction angle (the mineral compositions

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87

Fig. 2.2 X-ray diffraction energy spectrum graph of sediment samples from the Guanting Reservoir near Beijing, China (Zhao et al. 2011)

are distinguished by a series of characteristic lines corresponding to each mineral), and the vertical axis is the relative detection intensity. It is illustrated that the major components of Guanting Reservoir sediment particles are about 40% quartz, and about 20% albite, followed by calcite and muscovite (each accounted for about 10%), and the rest are dolomite, microcline, and amphibole. Both natural and cleaned sediment particles were used for biofilm cultivation (with diameters of 0.05–0.1 mm). The experimental water for biofilm cultivation should meet the requirement of maintaining the microorganism activity, and here, a water sample from the lotus pond at Tsinghua University, Beijing, China, was used. The bacterial density is determined as the total number of bacterial colonies per 1 mL of water cultured in nutrient agar medium for 24 h at 37 °C, i.e. a bacterial density of 22,600 cfu/mL in summer (August), and 15,800 cfu/mL in winter (December). Table 2.1 lists the measured water quality parameters of the experimental water in both summer and winter, indicating a slightly low trophic level. Moreover, the metabolic processes of bacteria require a continuous intake of nutrients from the surrounding environment, i.e. carbon and nitrogen sources, and inorganic salts. The carbon source such as carbohydrate, fat, amino acid, and protein is utilized to form the carbon containing substances of microbial cells and supply the required energy for microbial growth, reproduction, and movement. The nitrogen source is used to support the synthesis of microbial protein, commonly including ammonium, urea, ammonium sulfate, and ammonium nitrate. The required inorganic salts mainly include phosphate, sulfate, chloride, and carbonate that contain potassium, sodium, calcium, magnesium, iron, and other elements

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Table 2.1 Water quality parameters of the experimental water from the lotus pond at Tsinghua University, Beijing, China Parameters

TN (mg/L)

TP (mg/L)

DO (mg/L)

CODMn (mg/L)

NH4+-N (mg/L)

Summer 1.48

: f ðT Þ ¼ exp½bT ðT  T0B Þ

ð3:9Þ

where N, I, T, and T0B are the nutrient concentration, illumination intensity, temperature, and optimal temperature for biofilm growth, respectively; kN and kI are the half-saturation coefficients for nutrients and illumination, respectively; and bI and bT are the illumination and temperature dependence coefficients for biofilm growth, respectively. The substrata condition is an important factor influencing the bacterial community (see Sect. 2.3.1) and biofilm growth. Fang et al. (2017a) introduced a function of f(S) to further incorporate the effects of sediment size, i.e. f ð SÞ ¼

1 1 þ kD D

ð3:10Þ

where D is the sediment diameter (mm) and kD is the inverse half-saturation coefficient for sediment size (mm−1). It is assumed that the biofilm growth function also is limited by sediment size, because fine sediment is conducive to biofilm accumulation, while coarse sediment contains less biofilm. Thus, the biofilm growth term in Eq. 3.7 represents an exponential increase limited by biofilm thickness (due to the poorer nutrient conditions in the deeper biofilm layers than the surface layers), substrata, nutrients, illumination, and temperature. The detachment function generally consists of chronic, autogenic, or catastrophic detachment. Graba et al. (2010) proposed three functions of hydrodynamic-dependent chronic detachment which incorporate the discharge, friction velocity, and dimensionless roughness height separately, i.e.

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159

8 < cdet QB Chronic detachment ¼ cdet U B : cdet ksþ B

ð3:11Þ

where Q is the flow discharge (m3/s); U* is the friction velocity (m/s); k+s is the dimensionless roughness height; cdet is the chronic detachment coefficient with the units of s/(m3 d), s/(m d), or d−1. Thus, the chronic detachment is proportional to hydrodynamic factors and biomass. The autogenic detachment is assumed to be mainly triggered by the bacterial degradation of the biofilm, and the catastrophic detachment is generally due to flooding, i.e. Autogenic detachment ¼ cauto Bb B

ð3:12Þ

Catastrophic detachment ¼ fflood ðQÞ  Q  B

ð3:13Þ

where cauto is the auto-detachment coefficient (g/(cells d)); Bb is the active bacterial density (cells/g) which can be expressed as the following modified equation   dBb 1 B ¼ lBb ebBb ðTT0Bb Þ  c0det Bb 1 þ kinv;Bb Bb kB þ B dt

ð3:14Þ

where lBb is the maximum specific growth rate for active bacteria (d−1) at the reference temperature, T0Bb; bBb is the temperature dependence coefficient; kinv,Bb is the inverse half-saturation coefficient for active bacterial density (g/cells); kB is the half-saturation coefficient of biomass for active bacteria growth (mg/g); and c′det is the bacterial detachment coefficient (d−1). Thus, the active bacterial density accrual is described as an exponential growth limited by temperature, active bacterial density, and biomass. Moreover, the catastrophic detachment function fflood(Q) in Eq. 3.13 can be expressed as  fflood ðQÞ ¼

0 ccat

for Q\Qc for Q  Qc

ð3:15Þ

where ccat is the catastrophic detachment coefficient (d−1) and Qc is a critical discharge for catastrophic detachment. Equations 3.7–3.15 can be used to simulate the dynamics of biofilm growth.

3.1.3

Validation of Biomass Dynamics Model

The substrata and hydrodynamic conditions are important environmental factors influencing the bacterial community, which also significantly affect the biofilm growth. In Sect. 2.3.1, biofilms were cultivated using a specially designed cylinder

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under both static and dynamic water flow conditions (see Fig. 2.24), to separately consider the effects of sediment size and hydrodynamic conditions (Fang et al. 2017a). The experiments were done for a period of eight weeks, and about 3–5 g of surface sediment was taken weekly to determine the evolution of biomass. Triplicates were taken to ensure the accuracy of measurements. In this sub-section, these results will be used as an example to validate the previously described biomass dynamics model (i.e. Eqs. 3.7–3.15).

3.1.3.1

Evolution of Biomass

Biofilms are amorphous complex matrices comprising living microorganisms (e.g. bacteria, microalgae, and fungi) and their metabolic products (e.g. EPS). The sediment loss on ignition (LOI) is a traditional and convenient measure of organic content (Grabowski et al. 2011; Hagadorn and Mcdowell 2012) that can be regarded as an indirect estimation of biomass. In the experiments, the collected bio-sediment samples were dried at 105 °C, and then, the LOIs were determined using a muffle furnace at 550 °C for 8 h. The amount of biomass was expressed as the mass of organic matter per gram of sediment (mg/g). The initial organic matter before biofilm cultivation was set as the background value, and all the presented results were background corrected. It is worth noting that the experimental water with additional nutrients was refreshed every week to ensure a high nutrition level during the experiment, i.e. adequate nutrients for biofilm growth. Biomass dynamics expressed as LOI (mean ± standard error) are listed in Table 3.1 and shown in Fig. 3.3, including both the static and dynamic water flow conditions. It can be found that the evolution of biomass could be classified into different stages. Biomass increased slowly in the first few weeks, followed by an exponential growth period reaching the peak value around day 42. Subsequently, a phase of biomass loss was observed when the detachment term was greater than the growth term. A t-test showed that there were significant differences between the

Table 3.1 Biofilm dynamics (mean ± standard error) expressed as LOI (mg/g) (Fang et al. 2017a) Time (d)

Static water conditions Mean biomass Standard error

Dynamic water flow conditions Mean biomass Standard error

7 14 21 28 35 42 49 56

0.47 1.42 3.24 4.27 6.03 8.94 5.67 4.09

0.32 0.97 1.79 2.28 3.36 5.50 3.67 2.80

0.22 0.65 0.62 0.58 1.37 1.34 2.22 2.59

0.16 0.48 0.23 0.56 0.94 2.02 1.40 1.30

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Fig. 3.3 Temporal variations of biomass expressed as LOI (mean ± standard error) and the measured temperature (Fang et al. 2017a)

biomass under static and dynamic water flow conditions (p < 0.01, n = 8). Overall, a relatively larger increase rate was observed under static water conditions in the phase of growth, and thus, more biomass was obtained at day 42 compared to that under dynamic water flow conditions, i.e. 8.94 ± 1.34 mg/g and 5.50 ± 2.02 mg/g for static and dynamic water flow conditions, respectively (see Table 3.1). Thus, the hydrodynamic condition can inhibit biofilm accumulation in the case of adequate nutrients. However, the cultivated biofilm was more compact due to the shear effects under dynamic water flow conditions, resulting in a relatively slower decrease rate of biomass in the detachment phase (see Fig. 3.3). Therefore, the application of shear stress resulted in both detachment and compression of the cultivated biofilm (Paul et al. 2012). The detailed biomass evolution under static water conditions is shown in Fig. 3.4a–c, which correspond to fine sediment (0.02–0.05 mm), medium-grained sediment (0.05–0.1 mm), and coarse sediment (0.1–0.2 mm), respectively, and the

Fig. 3.4 Evolution of biomass under static water conditions with different sediment sizes, i.e. a 0.02–0.05, b 0.05–0.1, and c 0.1–0.2 mm; and d–f the corresponding temporal dynamics of the growth term and autogenic detachment (Fang et al. 2017a)

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163

x- and y-axes represent the cultivation period (d) and biomass (mg/g), respectively. The average biomass during the eight weeks of cultivation was 5.67 ± 3.20, 4.31 ± 2.47, and 2.82 ± 2.18 mg/g for fine, medium-grained, and coarse sediment, respectively, and the corresponding peak values of biomass reached at day 42 were 10.67 ± 0.63, 8.76 ± 0.73, and 7.40 ± 0.54 mg/g, respectively, i.e. more biofilm was formed on fine sediment than coarse sediment. Moreover, a t-test showed that there were significant differences among the biomass of different-sized sediment, with all the p values estimated to be smaller than 0.05 (n = 8). In addition, Fig. 3.5a–c show the evolution of biomass under dynamic water flow conditions for sediment exposed to velocities of 0.1, 0.15, and 0.2 m/s (i.e. sediment placed at r = 20, 30, and 40 cm, respectively, and the corresponding friction velocities are estimated as 0.00167, 0.00255, and 0.00461 m/s, respectively, see Fig. 2.26), respectively. A larger velocity indicates more biomass loss, probably resulting in less biofilm accumulation on sediment particles. Accordingly, the maximum biomass was observed for sediment exposed to a velocity of 0.1 m/s, followed by those exposed to velocities of 0.15 and 0.2 m/s. Similar results also were obtained by Paul et al. (2012), i.e. the biofilm thickness decreased with the increasing shear stress applied. The average biomass for sediment exposed to these three velocities was 3.58 ± 2.20, 2.69 ± 1.68, and 1.50 ± 0.85 mg/g, respectively, and the corresponding peak values of biomass reached at day 42 were 8.10 ± 0.62, 5.25 ± 0.56, and 3.16 ± 0.32 mg/g, respectively. Similarly, a t-test also showed that there were significant differences among the biomass of sediment exposed to different velocities, with all the p values estimated to be smaller than 0.05 (n = 8).

3.1.3.2

Validation of Model

As described in Sect. 3.1.2, Eqs. 3.7–3.15 can be used to simulate the dynamics of biofilm growth. Here, the function f(N) is close to 1 due to the adequate nutrients in the experiment, so it is simply assumed that f(N) = 1. Meanwhile, the formed biofilm is mainly bacterial biofilm which has a low requirement for illumination (in contrast to algal biofilms with a high illumination requirement), so the function f (I) in Eq. 3.8 is ignored. Moreover, the catastrophic detachment in Eq. 3.13 also is ignored due to the small velocity applied in the experiments, only considering the chronic detachment due to friction velocity (i.e. the expression related to the friction velocity in Eq. 3.11 is applied) and the autogenic detachment triggered by the bacterial degradation of biofilms (i.e. Eq. 3.12). Then, Eq. 3.7 can be rewritten as dB 1 1 ¼ lmax B ebT ðTT0B Þ  cdet U B  cauto Bb B dt 1 þ kinv;B B 1 þ kD D

ð3:16Þ

Thus, in this section, Eqs. 3.16 and 3.14 were used for the simulation of biomass dynamics. These two equations were solved using the classical Runge–Kutta method using the ode45 function of MATLAB, with a fixed time step of 0.1 d. The

Fig. 3.5 Evolution of biomass under dynamic water flow conditions for sediment exposed to different velocities, i.e. a 0.1, b 0.15, and c 0.2 m/s; and d–f the corresponding temporal dynamics of the growth, chronic detachment, and autogenic detachment terms (Fang et al. 2017a)

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165

initial biomass was determined by a numerical parameterization and set as 0.02 mg/ g. An average bacterial density of 3  1010 cells/g ash-free dry mass (AFDM) was reported by Lyautey et al. (2003), with which the initial Bb was derived as 6  105 cells/g. Model parameters were adjusted to best fit the simulated biomass to the experimental data. The normalized root mean square error (NRMSE) of biomass was calculated to assess the model performance, i.e. vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u Nm 1u 1 X NRMSE ¼  t ðYi  Xi Þ2 X Nm

ð3:17Þ

i¼1

 is the where Xi and Yi represent the measured and simulated values, respectively, X average value of all measured data, and Nm is the number of measurements. The simulated biomass evolution under static water conditions is compared with the experimental data in Fig. 3.4a–c, and the parameters that give the best fit of the biomass dynamics are listed in Table 3.2. Most parameters were fixed for the simulation of different experimental conditions, except for the maximum specific growth rate, lmax, and auto-detachment coefficient, cauto. The arithmetic mean values of sediment diameter were sequentially applied, i.e. 0.035, 0.075, and 0.15 mm. As there was a greater potential for biofilm growth for fine sediment, a larger lmax was applied for fine sediment, i.e. values of 0.35, 0.33, and 0.31 d−1 for fine, medium-grained, and coarse sediment, respectively. Meanwhile, a smaller cauto was used for fine sediment due to the stronger linkages between biofilm and sediment that result in less autogenic detachment. Overall, the variation trends of biomass dynamics with different sediment sizes were well simulated, i.e. the biomass experienced a growth phase and a reduction phase successively, and more biomass was formed for fine sediment than coarse sediment. The peak values of biomass also were well reproduced. The NRMSE of biomass was 0.173, 0.269, and 0.375 for fine, medium-grained, and coarse sediment, respectively. The evolution of biomass is the outcome of the growth and detachment terms (i.e. autogenic detachment for static water condition, see Eq. 3.16). To better understand the biomass dynamics, these terms are plotted separately in Fig. 3.4d–f, which exhibit fluctuations due to the effects of temperature. The growth term, an Sshaped growth curve, reached the maximum value around day 35, with a value of approximately 0.61, 0.53, and 0.43 mg/(g d) for fine, medium-grained, and coarse sediment, respectively, i.e. a decrease of 13.1 and 29.5%. The exponential increase of autogenic detachment was related to the evolution of active bacterial density, with the increase rate accelerating after day 30. It was observed that the biomass reached the peak value around day 42 when the autogenic detachment had the same magnitude as the growth term, and then, the biomass decreased due to the further increase of autogenic detachment. Both the growth and autogenic detachment terms decreased after day 56, and the difference between these two terms decreased with time so that the biomass would gradually achieve a stable condition. The simulated biomass evolution under dynamic water flow conditions is shown in Fig. 3.5a–c to compare with the experimental data, and Table 3.2 also lists the

lmax kinv,B kD D bT T0B cdet U* cauto lBb bBb T0Bb kinv,Bb kB c′det NRMSE

Parameters

d g/mg mm−1 mm °C−1 °C s/(m d) m/s g/(cells d) d−1 °C−1 °C g/cells mg/g d−1

−1

Units

0.35 0.56 1.2 0.035 0.1 24 20 0 2.8  10−16 0.1 0.56 20 1.0  10−13 0.1 0.0585 0.173

0.33 0.56 1.2 0.075 0.1 24 20 0 3.5  10−16 0.1 0.56 20 1.0  10−13 0.1 0.0585 0.269

Static water conditions 0.02–0.05 mm 0.05–0.1 mm 0.31 0.56 1.2 0.15 0.1 24 20 0 4.8  10−16 0.1 0.56 20 1.0  10−13 0.1 0.0585 0.375

0.1–0.2 mm 0.33 0.56 1.2 0.087 0.1 24 20 0 3.7  10−16 0.1 0.56 20 1.0  10−13 0.1 0.0585 0.208

Average value 0.36 0.56 1.2 0.075 0.1 24 20 0.00167 2.5  10−16 0.1 0.56 20 1.0  10−13 0.1 0.0585 0.290

0.36 0.56 1.2 0.075 0.1 24 20 0.00255 3.5  10−16 0.1 0.56 20 1.0  10−13 0.1 0.0585 0.146

0.36 0.56 1.2 0.075 0.1 24 20 0.00461 4.5  10−16 0.1 0.56 20 1.0  10−13 0.1 0.0585 0.321

Dynamic water flow conditions 0.1 m/s 0.15 m/s 0.2 m/s

Table 3.2 Parameters of model simulation under static and dynamic water flow conditions (Fang et al. 2017a)

0.36 0.56 1.2 0.075 0.1 24 20 0.00295 3.5  10−16 0.1 0.56 20 1.0  10−13 0.1 0.0585 0.216

Average value

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167

parameters that give the best simulation. The friction velocities of 0.00167, 0.00255, and 0.00461 m/s (see Fig. 2.26) were sequentially applied, and a larger cauto was used for sediment exposed to a greater velocity, as the increased shear stress inhibits biofilm accumulation. The variation trends of biomass dynamics were well simulated under different hydrodynamic conditions, and more biomass was observed under a smaller velocity. The NRMSE of biomass was 0.290, 0.146, and 0.321 for sediment exposed to velocities of 0.1, 0.15, and 0.2 m/s, respectively. Similarly, the growth and detachment terms (both velocity-dependent chronic detachment and autogenic detachment) are separately plotted in Fig. 3.5d–f, which also experience fluctuations due to the effects of temperature. The S-shaped growth term reached the maximum values of approximately 0.54, 0.51, and 0.42 mg/(g d) around day 35 for sediment exposed to velocities of 0.1, 0.15, and 0.2 m/s, respectively. The autogenic detachment also increased exponentially but with a smoother increase compared with that under static water conditions, i.e. the autogenic detachment term increased to 0.39–0.74 mg/(g d) around day 56, while it was 0.75–1.20 mg/(g d) under static water conditions. Due to the constant rotation speed in the experiments (i.e. a constant friction velocity), the chronic detachment was directly proportional to the biomass, as indicated by Eq. 3.11. Thus, it was synchronized with the growth term which was also proportional to the biomass, and the ratio between the chronic detachment and growth terms increased with the increasing friction velocity. Although the biomass loss caused by autogenic detachment was smaller under dynamic water flow conditions, the additional flow induced loss led to less biofilm growth than that under static water conditions. The comprehensive role of growth, chronic detachment, and autogenic detachment terms resulted in more biomass under a smaller velocity. Similarly, the biomass gradually achieved a stable condition after biofilm growth for 56 days. Moreover, all the measured biomass and the corresponding simulated values are directly compared in Fig. 3.6, with the solid line indicating that the simulated

Fig. 3.6 Comparison between the simulated and measured biomass. a Static water condition and b dynamic water flow condition

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Fig. 3.7 Comparison of the measured biomass dynamics and the simulated values using the average values in Table 3.2 for both static and dynamic water flow conditions (Fang et al. 2017a)

values equal to the measured values, i.e. y = x. Thus, it can also be seen that the simulated results are in reasonable agreement with the measurements, i.e. a good performance of the biomass dynamics model. To further test the reliability of the biomass dynamics model, the average values of parameters in Table 3.2 were used for model simulation, including the average diameter of three groups of size-fractionated sediment under static water conditions (i.e. 0.087 mm) and the average friction velocity under dynamic water flow conditions (i.e. 0.00295 m/s). Figure 3.7 shows the comparison between the measured and simulated biomass dynamics, where solid circles and hollow triangles denote the measured biomass (mean ± standard error) under static and dynamic water flow conditions, respectively, and the solid and dashed lines represent the simulated values. It can be observed that the simulated biomass dynamics were also in good agreement with the measured values, and the NRMSE of biomass was 0.208 and 0.216 under static and dynamic water flow conditions, respectively. Thus, the biomass dynamics model exhibits good reliability and can reasonably reflect the evolution of biomass in the laboratory experiments, with the potential capability of modeling biofilm growth under various environmental conditions.

3.1.3.3

Discussion on Biofilm Growth

According to the biomass dynamics model, biofilm growth can be well simulated considering the effects of substrata (sediment size) and hydrodynamic conditions. The heterogeneous biofilm growth exerts different impacts on aqueous systems and significantly increases the complexities of the flow and benthos. The substrata and hydrodynamic conditions are important environmental factors influencing the bacterial community, which also significantly affect the biofilm growth. The effects of sediment size and hydrodynamics on bacterial communities have been discussed in Sect. 2.3. Similarly, their effects on biofilm growth will be simply discussed.

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Sediment particles have a strong ability to bind nutrients in natural waters due to their specific surface area and surface active functional groups (Fang et al. 2013, 2014a). The smaller the particle size, the larger the specific surface area and the greater amount of potential surface active sites, leading to a stronger adsorption capacity. The accumulation of nutrients provides food sources for the metabolic activities of microorganisms, which is the prerequisite of biofilm growth. Moreover, fine sediment is more conducive to bacterial attachment as described in Sect. 2.3.2 (Jiang et al. 2007), which is also beneficial to biofilm growth. Meanwhile, the hydraulic conductivity of the surface sediment layer is important for mass transfer at the sediment–water interface, which also affects biofilm growth. Fine sediment loses permeability much faster and is denser than coarse sediment (Nelson 1994; Wilson et al. 2008). The corresponding mass transfer of nutrients and redox partners might be limited due to the small hydraulic conductivity which then restricts biofilm growth. Thus, the effects of sediment size on biofilm growth depend on these two interrelated factors, which is similar to its effects on bacterial communities. For cohesive sediment deposits with a size range of 0.02–0.2 mm, the contribution of sediment size to the available surface area for microbial colonization and nutrient accumulation might be more significant than its contribution to the permeability, so relatively more biomass was observed for fine sediment than coarse sediment. Nevertheless, the effects of sediment size on permeability should also be considered when focusing on a wider range of sediment sizes. Under dynamic water flow conditions, the exerted shear stress might destroy the biofilm structure leading to biofilm detachment (Paul et al. 2012), i.e. the hydrodynamic-dependent chronic detachment term in the biomass dynamics model (see Eq. 3.11). More biomass loss is expected under a larger friction velocity which probably results in less biofilm accumulation on sediment particles. However, besides the chronic detachment, the diffusion of nutrients can be enhanced due to the turbulent effects (Higashino et al. 2009), i.e. an increase of the available nutrients in the deep biofilm layer, thus, benefiting the biofilm growth. As listed in Table 3.2, a larger lmax (=0.36 d−1) was applied under dynamic water flow conditions, probably due to the more significant nutrient exchange at the sediment– water interface. Thus, the effects of hydrodynamics on biofilm growth are a combination of chronic detachment and the enhancement of nutrient diffusion. For the biofilm cultivation experiment described in Sect. 2.3.1, the chronic detachment was more dominant, thus, resulting in less biofilm growth when exposed to a greater velocity. The average biomass decreased by 24.9 and 58.1% for sediment exposed to velocities of 0.15 and 0.2 m/s, respectively, compared with that exposed to 0.1 m/s. Presumably, there might be a range of low velocities over which the chronic detachment is relatively small, while the effects of hydrodynamics are dominated by the enhancement of the nutrient supply, i.e. probably the most ideal condition for biofilm growth. The hydrodynamic conditions are neither totally stagnant water nor constant flows in natural systems, but they can be regarded as a combination of different flow velocities and sediment substrata. Thus, the presented experimental and modeling results can improve the understanding of complex phenomena under natural

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conditions. However, these results should also be applied with caution due to the simplification of natural systems in the laboratory experiments. More studies with a wider range of flow velocities and sediment sizes are expected to derive more general results, and appropriate parameters should be used to reveal the different conditions when applying the model to natural systems.

3.2

Bedform and Resistance of Bio-sediment Bed

As water flows over a bed surface composed of loose sediment particles, the exerted shear stress would cause the regular movement of sediment particles, finally resulting in certain repeated bedforms. The controlling factors for the mobility of bed sediment include both the hydrodynamic conditions and sediment properties, i.e. the bedform is a result of the interactions between hydrodynamics and bed sediment (Fang et al. 2017b). However, the physical mechanisms for the formation of various bedforms are different, and there is no unified conclusion yet. It is necessary to establish criteria for classification to predict the bedforms according to the flow and sediment conditions, which currently is mainly based on the empirical relations derived from experimental and field data. Biofilm growth might increase the attachment within deposits, which significantly enhances biostabilization and further influences the bedform and the resistance to flow. For example, Malarkey et al. (2015) showed that the biological cohesion of biofilms was far stronger than the physical cohesion in bedform development, and biofilms were the key controlling factor on bedform dynamics which are crucial for sediment flux by inhibiting sediment from moving independently. Biofilm growth on sediment has been quantitatively studied using a biomass dynamics model in the previous section. Here, after a brief introduction of bedforms, a flume experiment is designed to identify the bedform of a bio-sediment bed and its dimensions, and then, the resistance to flow is further discussed (Cheng 2016; Fang et al. 2017b).

3.2.1

Introduction of Bedforms

Bedform development and bed resistance to flow for noncohesive sediment bed have been primarily studied using traditional sediment transport concepts. As the stream power (i.e. product of the mean velocity and bed shear stress) increases, the bed topography for noncohesive sediment changes in a sequence of flatbed without sediment motion ! ripples ! dunes ! transition ! flatbed with sediment motion ! antidunes ! chutes and pools (Simons et al. 1961; Chien and Wan 1999). Bed resistance varies significantly among the different bedform types, which are closely related to the flow regimes (Simons and Richardson 1966). A number of approaches have been proposed to classify the bedform, determine the dimensions, and

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calculate the corresponding bed resistance (Simons et al. 1961; Simons and Richardson 1966; van Rijn 1984; Yalin 1992; Chien and Wan 1999; Dey 2014). If the sediment is coarse enough, ripples are not formed; in contrast, dunes are not formed for a very fine sediment (Guy et al. 1966; Mantz 1992). As the sediment size decreases, the differences in the bedform characteristics and their dimensions (Mantz 1992; Baas 1994), as well as the corresponding flow regimes and bed resistance, are prevalent. Bedform is defined by the characteristics of bed configuration for a given sediment size under a flow regime (Simons et al. 1961). Generally, there are three types of flow regimes for open channels, i.e. subcritical flow (Fr < 1), critical flow (Fr = 1), and supercritical flow (Fr > 1), where the flow Froude number Fr ¼ pffiffiffiffiffi U= gh [U is the average flow velocity, g is the gravitational acceleration, and h is the water depth] reflects the ratio of flow inertia to gravity. Similarly, three flow regimes can be defined for moving bed channels which correspond to different bedforms, including (i) the lower flow regime, namely ripples, ripples on dunes, and dunes; (ii) the transition zone, namely washed-out dunes; and (iii) the upper flow regime, namely flatbed, antidunes, chutes and pools (Simons and Richardson 1963; Dey 2014). Figure 3.8 shows various phases of bedform development with the increasing flow rate. Thus, the bedform is closely related to the flow regime. Meanwhile, bedforms also depend on the physical properties of bed sediment, particularly the sediment size, and the occurrence of various bedforms is associated with bed load transport, which can be regarded as an expression of sediment transport. Table 3.3 summarizes the classification and characteristics of bedforms for alluvial rivers.

Fig. 3.8 Development of bedforms. a Ripples ! b ripples on dunes ! c dunes ! d flatbed ! e antidunes ! f chutes and pools (revised from https://baike.baidu.com)

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Table 3.3 Classification and characteristics of bedforms in alluvial rivers (Shao and Wang 2005) Bedform

Shape

Dimension

Characteristics

Remarks

Ripples

A long upstream face with a gentle slope and a short and steep downstream face. The former is 2–4 times as long as the latter

The wave height is 0.5–2 cm, with the greatest value no more than 5 cm; the wave length does not exceed 30 cm, within the range of 1–15 cm; and the sediment size is generally finer than 0.6 mm

Erosion occurs on the upstream face, and deposition on the downstream face; the motion of ripples is far slower than the flow

Dunes

Similar to ripples. The ratio of wave length to wave height is up to 100–500 in large rivers

The wave length can be hundreds of meters or even a few kilometers, and the wave height is 1–3 m. Finer sediment corresponds to a greater wave length

Flatbed

Flat

Antidunes

Close to the sinusoids

Erosion occurs on the upstream face, and deposition on the downstream face; the motion of dunes is far slower than the flow, depending on the bed load transport rate Sediment particles are moving on the bed surface, namely “moving flatbed.” The Froude number, Fr, is 0.84–1.0, and finer sediment corresponds to a smaller Fr Deposition occurs on the upstream face, and erosion on the downstream face. The sediment moves downstream, while the bedform moves upstream

Ripples are related to the physical parameters near the riverbed and have little correlation with the water depth. The occurrence is due to the unstable viscous layer near the boundary (e.g. bursting) The occurrence is directly related to the large-scale turbulence structures of the flow

Chutes and pools

The minimum wave length is 2pU2/g (Kennedy 1969)

The increasing flow velocity leads to a transition from dunes to antidunes

It is determined by the time-averaged flow condition and is in phase with the water surface waves

These develop in extremely steep rivers such as mountain rivers

3.2 Bedform and Resistance of Bio-sediment Bed

3.2.2

173

Bedforms of Bio-sediment Bed

For cohesive sediment (i.e. fine sediment with mud, silt, and clay), studies have revealed the role of clay-induced cohesion (physical properties) on sediment incipient motion and the processes, characteristics, and dimensions of bedform development (van den Berg and van Gelder 1993; Schindler et al. 2015). For example, Baas et al. (2013) proposed a time-dependent model for the bedform dimensions in mixed sand-mud, and the effect of cohesive forces was discussed. Moreover, similar studies were done to understand the role of biofilm-induced adhesion (biological properties) on the sediment bed (Hagadorn and Mcdowell 2012; Malarkey et al. 2015; Parsons et al. 2016). Results show that both physical cohesion and biological adhesion markedly change the flow conditions for sediment motion and reduce bedform sizes. Moreover, biofilm-induced biological adhesion is more effective than clay-induced physical cohesion, and their combined effects can alter the bedform dimensions by up to an order of magnitude (Parsons et al. 2016). Thus, biofilms influence the sediment beds by embedding the particles and permeating the void space, to enhance the cohesive force of sediment particles and offer an additional adhesion force (Gerbersdorf et al. 2008). Correspondingly, the erosion response of the sediment bed to the flow is significantly changed (Thom et al. 2015), and the bedform dimensions of fine sediment beds might be reduced compared to the sediment bed without biofilm under the same flow conditions (Malarkey et al. 2015; Parsons et al. 2016). In the following sections, the bedform of bio-sediment beds and the corresponding bed resistance to flow are further discussed through laboratory flume experiments, in which the biofilm is cultivated on fine-grained cohesive sediment (Fang et al. 2017b).

3.2.2.1

Experimental Setup and Procedure

The experiments were done using a flume 14 m long and 0.5 m wide at Tsinghua University, China (see Fig. 3.9). The effective width of the flume was narrowed down to 0.16 m for the first 6-m length and then extended to the original width of 0.5 m through a gradual 2-m-long transition. The experimental water was circulated within the flume by a pump system, and the total volume of the flume was about 10 m3 including the water-recirculation system. The flow discharge could be

Fig. 3.9 Plan view of the experimental flume

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measured by an electromagnetic flow meter, and the water levels along the flume were measured by point gauges. A stabilizing device (baffles) also was placed at the entrance of the flume. The test section, comprising a sediment recess that was 4.9 m long, 0.16 m wide, and 15 mm deep, was located at x = 1.0–5.9 m from the entrance, expressed by shading in Fig. 3.9. Before each experiment, the sediment sample was mixed thoroughly with freshwater and then allowed to settle for a day. Then, the supernatant was dumped and the sample was laid in the sediment recess. This flume also is used for other objectives in this book after certain modifications, and more details are provided in the corresponding sections. Biofilm was cultivated in the narrow part which was first blocked by baffles at the two ends. Sediment (collected from the Three Gorges Reservoir (TGR)) was sieved in freshwater to remove impurities and then air dried. Sediment samples with median sizes, D50, of 0.011, 0.038, 0.059, and 0.068 mm were successively used, with a clay (D < 4 lm) content of 14.7, 10.4, 7.9, and 1.9%, respectively. The sorting coefficients u [=(D75/D25)0.5] were 2.36, 4.67, 4.78, and 1.72 (where Dx is the diameter for which x percent of particles are finer). Meanwhile, water from the lotus pond of Tsinghua University was used for biofilm cultivation, which was also strengthened by nutrients including glucose, monopotassium phosphate (KH2PO4), sodium bicarbonate (NaHCO3), magnesium sulfate (MgSO4), ammonium chloride (NH4Cl), and calcium chloride (CaCl2) (refer to Sect. 2.1.2.1 and Table 2.2). Half of the experimental water was refreshed every day to replenish the nutrients. The temperature range was 17–21 °C, and natural light through the widows and a low illumination were provided during the biofilm cultivation. Under these environmental conditions, biofilms could be observed in 3–5 d, and the biomass varied slightly after 10 d (Fang et al. 2015). Thus, the cultivation period was set as 10 d for the experiments. Biofilms not only cover the surface but also embed the bed layer, permeate the pore spaces, bind particles, and change the sediment properties with depth (Tolhurst et al. 2008; Gerbersdorf et al. 2008, 2009). After the biofilm cultivation, the experimental water with additional nutrients was drained out by a siphon, and the baffles were removed. Then, the flume was slowly filled with freshwater, and the flow discharge was gradually increased until the erosion of the bio-sediment bed. For a given bed slope, the water depth was adjusted by a valve at the downstream end of the flume to achieve a uniform flow. The erosion lasted for approximately 30 min, and the velocity profiles along the flume centerline at x = 1, 3, and 4 m were measured by a propeller velocity meter (LGY-II, Nanjing Hydraulic Research Institute, Nanjing, China). At the end of each experiment, the bed morphology was recorded using a MASATOYO electronic profile indicator (MEPI) with a resolution of 1 mm, and the standard deviation of measurement was 0.5 mm. Altogether, 100  16 points were measured, i.e. Dx = 5 cm and Dy = 1 cm in the longitudinal and lateral directions, respectively. The bedform of original sediment bed also is studied for comparison applying a similar procedure, only without the process of biofilm cultivation.

3.2 Bedform and Resistance of Bio-sediment Bed

3.2.2.2

175

Identification of Bedforms

(1) Description of bedforms To obtain the bed morphology under different hydrodynamic conditions, experiments were done for six groups of bio-sediment beds and five groups of original sediment beds, and the results are summarized in Tables 3.4 and 3.5, respectively. For example, Fig. 3.10 presents the morphology of a bio-sediment bed showing bedforms under the flow condition of U = 0.8 m/s and h = 0.109 m and the median sediment size of D50 = 0.011 mm (i.e. Test No. B-1). Here, only the bed morphology in the range of 2–4 m is shown to eliminate the influences of inlet and outlet flow. Based on these morphological data, the characteristics of bedforms could be determined by extracting the lines along the longitudinal direction. Here, four lines that were parallel and near the centerline were extracted from the experimental bed morphology in Fig. 3.10 to determine the dimensions of the bedforms, as shown in Fig. 3.11. The characteristics of the bedforms (including bedform length, k, height, D, and steepness, D/k) and the corresponding flow conditions (discharge, Q, bed slope, J, water depth, h, shear velocity, U*, and Froude number, Fr) are listed in Table 3.4. The shear velocity, U*, was calculated using the bed slope and corrected by the method of Vanoni and Brooks (1957). As listed in Table 3.4, the maximum bedform height of the bio-sediment bed is about 1 cm, and the bedform length is greater than 30 cm. The relative water depth,

Table 3.4 Characteristics of the bedforms on bio-sediment beds for different flow conditions and sediment sizes (Fang et al. 2017b) Test No.

D50 (mm)

Q (m3/ h)

J (10−3)

h (m)

k (mm)

D (mm)

D/k

U* (m/s)

Fr

h/D50

B-1 B-2 B-3 B-4 B-5 B-6

0.011 0.038 0.059 0.059 0.059 0.059

45.45 62.55 65.77 60.74 40.66 33.17

3.86 4.38 5.00 3.96 1.83 1.41

0.1090 0.1375 0.1408 0.1406 0.1384 0.1252

340 460 440 450 440 400

2.1 10.6 5.6 8.6 8.1 5.3

0.0060 0.0231 0.0126 0.0191 0.0184 0.0133

0.050 0.059 0.065 0.057 0.038 0.031

0.70 0.68 0.69 0.64 0.44 0.42

9909.09 3618.42 2386.44 2383.05 2345.76 2122.03

Table 3.5 Characteristics of the bedforms on original sediment beds for different flow conditions and sediment sizes (Fang et al. 2017b) Test No.

D50 (mm)

Q (m3/ h)

J (10−3)

h (m)

k (mm)

D (mm)

D/k

U* (m/s)

Fr

h/D50

P-1 P-2 P-3 P-4 P-5

0.011 0.038 0.059 0.059 0.068

26.15 39.36 27.60 48.66 45.46

4.57 10.11 4.35 9.48 8.15

0.074 0.100 0.074 0.113 0.107

441.7 500.0 427.9 860.0 258.3

3.28 2.67 14.60 2.70 2.02

0.0075 0.0053 0.0341 0.0031 0.0078

0.049 0.091 0.047 0.092 0.086

0.72 0.69 0.76 0.71 0.72

6727.27 2620.73 1254.24 1915.40 1571.22

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Fig. 3.10 Morphology of a bio-sediment bed with D50 = 0.011 mm showing the bedform under the average velocity, U = 0.8 m/s, and water depth, h = 0.109 m, (i.e. Test No. B-1) (Fang et al. 2017b)

Fig. 3.11 Typical profiles of the bedform extracted from the experimental bed morphology in Fig. 3.10 (Fang et al. 2017b)

h/D50, is all greater than 2000 for these experimental conditions due to the fine sediment size, where the median sediment size of the original sediment is used for the calculation. To investigate the biofilm effects on bedforms, experiments for the original sediment bed also were done. For example, Fig. 3.12 shows the original sediment bed morphology with the same median size as Fig. 3.10 (i.e. D50 = 0.011 mm)

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Fig. 3.12 Morphology of an original sediment bed with D50 = 0.011 mm showing the bedform under the average velocity U = 0.61 m/s and water depth h = 0.074 m (i.e. Test No. P-1)

under the flow condition of U = 0.61 m/s and h = 0.074 m (Test No. P-1), and four extracted lines are shown in Fig. 3.13. The characteristics of the bedforms and the corresponding flow conditions are listed in Table 3.5. The maximum bedform height is close to 1.5 cm, and the bedform length ranges from 25 to 86 cm. The relative water depth is greater than 1000 also due to the fine sediment size. Meanwhile, a larger scale of bedform is observed for the original sediment bed with

Fig. 3.13 Typical profiles of the bedforms extracted from the experimental bed morphology in Fig. 3.12

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a relatively coarser size under similar flow conditions, implying the influence of clay-induced cohesive forces. It also is observed that the flow conditions for the bio-sediment bed were rarely the same as for the original sediment bed of the same median sediment size. These differences are mainly attributed to the different incipient velocities for the original and bio-sediment beds, because the flow conditions were set to ensure bed erosion in this study (i.e. the appearance of bedforms). Under similar flow conditions, the original sediment bed exhibits relatively greater fluctuations. Overall, the bedform dimensions in Table 3.5 decreased after biofilm growth, as listed in Table 3.4. As described in Table 3.3, the ripple height is less than 5 cm and the length is usually in the range of 1–15 cm with a maximum value of less than 30 cm for noncohesive sediment beds (Shao and Wang 2005). Applying such dimensional scaling, the bedforms on fine and cohesive sediment beds were classified as ripples (van den Berg and van Gelder 1993; Baas 1994; Baas et al. 2013). Tables 3.4 and 3.5 show that bedform heights on original and bio-sediment beds are not less than 2 cm, while most of the bedform lengths are greater than 30 cm. Therefore, the bedforms do not fall into the classical definition of ripples, implying a different mechanism from that of noncohesive sediment beds. Additionally, Fig. 3.10 shows that bedforms on bio-sediment bed are not as regular as that on noncohesive sediment beds, which usually have long upstream faces and short downstream faces for ripples and dunes (see Table 3.3). It can be observed that the bedforms were characterized by three-dimensional configurations having potholes on the bed. This feature may be attributed to the biofilm-induced adhesion and clay-induced cohesion, namely a scour-and-fill bed structure (van den Berg and van Gelder 1993). (2) Classification of bedforms In traditional studies, many methods are used to classify the bedforms of noncohesive sediment beds (Cheng 2016). The motive force of sediment motion is the force of flow exerted on the bed surface. The Shields parameter, H = U2*/[(s – 1) gD50], reflects the ratio of the shear stress acting on the bed surface and the effective gravity of sediment, which is a critical factor to determine the sediment transport rate, and, thus, the bed configuration. Here, s is the relative density of sediment (=qs/q); q and qs are the densities of water and sediment, respectively; and D50 is the representative size as used for noncohesive sediments. A larger H corresponds to a greater mobility of sediment. Hence, the Shields parameter is usually chosen to predict the bedform types (van Rijn 1984; van den Berg and van Gelder 1993; Chien and Wan 1999). Moreover, the previous researchers found that Fr has a critical influence on the formation of antidunes under the upper regime, while the particle Reynolds number, Re* (=U*D50/v, where v is the viscosity coefficient of water), for bed sediment is an important parameter for the development of ripples under the lower regime (Chien and Wan 1999). For the formation of dunes, besides Fr and Re*, other parameters such as h/D50, U*/x, and U/U* also play a key role, where x is the settling velocity of sediment particles, and the maximum value of Fr is about 0.6 for the dunes

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179

Fig. 3.14 Criterion (H vs. Fr) for the prediction of bedforms for noncohesive sediment (data from Garde and Albertson (1959)) and a comparison with the data plots for the original (cohesive) and bio-sediment (Fang et al. 2017b)

(Simons and Richardson 1963, 1966; van Rijn 1984; Yalin 1992; Chien and Wan 1999). However, few studies have been done on the bedform classification of cohesive and bio-sediment beds. Most of the previous studies focus on the bedform development until reaching an equilibrium state, and the time series models for bedform dimensions were developed (van den Berg and van Gelder 1993; Baas et al. 2013; Malarkey et al. 2015). Here, the method for noncohesive sediment is used to classify the bedform for original (cohesive) and bio-sediment beds. Tables 3.4 and 3.5 show that the Froude number Fr ranges from 0.4 to 0.8 in the experiments indicating a relatively high flow regime. Thus, the method of Garde and Albertson (1959) is used to define the bedform through a plot of H(Fr). Figure 3.14 shows the prediction of bedforms for original (cohesive) and bio-sediment using the criterion of H(Fr), and data for noncohesive sediment also are shown for comparison. Most of the data plots for original (cohesive) and bio-sediment are close to the dividing line between dunes and the transition zone for noncohesive sediment. Thus, the bedform was developed in a flow regime that would produce dunes to transition conditions for noncohesive sediment, which

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implies that the bed configuration would be dunes or transition if the original (cohesive) and bio-sediment were regarded as noncohesive sediment with the same median size. But in fact, the clay-induced cohesion and biofilm-induced adhesion enhance the bed stability, and a higher bed shear stress is required to reach a threshold of sediment motion (Righetti and Lucarelli 2007; Jacobs et al. 2011; Malarkey et al. 2015). Hence, the bedform on original (cohesive) and bio-sediment beds would lag behind those on a noncohesive sediment bed under the same flow conditions. Accordingly, the bedform dimensions and the resistance to flow also are different.

3.2.2.3

Relations Between Bedform Dimensions and Flow Conditions

The bedform dimensions are determined from the flow conditions and also sediment size (Chien and Wan 1999). For different types of bedforms, the dimensions— as well as the corresponding flow regimes—are essentially different, which accordingly result in different bed resistances to flow. Knowledge on bedform dimensions is, therefore, required to further determine the bed resistance to flow. As previously mentioned, the previous studies primarily focused on the temporal variation of bedform dimensions on cohesive and bio-sediment beds, i.e. from the initiation of sediment motion to an equilibrium state under a given flow condition, while the relation between bedform dimensions and flow conditions was rarely discussed. Therefore, the method applicable to noncohesive sediment is still applied to determine the bedform dimensions for bio-sediment beds (Fang et al. 2017b). There are generally two approaches to calculate the bedform dimensions (e.g. the length, k, height, D, and steepness, D/k), simultaneously considering the flow condition and sediment size. The first approach is to directly establish an empirical relation between bedform dimensions and flow parameters, such as Re*, η (=H/Hc, where Hc is the threshold Shields parameter), and T* [=(U*′ 2– U2*c)/ U2*c, namely the transport stage parameter, where U*′ is the shear velocity due to particles and U*c is the critical shear velocity] (Englund and Hansen 1966; van Rijn 1984; Yalin 1992). The second approach is to utilize the intermediate variable of bed load transport rate, i.e. incorporating the relation between bedform dimensions and bed load transport rate, and that between bed load transport rate and flow conditions (Ranga Raju and Soni 1976). The first approach is usually applied for bedforms of dune type using the flow parameters η, T*, and h/D; and here, the flow parameter η is chosen as the flow parameter for a given flow condition. Here, the dune steepness D/k is expressed as a function of the flow parameter η (=H/Hc), similar to the methods for determining the dune dimensions for noncohesive sediment. As the threshold Shields parameter, Hc, for cohesive and bio-sediment is much different from that for noncohesive sediment, a new Shields type diagram for the threshold of sediment motion is required (van den Berg and van Gelder 1993; Righetti and Lucarelli 2007; Fang et al. 2014b). Righetti and Lucarelli (2007) extended the threshold theory of noncohesive sediment to cohesive–adhesive sediment, in which the influence of biofilms was considered as an

3.2 Bedform and Resistance of Bio-sediment Bed

181

Fig. 3.15 Bedform steepness, D/k, as a function of the ratio of Shields parameter to its threshold value η (=H/Hc) (Fang et al. 2017b)

adhesive force. Fang et al. (2014b) applied a similar method to explore the biofilm effects on the erosion of fine sediment (D50 < 0.1 mm) with sufficient nutrients, and the threshold curve Hc(Re*) for bio-sediment is shown in Fig. 4.22. A more detailed discussion on the incipient motion of bio-sediment is presented in Sect. 4.2 . The variation of bedform steepness D/k with η for cohesive and bio-sediment beds is shown in Fig. 3.15. The steepness D/k initially increases with η until reaching a maximum value and then decreases as η further increases, but the maximum values are different for these two cases. Overall, the bedform steepness of the original (cohesive) sediment bed is larger than that of the bio-sediment bed under the same flow conditions, which may be attributed to the biofilm-induced adhesion. More experiments are required to clarify the role of clay-induced cohesion and biofilm-induced adhesion on the bedform dimensions. In Fig. 3.15, the

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3 Biofilm Growth and the Impacts on Hydrodynamics

data plots for noncohesive sediment also are presented for comparison (Yalin and Karahan 1979), with the nondimensional variable h/D50 also considered as a variable influencing the dune steepness. Yalin and Karahan (1979) also pointed out that the effects of h/D50 become imperceptible when it is greater than 100. Taking D50 as the representative size of cohesive sediment, the minimum value of h/D50 is greater than 2000 for the current experiments, so its influence on bedform dimensions would be insignificant. A comparison between the data of cohesive and noncohesive sediments (h/D50 > 100) made it evident that the steepness in the former case is smaller if the flow condition is the same, which is attributed to the clay-induced cohesion. Importantly, the effects of biofilms emerge by comparing the results of cohesive and bio-sediment beds. According to Yalin and Kaharan (1979), the equation of dune steepness can be expressed as: D ¼ 0:0127ðg  1Þeðg1Þf ðh=D50 Þ k

ð3:18Þ

where  f

h D50

¼

1 0:0778 ¼ gd  1 1  e0:01h=D50

ð3:19Þ

and ηd is the value of η corresponding to (D/k)max. For bio-sediment, the variation trend of bedform steepness with flow conditions is close to that for noncohesive sediment, but their maximum values of steepness are different. As shown in Fig. 3.15, the η value corresponding to the maximum bedform steepness (D/k)max is ηd = 6.13 for bio-sediment; thus, f(h/D50  2000) = 0.195 according to Eq. 3.19. Therefore, the bedform steepness for bio-sediment, identified as dunes, can be expressed as D ¼ 0:0127ðg  1Þe0:195ðg1Þ k

ð3:20Þ

Moreover, according to Yalin (1992), the dune length, k, is only dependent on the water depth h if the flow over an initial flat sediment bed is rough-turbulent. Here, the flow conditions for bio-sediment are mostly rough-turbulent (see Table 3.6), so the dune length can be given by linear fitting of the measured values of k and h in Table 3.4, i.e. k ¼ 3:2h

ð3:21Þ

Then, the bedform length, k, height, D, and steepness, D/k, for a bio-sediment bed can be determined using Eqs. 3.20 and 3.21.

3.2 Bedform and Resistance of Bio-sediment Bed Table 3.6 Characteristics of equivalent roughness due to bedforms on original (cohesive) and bio-sediment beds (Fang et al. 2017b)

3.2.3

183

Test No.

ks (mm)

Re*′ (=U*ks/m)

ks/D

B-1 B-2 B-3 B-4 B-5 B-6 P-1 P-2 P-3 P-4 P-5

0.41 5.79 4.94 5.09 5.08 2.61 0.45 0.51 11.70 0.42 0.33

20.5 341.6 321.1 290.1 193.0 80.9 22.1 46.7 549.9 38.8 28.4

0.195 0.546 0.882 0.592 0.627 0.492 0.137 0.192 0.801 0.156 0.163

Resistance of Bio-sediment Beds

As biofilms affect the bedform characteristics, the resistance of bio-sediment beds is different from that of the original sediment bed under a certain flow conditions. Because there is no universally recognized theory and method to calculate the resistance and transport rate for cohesive and bio-sediment beds, it is reasonable to apply noncohesive sediment transport theory. The bed resistance to flow consists of skin friction due to particles and form-drag friction due to bedforms. Thus, the determination of bedform dimensions, as described in Sect. 3.2.2.3, is an essential prerequisite to evaluate the bed resistance to flow (van Rijn 1984; Yalin 1992). van Rijn (1984) proposed an approach for noncohesive sediment to calculate the bed resistance by first determining the bedform dimensions from the flow and sediment conditions and then identifying an empirical relation between the bedform dimensions and hydraulic roughness to calculate the resistance. Meanwhile, in some cases, the hydraulic parameters such as water depth, h, and hydraulic radius, Rb, are calculated by iterative methods to indirectly derive the skin and form-drag frictions (Einstein and Barbarossa 1952; Engelund and Hansen 1966; Brownlie 1983). There are also some approaches wherein the total frictional resistance is calculated instead of decomposing resistance into these two components (White et al. 1979), where an index for determining the bedform type and iterations is required. In comparison, the approach proposed by van Rijn (1984) that calculates the bed resistance through the bedform dimensions is quite straightforward.

3.2.3.1

Equivalent Roughness of Bio-sediment Bedforms

The hydraulic roughness of a movable bed, ks, is caused by the roughness due to particles, ks′, and that due to bedforms, ks″, i.e. ks = ks′ + ks″. The former

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3 Biofilm Growth and the Impacts on Hydrodynamics

Fig. 3.16 Einstein correction factor, v, as a function of roughness Reynolds number, Re*′ (revised from Einstein 1950)

corresponds to the skin friction and the latter corresponds to the form-drag friction (Dey 2014). The generalized resistance equation for hydraulically smooth, transition, and rough flows was given by Einstein (1950) as follows:  U Rb ¼ 5:75 lg 12:27v U ks

ð3:22Þ

where ks is the equivalent roughness height; v is the correction factor as a function of ks/dL; and dL is the viscous sub-layer thickness (=11.6v/U*). The method proposed by Vanoni and Brooks (1957) can be used for the wall correction. Figure 3.16 shows the variation of v with the roughness Reynolds number, Re*′ (=U*ks/v), and v is a constant of unity if Re*′ > 116. For bio-sediment, the equivalent roughness, ks, can, thus, be obtained using Eq. 3.22 from the measured velocity, U, and the values are listed in Table 3.6, where the experimental results of original sediment bed also are listed. For a plane bed (i.e. flatbed), the equivalent roughness due to particles, ks′, is related to bed sediment size, such as Di for i = 50, 65, 84, and 90, and its general form can be expressed as ks′ = a1Di, where a1 is a coefficient. Regarding the roughness due to bedforms, Yalin (1972) introduced a functional relation as  D ks00 ¼ f D; k

ð3:23Þ

3.2 Bedform and Resistance of Bio-sediment Bed

185

Fig. 3.17 Non-dimensional equivalent roughness, ks″/D, for original (cohesive) and bio-sediment beds as a function of bedform steepness, D/k, including the data used by van Rijn (1984) for noncohesive sediment (Fang et al. 2017b)

Based on the experimental and field data, van Rijn (1982) then proposed a formula to calculate the form roughness as

 ks00 ¼ 1:1D 1  e25D=k

ð3:24Þ

As shown in Eq. 3.24, the form roughness is 0 for a plane bed (D = 0), and the maximum value is close to 1.1 times of the bedform height. In addition, Bartholdy et al. (2010) defined the virtual bed level and proposed a relation between the form roughness and dune height as ks″ = 0.57D. A similar method was later used by Bartholdy et al. (2015) to determine the relation between the form roughness and ripple dimensions as ks″ = 0.57D + 0.09(D/k2.0). Here, van Rijn’s (1982) approach was used to derive the resistance of the bio-sediment bed. The non-dimensional equivalent roughness, ks″/D, for original (cohesive) and bio-sediment bedforms is plotted against the bedform steepness, D/k, in Fig. 3.17 (data refer to Tables 3.4, 3.5 and 3.6), including the data used by van Rijn (1984) for noncohesive sediment. The equivalent roughness due to particles, ks′, for bio-sediment bed is determined by a1 = 3 and Di = D90, and the values of D90 are 0.023, 0.077, 0.100, and 0.105 mm corresponding to the median size, D50, of 0.011, 0.038, 0.059, and 0.068 mm, respectively. As shown in Fig. 3.17, the plots for original (cohesive) and bio-sediment beds are not far from those of noncohesive sediment, which is partially attributed to the much wider range of data plots for noncohesive sediment, and also the identical physical principle that controls the relation between the roughness height and bedform dimensions. Although the limited data cannot fully reflect the biofilm effects on bedform dimensions, the studies of Malarkey et al. (2015) and Parsons et al. (2016) clearly showed a reduction in bedform dimensions due to the biofilm mixed in both the cohesive and noncohesive sediment, indicating a change in the bed resistance, and, thus, different equivalent roughnesses under the same flow

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3 Biofilm Growth and the Impacts on Hydrodynamics

condition. The data plots for bio-sediment are fitted in Fig. 3.17, and the form roughness ks″ can be expressed as

 ks00 ¼ 1:2D 1  e40D=k

ð3:25Þ

As previously described, the roughness due to particles, ks′, for bio-sediment bed can be determined by a1D90. The total equivalent roughness ks (=ks′ + ks″) for bio-sediment is, therefore, expressed as

 ks ¼ a1 D90 þ 1:2D 1  e40D=k

ð3:26Þ

where a1 = 3 as suggested by van Rijn (1982). Table 3.7 summarizes the published experimental data for noncohesive, cohesive, and bio-sediment beds, including the bedform types and dimensions, and the corresponding flow regimes and equivalent roughness. For natural cohesive sediment, it is called mud when the sediment size is less than 63 lm, which usually contains clay ( 9.3%

0.41

0.23

m.c. 18%

EPS.c. 0.027– 0.073%

2.2– 2.8

0.24

m.c. 13.8%

Bio-sediment

1.9– 3.4

0.22

m.c. 5.4%

1.8– 7.5

0.41

0.239 c.c. 1.9– 14.1%

D (cm)

Cohesive

Fr

D50 (mm)

Sediment type

Table 3.7 (continued)

188 3 Biofilm Growth and the Impacts on Hydrodynamics

3.2 Bedform and Resistance of Bio-sediment Bed

189

closely related to the bedform steepness, i.e. a larger steepness generally corresponds to a greater value of ks. As shown in Table 3.7, the bedform dimensions of cohesive sediment are mostly within the scope of ripple dimensions for noncohesive sediment, which are influenced by the mud or clay content. A higher mud or clay content corresponds to smaller bedform dimensions. However, the bedform height on cohesive sediment beds with D50 = 0.033 mm is larger than that of a noncohesive sediment bed under the same flow regime, which is possibly caused by the higher clay content that induces a scour-and-fill structure and three-dimensional bed characteristics (van den Berg and van Gelder 1993). It was also observed by Schindler et al. (2015) that the bedform lengths are much larger than the ripple lengths of noncohesive sediment bed, while the bedform heights are close to the ripple heights. Similarly, the values of ks for cohesive sediment beds are also related to the bedform steepness. For bio-sediment, the bedform dimensions are still close to the ripple dimensions for noncohesive sediment under a low flow regime, except the bedform lengths obtained by Parsons et al. (2016). When there is a great EPS content (e.g. 1%), the sediment bed is still flat under a high flow regime, indicating that EPS significantly reduces the bedform dimensions. For the experiments described in Sect. 3.2.2, cohesive sediment was used as a substrate for biofilm cultivation, and the resultant bedform height is still within the proximity of ripple heights for noncohesive sediment, while the bedform lengths are closer to those of dunes corresponding to the flow regime.

3.2.3.2

Prediction of Chézy Coefficient in Flow over Bio-sediment Beds

If the flow condition and sediment size are known, the Chézy coefficient, C, can be calculated as   Rb Rb pffiffiffi C ¼ 5:75 g log 12:27v ¼ 18 log 12:27v ks ks

ð3:27Þ

Thus, given the flow velocity, U, water depth, h, river (flume) width, Bw, sediment sizes D50 and D90, densities of water, q, and sediment, qs, and kinematic viscosity of water, v, the Chézy coefficient, C, for a bio-sediment bed can be computed as follows: (1) Assume a shear velocity U*. (2) Compute the threshold Shields parameter Hc (or threshold shear velocity U*c) from Fig. 4.22. (3) Compute the ratio of Shields parameter to its threshold value: η = H/Hc = U2*/U2*c. (4) Compute the bedform length, k, using Eq. 3.21. (5) Compute the bedform steepness, D/k, using Eq. 3.20 and then the bedform height D.

0.027 0.249 0.809 1.023 1.213 1.187 1.018

0.2 0.3 0.4 0.5 0.6 0.7 0.8

0.027 0.027 0.027 0.229 0.761 0.875 0.827

Equivalent roughness ks (mm) Noncohesive sediment Bio-sediment

U (m/s) 59.528 47.668 39.343 37.795 36.702 36.916 38.042

59.518 61.804 63.147 48.293 39.98 39.063 39.53

Chézy coefficient C (m1/2/s) Noncohesive sediment Bio-sediment 0.0103 0.0139 0.0174 0.0182 0.0189 0.0188 0.0182

0.0103 0.0099 0.0097 0.0139 0.0172 0.0177 0.0175

Manning coefficient nM (s/m1/3) Noncohesive sediment Bio-sediment

Table 3.8 Influence of bio-sediment bedforms on the equivalent roughness, ks, Chézy coefficient, C, and Manning coefficient, nM (Fang et al. 2017b)

190 3 Biofilm Growth and the Impacts on Hydrodynamics

3.2 Bedform and Resistance of Bio-sediment Bed

(6) (7) (8) (9)

191

Compute the equivalent roughness, ks, using Eq. 3.26. Compute the Chézy coefficient, C, using Eq. 3.27. Compute a new shear velocity, U*|new = Ug0.5/C. Compare the new and assumed shear velocity values by setting an error value, say 10−6. If ∣ U*|new – U*∣/U* > 10−6, then U* = 0.5(U* + U*|new) and repeat Steps 1–9; otherwise, stop the computation.

To compare the bed resistance of noncohesive and bio-sediment beds under the same flow condition and sediment size, D50 = 0.038 mm, D90 = 0.09 mm, and h = 0.145 m are chosen for the calculation with various values of U (Bw = 0.16 m, q = 1000 kg/m3, qs = 2650 kg/m3, and v = 1.0  10−6 m2/s). Table 3.8 lists the changes of the equivalent roughness, ks, Chézy coefficient, C, and Manning coefficient, nM (=R1/6 b /C) for both noncohesive and bio-sediment. Under the same flow condition, the equivalent roughness, ks, and Manning coefficient, nM, become much smaller after biofilm growth, and the Chézy coefficient, C, becomes larger, implying a reduction in the bed resistance to flow due to the clay-induced cohesion and biofilm-induced adhesion. The maximum changes in the values of ks, C, and nM for bio-sediment beds are 96.7, 60.5, and 44.3% (i.e. when U = 0.4 m/s), respectively, as compared with those for noncohesive sediment beds. Moreover, for both noncohesive and bio-sediment beds, the value of ks increases with an increase in U and the value of C decreases with U.

3.3

Effects of Biofilm on Turbulence Characteristics

As previously described, biofilm growth would change the surface morphology of sediment and promote inter-particle linkages, subsequently changing the bedform dimensions and resistance to flow. Accordingly, the interactions between the flow and sediment bed would also be affected, leading to different turbulence characteristics as compared with the original sediment bed and further affecting sediment transport processes and mass exchange at the sediment–water interface (Graba et al. 2010; More et al. 2014). The presence, age, and structure of biofilms are important factors influencing the local hydrodynamic characteristics, e.g. the friction velocity, equivalent roughness, turbulent shear stress, and turbulence intensity (Moulin et al. 2008; Cheng et al. 2018). An acceleration of longitudinal mean velocity in the upper half-part of the flow and a decrease near the bottom (which is important for erosion) are generally observed after biofilm growth (Graba et al. 2010; Fang et al. 2017c). For example, Nikora et al. (2002) investigated the changes of turbulence characteristics due to biofilms using an Acoustic Doppler Velocimeter (ADV), and the results show that biofilm growth suppresses the mean velocity, turbulent shear stress, turbulence intensity, and vertical turbulent energy flux in the interfacial sub-layer (i.e. under the top of bed roughness). Thus, the penetration of large-scale eddies from the outer flow to the interfacial sub-layer is weakened after biofilm growth, which would further change the turbulent sweep events and influence the

192

3 Biofilm Growth and the Impacts on Hydrodynamics

mass transfer from the flow to the sediment layer. In this section, the effects of biofilms on turbulence characteristics over a cohesive sediment bed will further be described through a flume experiment (Cheng 2016; Cheng et al. 2018), which is important for understanding the processes of bio-sediment transport.

3.3.1

Experimental Setup and Procedure

The time series of velocities at different points along the water depth should be first measured to analyze the turbulence characteristics. Similar to Sect. 3.2.2.1, the experiments were done using the circulating flume 14 m long and 0.5 m wide at Tsinghua University (see Fig. 3.18). Here, the first 6-m length of the flume was not narrowed down to 0.16 m as in the example in Sect. 3.2.2.1 (Fig. 3.9) (i.e. the entire flume is 0.5 m wide), and a sediment recess that was 0.5 m long, 0.5 m wide, and 20 mm deep, was located at x = 10.05 m from the entrance (expressed by shading in Fig. 3.18). Sediment collected from the TGR was used in the experiments, and the median size, D50, was 0.065 mm, with a clay content of 4.7% and a sorting coefficient u of 1.75. Before the experiment, a sediment sample was mixed thoroughly with freshwater and then allowed to settle for a day. Afterward, the saturated sediment was deposited in the recess and scraped flat at the bed surface level. Two baffles were placed and sealed in the flume near the recess, and water from the lotus pond of Tsinghua University was used for biofilm cultivation with additional nutrients (half of the experimental water was refreshed every day). For more information, refer to Sects. 2.1.2.1 and 3.2.2.1. The temperature was approximately 20 °C during the biofilm cultivation, and the sunlight penetrated through the laboratory windows with no special treatment, i.e. a relatively weak light intensity was present. Similarly, the biofilm cultivation period was set as 10 d for the experiments. After the biofilm cultivation, the experimental water with additional nutrients was drained out and the baffles were removed. Freshwater was then slowly added to the flume, and the flow discharge was gradually increased by controlling the pump. The flow conditions of the experiment are listed in Table 3.9, including a low flow rate condition (Q = 69.0 m3/h) that corresponds to a flatbed to investigate the direct biofilm effects on turbulence characteristics (i.e. affecting the micro-morphology of

Fig. 3.18 Plan view of the experimental flume

3.3 Effects of Biofilm on Turbulence Characteristics

193

Table 3.9 Flow parameters of four experiments with variable discharges, Q, and biofilms (Cheng et al. 2018) Test No.

Q (m3/h)

h (cm)

U*s (cm/s)

U*s (cm/s)

Dzvb (cm)

z0 (10−3 cm)

P-1 69.0 15.25 1.28 1.28 0.055 0.70 P-2 136.0 13.63 2.90 2.78 0.407 1.70 B-1 69.0 15.03 1.25 1.27 0.006 0.45 B-2 136.0 13.62 2.99 2.60 0.162 0.45 Note B represents sediment bed with biofilm, and P represents sediment bed without biofilm. h represents the water depth; U*s is the friction velocity derived from the energy slope, pffiffiffiffiffiffiffiffiffiffi U s ð¼ s0 =qÞ is the value derived from the distribution of the Reynolds shear stress; Dzvb is the depth of virtual bed from the bed surface, and z0 is the zero-velocity level or roughness length, which are derived from the vertical logarithmic distribution of time-averaged longitudinal velocity

the bed surface), and a high flow rate condition (Q = 136.0 m3/h) to estimate the indirect effects of biofilms (i.e. affecting the bedform development). The specific values of flow discharge were firstly determined by the Shields curve for incipient motion of bio-sediment presented by Fang et al. (2014b), also refer to Sect. 4.2.3 and Fig. 4.22, and then adjusted by observations in a series of testing experiments. The water depth along the flume was measured by point gauges, and the flow velocity was measured using an Acoustic Doppler Velocimeter (16 MHz MicroADV, Sontek, U.S.) vertically to analyze the turbulence characteristics, as shown in Fig. 3.19, i.e. in the centerline of testing area and with a distance of 30 cm from the front end of the sediment recess. The interval of adjacent measured points increased with the increasing distance from the bed, i.e. 2–5 mm below 0.2 h and 5–10 mm above 0.2 h. The number of measured points depended on the water depth, and the measurement at each point lasted for 3–4 min which referred to the time applied by Nikora et al. (2002). As the sampling volume of the ADV is 5 cm below the probe, points within 5 cm from the water surface were not measured. The software HorizonADV was used to collect and review the data with a sampling frequency of 50 Hz, and the measured data were then filtered by an acceleration Fig. 3.19 Sketch of the settings for flow velocity measurement by an Acoustic Doppler Velocimeter (Cheng et al. 2018)

194

3 Biofilm Growth and the Impacts on Hydrodynamics

threshold algorithm to obtain the fluctuating velocities (Goring and Nikora 2002; Dey et al. 2012). After the velocity measurements, the flow was stopped gradually and the bed topography was then measured using a MASATOYO electronic profile indicator (MEPI). Moreover, the turbulence characteristics of the original sediment bed (i.e. sediment bed without biofilm) also were measured for comparison. The corresponding flow discharge and water depth also are listed in Table 3.9, i.e. the same flow conditions as for the experiments for the bio-sediment bed.

3.3.2

Biofilm Effects on Turbulence Characteristics

Overall, the influences of biofilms on the turbulence characteristics (i.e. through changing the boundary conditions) might be manifested in two aspects (Cheng 2016). On the one hand, biofilm growth changes the micro-topography of the original sediment bed through covering the bed surface, which then affects the flow and turbulence structures especially near the bed surface. On the other hand, biofilm growth changes the inter-particle interactions and enhances the adhesion, thus, affecting the erosion pattern of bed sediment, leading to different bed morphology under the same flow conditions, and in turn changing the flow and turbulence structures. These changes in the turbulence characteristics would ultimately influence the sediment transport. In this section, the turbulence characteristics for sediment beds with and without biofilms are compared, involving the Reynolds shear stress, time-averaged velocity, turbulence intensity, turbulent kinetic energy flux and budget, and conditional Reynolds shear stress.

3.3.2.1

Reynolds Shear Stress Distribution

Figure 3.20a shows the vertical distributions of nondimensional Reynolds shear stress (RSS), ^sð^zÞ, for sediment beds with and without biofilms under different flow conditions. The RSS, sð¼  qu0 w0 Þ, is scaled by the bed shear stress, s0 ð¼qU2 Þ, where u0 and w0 are the turbulent velocity fluctuations in the longitudinal and vertical directions, respectively, and the vertical distance, z, is scaled by the water depth, h, i.e. ^s ¼ s=s0 and ^z ¼ z=h: For two-dimensional open-channel flow, the vertical distribution of the RSS follows a linear law, i.e. ^s ¼ 1  ^z, outside of the viscosity-affected layer near the wall (Nezu and Nakagawa 1993; Dey et al. 2012). As two-dimensional flow is driven by gravity, the linear distribution is also called the gravity line, see Fig. 3.20a. Based on the vertical distribution of the RSS, the bed shear stress, s0 , can be obtained by extending the linear fitted line to the bed with data between the inflection point and free surface layer (z/h < 0.6). The corpffiffiffiffiffiffiffiffiffiffi responding friction velocity, U s ð¼ s0 =qÞ, for different cases are listed in Table 3.9.

3.3 Effects of Biofilm on Turbulence Characteristics

195

Fig. 3.20 Vertical distributions of a non-dimensional RSS, ^s, b time-averaged velocities, and c turbulence intensities for sediment beds with (triangle) and without (square) biofilms under the lower and higher discharge conditions (Cheng et al. 2018)

As shown in Fig. 3.20a, the RSS follows a linear distribution in the lower discharge case but a slight deviation from the gravity line when ^z [ 0:1 due to the non-uniformity of flow. In the case of the higher discharge, the data collapse to the gravity line when ^z [ 0:1: Meanwhile, there is no significant change for the non-dimensional RSS distribution on sediment beds with and without biofilms under the same flow discharge, reflecting that the biofilm effects on the RSS distribution are negligible. However, the magnitude of the RSS near the bed (represented by U*s) is slightly changed after biofilm growth, especially in the higher discharge case with a variation of about 6.5%, see Table 3.9.

196

3.3.2.2

3 Biofilm Growth and the Impacts on Hydrodynamics

Time-Averaged Velocity Distribution

Figure 3.20b shows the vertical distribution of non-dimensional time-averaged longitudinal velocity for sediment beds with and without biofilms under the two levels of flow discharge. The time-averaged velocity, u, is scaled by the friction velocity, U* (=U*s), and the distance from virtual bed level, z + Dzvb, is scaled by the water depth, h, i.e. here, ^z ¼ ðz þ Dzvb Þ=h expressed by logarithmic coordinates in Fig. 3.20b. It is observed that the time-averaged velocity for sediment beds with biofilms is larger than that without biofilms irrespective of flow discharge, i.e. the presence of biofilms increases the velocity. However, the increase is especially different under different flow discharges, and these increases are approximately 6.7 and 26% under the low and high flow discharge conditions, respectively, in the wall region. In general, the logarithmic law for time-averaged longitudinal velocity, u, is valid in the wall region where (z + Dzvb)/h < 0.2, i.e.  u 1 z þ Dzvb ¼ ln U jv z0

ð3:28Þ

where jv is the von Kármán constant; Dzvb is the depth of virtual bed from the bed surface; and z0 is the zero-velocity level or roughness length. The previous studies have shown that jv varies with sediment transport (Chien and Wan 1999; Nikora and Goring 2000; Dey et al. 2012). However, here, the sediment transport is very weak; thus, jv is assumed to be 0.41, i.e. the value in clear flow (Nezu and Rodi 1986). The estimated Dzvb and z0 from Eq. 3.28 also are listed in Table 3.9, indicating that both parameters significantly decrease with the presence of biofilms under the same flow discharge. For example, under the low discharge condition, the value of Dzvb decreases by 89% compared with a sediment bed without a biofilm (i.e. from 0.055 to 0.006 cm), and z0 decreases by 36% (i.e. from 0.70  10−3 to 0.45  10−3 cm). Under the high discharge condition, Dzvb and z0 decrease by 60% and 74%, respectively. Nevertheless, the magnitude of these parameters is small; thus, the presence of biofilms plays a role at a small scale.

3.3.2.3

Turbulence Intensity Distribution

Figure 3.20c shows the vertical distributions of relative turbulence intensities hru ð^zÞi and hrw ð^zÞi for all cases, i.e. the longitudinal and vertical components, pffiffiffiffiffiffi pffiffiffiffiffiffiffi respectively. The turbulence intensities ru ð¼ u0 2 Þ and rw ð¼ w0 2 Þ also are scaled by the friction velocity, U* (=U*s), and ^z ¼ ðz þ Dzvb Þ=h: The results show that the turbulence intensity in the longitudinal direction, hru i, decreases as the distance to the bed ^z increases. The vertical component hrw i also decreases with the increasing ^z in the upper flow layer, while it increases in the region of ^z\0:1 with the maximum value obtained near ^z ¼ 0:1. These results are consistent with the

3.3 Effects of Biofilm on Turbulence Characteristics

197

previous studies on the flow over smooth and rough beds (Nezu and Rodi 1986; Kironoto and Graf 1994; Song and Chiew 2001). The empirical formulas for the distributions of turbulence intensities as suggested by Nezu and Rodi (1986) also are shown in Fig. 3.20c, i.e. pffiffiffiffiffiffi u0 2 ¼ 2:26 expð0:88^zÞ h ru i ¼ U pffiffiffiffiffiffiffi w0 2 ¼ 1:23 expð0:67^zÞ hrw i ¼ U

ð3:29Þ

ð3:30Þ

Comparing the turbulence intensities above sediment beds with and without biofilms, no significant differences can be found under the low discharge condition. In the higher discharge case, however, the vertical component of turbulence intensity hrw i decreases in the wall region of ^z\0:2 due to the presence of a biofilm, and it is more uniformly distributed in the vertical direction. The maximum reduction of hrw i is approximately 18% near ^z ¼ 0:1 due to the presence of a biofilm. The distribution of hru i does not change significantly after biofilm growth, and there is only a slight reduction near the bed. Therefore, biofilm growth mainly affects the vertical component of turbulence intensity.

3.3.2.4

Turbulent Kinetic Energy Flux and Budget Distributions

The vertical distributions of non-dimensional turbulent kinetic energy (TKE) flux,

 i.e. Fku ¼ fku =U3 (where fku ¼ 0:5 u0 u0 u0 þ u0 w0 w0 ) and Fkw ¼ fkw =U3 (where

 fkw ¼ 0:5 u0 w0 w0 þ w0 w0 w0 ) for the longitudinal and vertical components, respectively, are shown in Fig. 3.21. Under the low discharge condition, Fku starts with a small positive value for sediment beds without biofilms, i.e. Fku 0.16 at ^z ¼ 0:04, and then decreases with the increasing ^z, which changes the sign at ^z 0:05. The value of Fku further decreases with the increasing ^z until ^z 0:2, where Fku −1.37, and then turns to increasing with a further increase of ^z. Dey et al. (2012) noted that a positive Fku implies a streamwise transport of TKE flux, while a negative Fku indicates that the TKE flux transports against the streamwise direction. Moreover, the vertical TKE flux Fkw also begins with a small positive value but increases with the increasing ^z until ^z 0:2, where Fkw 0.42, and then turns to slightly decreasing as ^z further increases. The value of Fkw remains positive throughout the water depth, indicating an upward transport of TKE flux. Overall, no regular differences in the vertical distribution of TKE flux can be observed for sediment beds with and without biofilms in the low discharge case. Under the high flow discharge condition, however, the vertical distributions of TKE flux are different from those under the low flow discharge condition. Fku starts with a positive value and decreases with an increase in ^z, which changes sign at ^z 0:1. The negative magnitude of Fku increases with ^z up to ^z 0:2 and then

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3 Biofilm Growth and the Impacts on Hydrodynamics

Fig. 3.21 Vertical distributions of non-dimensional turbulent kinetic energy flux components (Fku and Fkw) for sediment beds with (triangle) and without (quadrate) biofilms under the lower and higher discharge conditions (Cheng et al. 2018)

decreases until ^z 0:4. Finally, Fku remains a small negative value in the flow layer of ^z [ 0:4. In contrast, Fkw starts with a negative value and increases with the increasing ^z, which also changes sign at ^z 0:1. In the upper flow layer of ^z [ 0:1, the value of Fkw is positive, which increases with ^z up to ^z 0:2 and decreases with a further increase in ^z until ^z 0:4. Then, Fkw retains a small positive value in the flow layer of ^z [ 0:4. Overall, few differences are observed between the vertical distribution of TKE flux for sediment beds with and without biofilms in the scattered data of Fig. 3.21. However, as the friction velocity on a bio-sediment bed is 6.5% smaller than that without a biofilm, the TKE flux components in the longitudinal and vertical directions decrease due to biofilm growth. The TKE budget for a uniform open-channel flow is given as follows (Nezu and Nakagawa 1993): @U @fkw 1 @p0 w0 @2k u0 w0 ¼ eþ þ m 2 @zffl} q @z @z @z |fflfflfflfflfflffl{zfflfflfflfflffl |{z} |fflfflffl{zfflfflffl} |ffl{zffl} Tp

TD

PD

ð3:31Þ

vD

where Tp is the TKE production rate, e is the TKE dissipation rate, TD is the TKE diffusion rate, PD is the pressure energy diffusion rate, vD is the viscous diffusion

3.3 Effects of Biofilm on Turbulence Characteristics

199


 rate, p′ is the pressure fluctuation, and k is the TKE defined as 0:5 u0 2 þ v0 2 þ w0 2 . The viscous diffusion rate vD is relatively small and, thus, negligible. The TKE dissipation rate e is calculated using Kolmogorov’s second hypothesis, the details of which are described in Dey et al. (2012). Then, the pressure energy diffusion rate, PD, can be calculated from Eq. 3.31 as PD = TP – e –TD. The parameters Tp, e, TD, ^ D ,T^D , and P ^D, and PD are all scaled by h=U3 to be non-dimensional values as T^p , E and the vertical distributions of these TKE budget components reflect the TKE production and transfer of the turbulence. Figure 3.22 shows the vertical distribution of TKE budget components under the low flow discharge condition. The TKE production rate, T^p , corresponds to the conversion of energy from the time-averaged flow to the turbulence, which presents a near-bed amplification and decreases with increasing ^z. Negative values of T^p are also observed at some points, implying an inverse energy conversion due to the ^ D , also decreases with the increasing ^z in a flow fluctuation. The dissipation rate, E ^ D is almost equal to T^p in similar way to the variation of T^p . It can be observed that E the wall region, implying that most of the turbulent kinetic energy dissipates locally. In the upper flow layer of ^z [ 0:2, however, the TKE production rate is less than the dissipation rate, revealing that TKE has been transported or produced in

^ D , c T^D , and d P ^ D ] for Fig. 3.22 Vertical distributions of TKE budget components [a T^p , b E sediment beds with (triangle) and without (quadrate) biofilms under the lower flow discharge condition (Cheng et al. 2018)

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3 Biofilm Growth and the Impacts on Hydrodynamics

other ways. The variation of T^D with ^z is scattered in the near-bed region (^z\0:3), and both negative and positive values can be observed. However, T^D becomes ^ D decreases with almost zero in the upper flow layer, i.e. invariant with ^z. P increasing ^z with the negative magnitudes, and the values are also scattered, and ^ D suggest a some positive values can be observed. The negative values of T^D and P gain in the turbulence production, which balances the TKE production rate, T^p , and ^ D . It also is observed that there are few differences between TKE dissipation rate, E the distributions of TKE budget components for sediment beds with and without biofilms, i.e. the biofilm effects on the TKE budget are negligible under the low flow discharge condition. Figure 3.23 shows the vertical distribution of TKE budget components under the ^ D , and T^D with ^z are similar to high flow discharge condition. The variations of T^p , E ^ D inverts and those under the low flow discharge condition, while the variation of P becomes almost zero in the flow layer of ^z [ 0:3. In the wall region, TKE dissi^ D , are much smaller than the production rate, T^p , and the maximum pation rates, E ^ D , which implies that most of the value of T^p is approximately 3.5 times that of E TKE is transferred by turbulent kinetics or pressure diffusion to the upper or lower

^ D , c T^D , and d P ^ D ] for Fig. 3.23 Vertical distributions of TKE budget components [a T^p , b E sediment beds with (triangle) and without (quadrate) biofilms under the higher flow discharge condition (Cheng et al. 2018)

3.3 Effects of Biofilm on Turbulence Characteristics

201

^ D in the upper flow layer of ^z [ 0:3. flow layer. However, T^p is almost equal to E Similar to the low flow discharge condition, regular changes in the TKE production ^ D , due to biofilms rate, T^p , diffusion rate, T^D , and pressure energy diffusion rate, P cannot be observed in the scattered data of Fig. 3.23. However, the change in the ^ D , is relatively significant, which decreases by approximately dissipation rate, E 12% in the near-bed region of ^z\0:3, as shown in Fig. 3.23b.

3.3.2.5

Conditional RSS Distributions

Bursting events caused by the motion of coherent eddies are categorized by conditional RSS production, and they are the governing mechanisms for the production of Reynolds shear stress, which determine the momentum and energy transfer between the near-bed region and outer flow region (Nikora and Goring 2000), and, hence, determine the mass transport in the flow such as sediment entrainment and bedload transport (Dey et al. 2011, 2012). The characteristics of bursting events can be detected by quadrant analysis of velocity fluctuations u0 and w0 (Lu and Willmarth 1973), and four types of events are identified: (i) outward interactions, E1: i = 1, u0 [ 0, w0 [ 0; (ii) ejection, E2: i = 2, u0 \0, w0 [ 0; (iii) inward interactions, E3: i = 3, u0 \0, w0 \0; and (iv) sweep, E4: i = 4, u0 [ 0, w0 \0. The fractional contribution from the event Ei (i = 1, 2, 3, or 4) toward RSS production is given by: 1 1 Si;H ð^zÞ ¼ 0 0  lim T !1 Ts uw s

Z

Ts

u0 ðtÞw0 ðtÞki;H ð^z; tÞdt

ð3:32Þ

0

where Ts is the sampling duration; t represents time; ki;H ðtÞ is the detecting function; and ki;H ðtÞ ¼ 1 if the ðu0 ; w0 Þ pair is in quadrant i with ju0 w0 j  Hru rw , otherwise, ki;H ðtÞ ¼ 0. Here, H is the hole size, which draws a clear distinction between the strong events outside the hole and the weak ones inside it. The changes in the fractional contributions of bursting events toward RSS reflect the biofilm effects on the turbulence structure. Here, the data of Si,H(^z) with H = 0 are shown in Fig. 3.24. Under the low flow discharge condition, for sediment beds without biofilms (i.e. Fig. 3.24a), E2 and E4 events contribute approximately 65% and 63% to the total RSS production at the point nearest to the bed, respectively, and the fractional contributions of E2 events increasingly exceed those of E4 events with increasing ^z. This implies that high-speed fluid parcels from the upper flow region revoke the arrival of low-speed parcels from the near-bed zone. On the other hand, E1 events contribute minimally to the total RSS production, i.e. 13% near the bed, and the contributions of E3 events exceed those of E1 events slightly with a percent of 15%. The vertical distribution of the contributions of E1 events is almost the same as that of E3 events, and their variation amplitudes are especially small from the bed to upper flow layer (i.e. less than 10%). For bio-sediment bed (i.e. Fig. 3.24b), at the

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3 Biofilm Growth and the Impacts on Hydrodynamics

Fig. 3.24 Vertical distributions of Si,0 for sediment beds without [(a) and (c)] and with [(b) and (d)] biofilms under the lower and higher flow discharge conditions (Cheng et al. 2018)

point nearest to the bed, E2 and E4 events contribute approximately 68% and 62%, respectively, which are almost the same as those for sediment beds without biofilms. The contributions of E1 and E3 events almost remain constant in the vertical direction, i.e. approximately 15% and 16%, respectively. Overall, biofilm effects on the fractional contributions of bursting events are not apparent for flatbeds under the low discharge condition. Under the high flow discharge condition, for sediment beds without biofilms (i.e. Fig. 3.24c), the contributions of E4 events exceed those of E2 events in the near-bed region of ^z  0:1, which contribute 67% and 64% to the total RSS production at the point nearest to the bed, respectively. This is probably due to the bed erosion causing roughness with a scale larger than the particles and also weak sediment transport on the bed (Nikora and Goring 2000; Dey et al. 2012). In the upper flow layer of ^z [ 0:1, however, the contributions of E2 events become larger than those of E4 events and the difference increases with increasing ^z. E1 events still provide minimal contributions, and the contributions of E3 events are almost the same as E1 events, i.e. approximately 15% throughout the water depth. In comparison, the changes in the fractional contributions of bursting events are apparent in the presence of biofilms, see Fig. 3.24d. In the near-bed zone of ^z  0:1, the contributions of E4 and E2 events are almost the same, which increase to 74% and 71% at the point nearest to the bed, respectively. Meanwhile, the contributions of E1 and E3 events also increase to 21% and 24%, respectively. The contributions

3.3 Effects of Biofilm on Turbulence Characteristics

203

Fig. 3.25 Topography of sediment beds without (a and c) and with biofilms (b and d) under the lower and higher discharge conditions (Cheng et al. 2018)

of E2 and E4 events decrease, however, at the same relative position compared with those for the original sediment bed (i.e. Fig. 3.24c), suggesting that the influence of sweep and ejection events is relatively weaker for sediment beds with biofilms. Many researchers have found that E4 events are the governing mechanisms for sediment transport (Nikora and Goring 2000; Dey et al. 2011, 2012). Thus, biofilm growth on a sediment bed would change the bursting events, which inhibits the sediment motion and increases bed stability. Moreover, the presence of biofilms on sediment beds not only influences the flow properties, but also influences the bed morphology, as described in Sect. 3.2. Figure 3.25 shows the bed morphology in these four experiments, i.e. sediment beds with and without biofilms under the lower and higher flow discharge conditions. The bed surface is almost flat under the low discharge condition, as the shear stress exerted on the bed is smaller than the critical value for sediment incipient motion. However, under the high discharge condition, sediment beds with and without biofilms are eroded. The average erosion depth for the original sediment bed is about 6 mm, and it is about 2.5 mm for the bio-sediment bed, which also illustrates that the stability of the sediment bed is enhanced due to biofilm growth.

204

3.3.3

3 Biofilm Growth and the Impacts on Hydrodynamics

Implications

The turbulence characteristics on sediment beds with and without biofilms are compared in the preceding section. Overall, biofilms affect the turbulence characteristics by changing the boundary condition in two ways. One is changing the interactions between flow and sediment through covering the bed surface under the lower flow discharge condition, and the other is changing the bedform characteristics under the higher flow discharge condition. Under the lower flow discharge condition, the sediment bed is almost flat and the turbulence characteristics including the RSS, relative turbulence intensity, TKE flux, and budget components and bursting events are almost unchanged after biofilm growth. However, the change of the time-averaged velocity is visible, and the variations of roughness length and virtual bed height are observed at a millimeter scale, indicating that the presence of biofilms on the fixed sediment bed reduces the bed resistance. Nikora et al. (1997, 2002) concluded that a biofilm growing on the gravel bed increases the roughness length as well as the resistance to the flow. However, some other studies, which were also done on rough beds consisting of gravel, cobbles, and artificial roughness elements, show that the presence of biofilms decreases the roughness length and bed resistance (Labiod et al. 2007; Graba et al. 2010). Moreover, it is also stated that the structures of biofilms, such as the compactness and the size of filaments, play an important role changing the hydrodynamic parameters (Moulin et al. 2008). Here, it is observed that the biofilm covering the sediment bed is of a millimeter scale which binds tightly with the sediment. Thus, the direct disturbance of the flow is quite limited, and the turbulence characteristics are only slightly changed. Under the higher flow discharge condition, there are significant changes of bed morphology due to biofilm growth, indicating that biofilms have a great impact on the bed stability which inhibits the erosion of sediment. Moreover, the changes in RSS, time-averaged velocity, roughness length, turbulence intensity, and even the bursting events are larger than those for flow over a flatbed, implying that the indirect impact of biofilms on the turbulence characteristics through changing the bedform is greater than its direct influence through covering the sediment bed. Unfortunately, due to the limited accuracy of experimental data (Cheng et al. 2018), no statistical results on the changes of TKE flux and budget components in the near-bed region are yet available, and further studies are still needed.

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Chapter 4

Bedload Transport of Bio-sediment

Bed sediment is subjected to shear stress induced by the flow. With an increase in the shear stress, sediment particles successively experience the destruction of the bed layer, incipient motion, and transport processes. Sediment transport is the focus of sediment research, including bedload and suspended load transport. As described in the previous chapters, biofilm growth changes the basic characteristics of sediment particles and influences the resistance to flow and the corresponding turbulence characteristics, which then affects sediment transport processes. Thus, it is necessary to study the transport characteristics of bio-sediment. This chapter mainly introduces the bedload transport of bio-sediment, and suspended load transport will be introduced in Chap. 5. Meanwhile, biofilms influence sediment beds by embedding the particles and permeating the void spaces to enhance the cohesive force among the sediment particles and offering an additional adhesion force (Gerbersdorf et al. 2008; Fang et al. 2017). Accordingly, the rheological properties and the threshold bed shear stress (or threshold shear velocity) for erosion are changed (Righetti and Lucarelli 2007; Fang et al. 2012, 2014). Thus, this chapter describes the bedload transport of bio-sediment from the aspects of rheological properties, incipient motion, and bedload transport rate.

4.1

Rheological Properties of Bio-sediment

The mechanical properties of biofilms are the basis to understand their effects on the physical sediment transport, which should be first considered when studying the incipient and settling motion of bio-sediment, and also the detachment of biofilms.

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer-Verlag GmbH, DE, part of Springer Nature 2020 H. Fang et al., Mechanics of Bio-Sediment Transport, https://doi.org/10.1007/978-3-662-61158-6_4

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4.1.1

4 Bedload Transport of Bio-sediment

Introduction of Rheology

Rheology, a phenomenon that cannot be ignored in nature, describes the flow of matter under conditions in which the matter responds to an applied force with plastic flow rather than deforming elastically. The law of Newtonian inner friction is conditional on laminar flow for all fluids, and it is exactly the rheological model describing a Newtonian fluid, i.e. sR ¼ l

du dy

ð4:1Þ

where sR is the shear stress in the fluid; du=dy is the strain rate, u is the velocity in the streamwise direction, x, and y is the vertical direction; and l is a constant of proportionality under a given temperature, i.e. the dynamic viscosity of the fluid. Thus, Newtonian fluids can be characterized by a single coefficient of viscosity for a specific temperature, which changes with the temperature but does not change with the strain rate. Actually, only a small group of fluids exhibit such a constant viscosity, and a large class of fluids whose viscosity changes with the strain rate are called non-Newtonian fluids (i.e. not conforming to Eq. 4.1). Accordingly, an apparent viscosity, lapp, is defined for non-Newtonian fluids as lapp ¼

sR du=dy

ð4:2Þ

The classification of fluids based on the shear stress versus strain rate relation is listed in Table 4.1. Table 4.1 Classification of fluids based on the shear stress vs. strain rate relation Classification Viscoelasticity

Description Time-dependent

Pure viscosity Time-independent

Multiple types Thixotropic Rheopectic Pseudoplastic Dilatant Bingham plastic

Newtonian fluids

– lapp decreases with duration of stress lapp increases with duration of stress lapp decreases with increased stress; sR ¼ lðdu=dyÞnR ; nR \1 lapp increases with increased stress; sR ¼ lðdu=dyÞnR ; nR [ 1 A linear shear stress vs. strain rate relation but a yield stress, sy , is required; sR ¼ sy þ lðdu=dyÞ

Yield pseudoplastic

Pseudoplastic with a yield stress; sR ¼ sy þ lðdu=dyÞnR ; nR \1

Yield dilatant

Dilatant with a yield stress; sR ¼ sy þ lðdu=dyÞnR ; nR [ 1 The shear stress vs. strain rate curve is linear and passes through the origin

4.1 Rheological Properties of Bio-sediment

211

The rheological property describes the relation between the shear stress and strain rate. The rheological property of cohesive sediment is an important and complex subject in the theoretical study of sediment transport (Babatope et al. 2008; Schatzmann et al. 2003). If cohesive sediment is suspended in the water, it follows different rules at different sediment concentrations. That is, the suspension belongs to a Newtonian fluid at a small sediment concentration, while it becomes a Bingham fluid or pseudoplastic fluid with an increasing sediment concentration. Moreover, when discussing the rheological property of sediment deposits (sludge a type of non-Newtonian fluid), which is different from that of clear water and varies with sediment concentration, particle size, mineral composition, and water quality (CHES 1992), the change of initial stiffness is the general focus. For example, fine sediment exhibits a greater initial stiffness; the initial stiffness increases rapidly with increasing sediment concentration, which might be proportional to the 4th or 5th power of sediment concentration. The initial stiffness in the seawater is 1.4–1.7 times that in river water under the same sediment concentration, and it increases rapidly within a salinity range of 5‰ while it changes slightly after exceeding this salinity. In addition, the corresponding common rheological equations are as follows 0:5 0:5 0:5 (Han 1991): (1) Casson model, i.e. s0:5 R ¼ sy þ l ðdu=dyÞ , which is mainly applicable to suspensions with fine particles and a large electrical viscosity (e.g. clay slurry); (2) Bingham model, i.e. sR ¼ sy þ lðdu=dyÞ, which is applicable to the pulp, mud, or coal slurry with high concentrations; (3) power law model, i.e. sR ¼ lðdu=dyÞnR , which is mainly applicable to polymer solutions or suspensions containing polymers; and (4) yield plastic model, i.e. sR ¼ sy þ lðdu=dyÞnR , which can be approximated as a Bingham model when the strain rate du=dy varies moderately, and also can be approximated as a power law model when the yield stress sy is small.

4.1.2

Rheological Experiments

The excretion of biofilms by microorganisms forms a cohesive matrix that surrounds sediment particles, which is generally important in mediating the rheological properties of cohesive sediment (Ruddy et al. 1998; de Brouwer et al. 2000; Fang et al. 2012). However, so far, there have been few studies on the rheological properties of bio-sediment. Here, the biofilm effects on rheological properties of cohesive sediment are investigated (Zhao 2010; Fang et al. 2012). Bio-sediment with different cultivation periods is obtained by laboratory experiments to test the rheological properties, based on which rheological equations for bio-sediment are proposed. Although the biochemical properties of biofilms are influenced by various environmental parameters, their viscoelastic properties might be generally consistent (Towler et al. 2003; Flemming and Wingender 2010).

212

4.1.2.1

4 Bedload Transport of Bio-sediment

Experimental Apparatus

A rotational rheometer evaluates the rheological behavior, e.g. apparent viscosity, through measuring the shear stress on the rotor surface at different shear rates (Gao et al. 2006). Here, the MCR300 advanced extension rheometer (Anton Paar GmbH, Austria), i.e. a stress-controlling rotational rheometer, was used to measure the rheological properties of bio-sediment (see Fig. 4.1). The main parameters of the MCR300 are as follows: (1) temperature range: −30 to 350 °C; (2) viscosity range: 1 mPa s–106 Pa s; (3) torque range: 0.5 lN m–150 mN m; (4) frequency range: 10−4 to 100 Hz; and (5) shear stress range: 10−3 to 105 Pa. Before the experiments, the viscosity of distilled water was measured to test the capability of the MCR300 rheometer, and the relation between shear stress and strain rate is shown in Fig. 4.2. The results show that the viscosity of distilled water is 10−3 Pa s at room temperature (about 20 °C) which is consistent with the known values, indicating a reliable performance of the rheometer.

Fig. 4.1 A MCR300 advanced extension rheometer

Fig. 4.2 Relation between shear stress and strain rate for distilled water measured by a MCR300 (Fang et al. 2012)

4.1 Rheological Properties of Bio-sediment

4.1.2.2

213

Experimental Procedure

First, a biofilm cultivation experiment was done as described in Sect. 4.2.1.2 to obtain bio-sediment samples with different cultivation periods. Surface sediment collected from the Guanting Reservoir near Beijing, with a diameter of 0.05– 0.1 mm, was used for the cultivation. 20 g of sediment samples was added to a 3.5 L experimental solution, i.e. freshwater from the lotus pond at Tsinghua University with additional nutrients; meanwhile, 0.5 L of experimental water was refreshed every day to replenish the nutrients for 10 weeks. The secreted biofilm coated the particles, permeated the void spaces, and gradually changed the sediment properties. Moreover, sediment of the same weight (i.e. 20 g) was immersed in distilled water for the same period as a blank sample (referred as the original sediment), to compare the rheological properties with that of bio-sediment. The rheological properties of sediment samples were measured once a week. Each time, the supernatant (i.e. experimental solution or distilled water) first was removed, and then, about 20 mL saturated sludge was retained for the measurement. Given a weight of 20 g of sediment, the concentration of saturated sludge is about 1000 g/L. The rheological property of bio-sediment was measured twice each time to determine its change after the original state of bio-sediment was destroyed by the first measurement, and the second measurement was made 10 min after the first using the remaining sediment sample. Moreover, to compare the influence of experimental solution and distilled water on the rheological properties of the sludge (i.e. the effects of water quality), two samples of 20 g of sediment were separately immersed in the experimental solution and distilled water for 2 h. The water was then eliminated, and the rheological properties of the remaining sediment were measured, as shown in Fig. 4.3. It was found that, for high-concentration sludge, the effect of experimental solution and distilled water on the rheological properties is negligible.

Fig. 4.3 Effects of experimental solution and distilled water on the rheological properties (Fang et al. 2012)

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4 Bedload Transport of Bio-sediment

4.1.3

Rheological Properties of Bio-sediment

4.1.3.1

Rheological Curves of Bio-sediment

Figure 4.4 shows the rheological properties of the experimental sediment from the first week to the tenth week, showing the biofilm effects on rheological properties. In each sub-figure, the blue and red curves are the rheological curves of bio-sediment for the first and second measurements, respectively; and the green curve is the rheological curve of the original sediment that is immersed in distilled water. For original sediment immersed in the distilled water, the rheological curves all approximate a straight line for different weeks (see the green curves in Fig. 4.4, which only bend slightly at the bottom), exhibiting the characteristics of Bingham fluids. The apparent viscosity increases slightly with time mainly due to the effects of compaction on the porosity of the original sediment, as shown in Fig. 4.5. In contrast, the rheological behavior of bio-sediment exhibits the characteristics of a plastic fluid with thixotropy (see the blue and red curves in Fig. 4.4, which represent the first and second measurements, respectively). The strain rate is initially proportional to the shear stress, i.e. the rheological properties of a plastic fluid. However, the shear stress remains almost constant when the strain rate exceeds a critical value, so the bio-sediment structure reaches a dynamic equilibrium between breakup and recovery, and thereby displays a degree of thixotropy. Thixotropy reflects the characteristic that the structural strength of sludge is gradually disrupted under the action of shear stress. If the strain rate remains constant, thixotropy is apparent as a reduction of shear stress with time until the appearance of a dynamic equilibrium state in which the shear stress does not change anymore, implying that the sludge flows more easily. Meanwhile, it can be found that the yield stress, steady shear stress, and apparent viscosity of bio-sediment all gradually increase with increasing biofilm cultivation period (i.e. with increasing biomass) through comparison of the rheological curves from the first week to the tenth week, indicating a significant effect of biofilms on the rheological property. In addition, the rheological properties were measured again after the bio-sediment was set aside for 10 min from the first measurement. The trends of variation were similar to those obtained during the first measurement, while both the yield stress and steady shear stress were significantly reduced.

4.1.3.2

Analysis of the Rheological Structure

Figure 4.6 shows the ESEM images of bio-sediment before and after ultrasonic oscillation. The biofilms exert effects not only on individual sediment particles, but also on sediment groups via adhesion, see Fig. 4.6a. The biofilms among sediment particles are destroyed when subjected to certain mechanical action (e.g. ultrasonic oscillation), whereas the biofilms covering the particles remain, see Fig. 4.6b.

4.1 Rheological Properties of Bio-sediment

215

Fig. 4.4 Rheological curves for the experimental sediment. The curves marked with “ ” and “ ” are the rheological curves of bio-sediment for the first and second measurements, respectively; and the curves marked with “ ” are the rheological curves of the original sediment that is immersed in distilled water (Fang et al. 2012)

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4 Bedload Transport of Bio-sediment

Fig. 4.5 Rheological curves of the original sediment over time. The different colors and symbols 4 weeks, 5 weeks, represent different times as follows: 1 week, 2 weeks, 3 weeks, 6 weeks, 7 weeks, 8 weeks, 9 weeks, and 10 weeks

Fig. 4.6 ESEM images of bio-sediment a before and b after ultrasonic oscillation (Fang et al. 2012)

Therefore, the destruction of the bio-sediment structure involves two processes, i.e. the breaking of (biofilm-generated) weak links among the sediment particles and the disappearance of bio-sediment adhesion. The former is irreversible, and the corresponding response in terms of the rheological properties is a decline in the yield stress in the rheological curves. The yield stress is a critical stress when the sludge starts to flow, and sludge with a smaller yield stress starts to flow more easily. As shown in Fig. 4.4, the yield stress of bio-sediment for the second measurement is always smaller than that for the first measurement, which is because the weak links among sediment particles have been destroyed during the first rheological experiment, while they are not restored for the second measurement. Accordingly, the resultant sludge starts to flow more easily. Bio-sediment adhesion can recover to some extent after the shear stress is eliminated, i.e. after the first rheological measurement, and the response in the

4.1 Rheological Properties of Bio-sediment

217

rheological curves is a cracking of the structural consistency. The rheological curves of bio-sediment for the second measurement have similar characteristics as those for the first measurement but with some reduction in the shear stress. The similarity is due to the recovery of bio-sediment adhesion that is mainly generated by the biofilm covering the sediment particles. As shown in Fig. 4.6b, biofilms on the particles remain after some mechanical action, which maintains a portion of the rheological properties. Meanwhile, the reduction is because the bio-sediment adhesion could only partially recover rather than completely recover, so the viscosity decreases to some extent. 4.1.3.3

Rheological Model of Bio-sediment

As previously mentioned, the rheological curves of bio-sediment reveal the characteristics of plastic fluids with thixotropy, and there is a single-valued relation between the shear stress, sR , and strain rate, du=dy. These rheological curves should be mathematically described by piecewise functions based on the critical strain rate at which the bio-sediment structure reaches a dynamic equilibrium. Moreover, the rheological property of bio-sediment is closely related to the biofilm. The adhesion among sediment particles increases with biofilm growth, and accordingly, a larger shear stress is needed to break the bio-sediment structure for the flow of sludge, i.e. a greater resistance is present. Correspondingly, all the rheological parameters increase with biofilm growth, so the shear stress vs. strain rate relation is a set of curves as a function of cultivation period t, see Fig. 4.7. The yield stress, steady shear stress, and viscosity of bio-sediment all gradually increase over time. Moreover, the changes of the rheological properties are readily apparent during the first seven weeks, whereas those in the subsequent three weeks are moderate. According to the properties of the rheological curves, the rheological equations of bio-sediment are defined as
 8 du \_c < sy ðtÞ þ lðtÞ du dy
dy  sR ðtÞ ¼ du  c_ : se ðtÞ dy

ð4:3Þ

where sy ðtÞ and lðtÞ are the yield stress and dynamic viscosity coefficient, respectively, of bio-sediment cultivated for t days before reaching a stable structure; se ðtÞ is the stable shear stress, i.e. the value after bio-sediment achieves a stable structure; and c_ is the steady (critical) strain rate. As shown in Fig. 4.7, although the shear stress at which bio-sediment reaches a stable structure is different for bio-sediment cultivated for different times, the steady strain rate c_ is always in the range of 15–24 s−1 for the first rheological measurement and 5–15 s−1 for the second measurement, illustrating that the adhesion of bio-sediment falls within a tolerance range. Figure 4.8 shows the change of sy , l, and se over time (i.e. biofilm cultivation period), the curves are derived by fitting Eq. 4.3 with the measured rheological

218

4 Bedload Transport of Bio-sediment

(a) Rheological curves of bio-sediment from the first measurement

(b) Rheological curves of bio-sediment from the second measurement Fig. 4.7 Rheological curves of bio-sediment over time. The different colors and symbols 4 weeks, 5 weeks, represent different times as follows: 1 week, 2 weeks, 3 weeks, 6 weeks, 7 weeks, 8 weeks, 9 weeks, and 10 weeks (Fang et al. 2012)

curves in Fig. 4.7. It can be found that these parameters gradually increase over time and tend to remain stable from the eighth week, indicating that biofilm growth basically reaches a steady state at that time. The variations of sy ðtÞ, lðtÞ, and se ðtÞ reflect the biofilm growth condition, involving factors such as microbial species, nutrition, and temperature. Here, it is simply assumed that the variations of these parameters with biofilm cultivation period can be expressed as /ðtÞ ¼ k0 þ

n X

ki ekj t

ð4:4Þ

i;j¼1

where /ðtÞ represents the parameters sy ðtÞ, lðtÞ, or se ðtÞ; k0, ki, and kj are the fitting coefficients based on the data in Fig. 4.8, and n represents the number of terms of ki and kj. Figure 4.9 shows the relation between the correlation coefficient, R, and the fitting term n in Eq. 4.4, revealing that the exponential form can reasonably fit the

4.1 Rheological Properties of Bio-sediment

219

Fig. 4.8 Original and fitted curves of sy , l, and se . The curves marked with “ ” and “ ” are the original and fitted curves of the rheological parameter changes of bio-sediment for the first rheological experiment, respectively, and the curves marked with “ ” and “ ” are the original and fitted curves for the second measurement, respectively (Fang et al. 2012)

function of sy ðtÞ, lðtÞ, and se ðtÞ. The correlation coefficient, R, is greater than 0.95 and tends to stabilize with increasing n. According to Fig. 4.9, the values of n in Eq. 4.4 are taken as nsy ¼ 4, nl ¼ 3, and nse ¼ 3, i.e. when the correlation coefficient starts to stabilize. Correspondingly, the expressions for the rheological parameters over time are as follows:

220

4 Bedload Transport of Bio-sediment

Fig. 4.9 Relation between the correlation coefficient, R, and the fitting term n for the two measurements (Fang et al. 2012)

For the first rheological measurement of bio-sediment: 8 < sy ðtÞ ¼ 36:10 þ 54:89e0:065t þ 149:14e0:051t  79:47e0:059t  94:06e0:059t lðtÞ ¼ 2:45  148:75e0:151t þ 322:06e0:179t  187:07e0:211t : se ðtÞ ¼ 61:41  6484:17e0:173t þ 12003:78e0:146t  5844:64e0:124t ð4:5Þ and for the second measurement of bio-sediment: 8 < sy ðtÞ ¼ 78:65  158:80e0:124t  76:91e0:0007t þ 494:44e0:164t  363:60e0:195t lðtÞ ¼ 251:76  3:50e0:014t  4633:40e1:190t  247:60e0:0005t : se ðtÞ ¼ 18:53  855:59e0:788t  141:24e0:0347t þ 160:97e0:033t ð4:6Þ where t is time. The corresponding fitting curves of the rheological parameters also are shown in Fig. 4.8, and there are good correlations between the original and fitted curves with all the correlation coefficients, R, greater than 0.99 (as shown in Fig. 4.9). Knowledge on the rheological properties of cohesive sediment is important for understanding sediment transport processes, but a single viscosity is insufficient to

4.1 Rheological Properties of Bio-sediment

221

describe the constitutive equation of complex sediment under different flow conditions. Thus, an appropriate method is to determine the rheological behavior of flow mixtures (e.g. intense bedload transport), and the flow characteristics can then be determined analytically or numerically by solving the flow equations combining the constitutive equation and the particular initial/boundary conditions (Batchelor 1967; Middleton and Wilcock 1994). Meanwhile, field observations have shown that one of the main characteristics of hyper-concentrated viscous flow is the yield stress (Johnson 1970; Coussot 1992; Whipple and Dunne 1992), which is associated with the interaction network of clay particles that must be broken before the flow occurs (van Olphen 1977; Coussot et al. 1993). Sludge of bio-sediment has a different rheological behavior, mostly as a consequence of the diversity of the biofilm composition (de Brouwer et al. 2002). Although numerous constitutive models have been proposed for sediment transport studies, e.g. the Bingham model (Bisantino et al. 2010), the development of equations describing the rheological properties of bio-sediment is still limited, but is essential for modeling sediment dynamics combining new environmental issues. Here, the rheological equations for bio-sediment were derived from experimental data, which are expected to be useful for a preliminary calculation of bio-sediment transport, and for deciding whether more detailed calculations are required at the expense of complexity. Similarly, bio-sediment transport includes suspended load and bedload transport with different mechanisms. The forces acting on sediment particles should first be calculated to enable a judgment of the form of sediment transport based on the rheological models of bio-sediment. Then, for bedload transport (treated as a type of hyper-concentrated flow), the behavior can be modeled by solving the flow equations incorporating the rheological models and initial/boundary conditions.

4.2

Incipient Motion of Bio-sediment

There are three basic laws of sediment transport according to the forms of motion, i.e. the laws of incipient motion, settling, and sediment carrying, which are related to each other but also relatively independent (Cheng 2016). In aquatic ecosystems, nutrient enrichment encourages microbes to grow on solid surfaces. The discrepancy in the critical erosion velocity and settling velocity between biogenic and original sediment eventually leads to different sedimentation processes and geomorphology (Fang and Wang 2000; Fang et al. 2014). Incipient motion is an important critical condition in fluvial processes that sediment starts to move under the action of flow, which is essential for the estimation of sediment transport. It is the result of the mutual action between sediment particles and flow, which is generally expressed as the shear stress (drag force), mean velocity, and stream power for incipient motion. Previous studies have shown that sediment stability is enhanced due to biofilm growth, thus increasing the incipient velocity of sediment (Righetti and Lucarelli 2007; Gerbersdorf et al. 2008;

222

4 Bedload Transport of Bio-sediment

Fang et al. 2014), which might cause one order decrease of the sediment transport rate in the surface biofilm layer (Watanabe et al. 2008; Stone et al. 2011). In this section, the incipient motion of bio-sediment will be introduced, following a brief introduction on the incipient motion of noncohesive and cohesive sediment.

4.2.1

Incipient Motion of Noncohesive and Cohesive Sediment

A considerable number of experimental and theoretical studies have been done on the incipient motion of sediment, especially for noncohesive particles. Kramer (1935) recommended that the movement of bedload can be divided into four stages: (i) no sediment motion, i.e. all the sediment on a bed is still; (ii) sparse sediment motion, i.e. only a few fine sediment particles move on a bed; (iii) mean sediment motion, i.e. sediment particles finer than the median diameter, D50, move on a bed which are countless; and (iv) strong sediment motion, i.e. all sizes of sediment move and the bed changes progressively. There is a critical particle size for the incipient motion conditions of sediment. For sediment particles coarser than the critical size, the incipient velocity increases with the increasing particle size; while for sediment particles finer than the critical size, the incipient velocity increases with the decreasing particle size, which is not only due to the shielding effects of the laminar sub-layer but also the effects of cohesion among fine particles.

4.2.1.1

Noncohesive Sediment

For noncohesive sediment, the condition for incipient motion is commonly determined in terms of shear stress (drag force) or mean velocity. In 1936, Shields (1936) proposed a shear stress equation of incipient motion for noncohesive sediment based on the theoretical analysis and the experimental results of four types of sediment with different densities, i.e. a relation between the critical Shields number, Hc ð¼sc =ðcs  cÞDÞ (where sc = critical shear stress for incipient motion, cs = specific weight of sediment, c = specific weight of water, and D = sediment particle diameter), and particle Reynolds number for bed sediment, Re ð¼U D=mÞ (where U = shear velocity and m = kinematic viscosity of water), indicating that the ratio of the shear stress acting on the sediment surface to the particle weight is a function of the particle Reynolds number when sediment particles start to move (see Fig. 4.10), i.e.   sc U D ¼f m ðcs  cÞD

ð4:7Þ

4.2 Incipient Motion of Bio-sediment

223

Fig. 4.10 Incipient motion condition for noncohesive sediment (Shields curve and its modifications) (Author references Tison (1948); C. M. White = White (1940); C. H. Li = Li and Sun (1964); Mantz (1977); S. J. White = White (1970); Yalin and Karahan (1979)) (Chien and Wan 1999, with permission from ASCE)

Thereafter, many modifications have been applied to the Shields curve, e.g. White (1970), Mantz (1977), Tison (1948), and Li and Sun (1964), as shown in Fig. 4.10. These modifications with new experimental results found that a Shields number of 0.06 was slightly high at a high particle Reynolds numbers (Re* > 1000) and should be in the range of 0.04–0.06 (and a value of approximately 0.045 was suggested by Miller et al. (1977)). Meanwhile, for the condition of low particle Reynolds numbers (Re* < 2), Shields (1936) assumed that the incipient shear stress was independent with particle size, and the curve was a straight line with a 45° slope. However, it has been proven that this hypothesis was not true according to the new experimental results; and the incipient motion of fine sediment also is related to the particle size although these particles are hidden in the viscous sub-layer, resulting in a smaller slope than that of a 45° line. Moreover, the results of incipient motion under laminar flow conditions also are shown in Fig. 4.10 (Yalin and Karahen 1979), indicating that the drag force required under laminar flow is generally larger than that under turbulent flow. For turbulent flow with a smooth boundary, the flow pattern near the boundary is similar to that under laminar flow due to the laminar sub-layer. For this condition, the data for these two regimes fall together with an asymptote expressed as sc ¼ 0:1Re0:3  ðcs  cÞD

ð4:8Þ

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4 Bedload Transport of Bio-sediment

The scattered nature of experimental data in Fig. 4.10 is mainly due to the randomness resulting from five aspects, including the statistical characteristics of the forces exerted on particles, flow turbulence and bursting properties, measurement accuracy of test instruments and the influence of instrument operation, particle gradation, and particle shape. Some evaluations considered that the particles tested by Shields (1936) were not uniform, leading to a 15–25% higher deviation compared with the real incipient shear stress (Egiazaroff 1967). The bed boundary condition is not substantially changed by the motion of uniform sediment. Therefore, the incipient motion for uniform sediment is not changed when part of the sediment has been removed, which can be treated as a steady phenomenon. For non-uniform sediment, however, the incipient motion of bed material also is the beginning of the armoring process of the bed surface, i.e. an unsteady phenomenon. Thus, the sorting of sediment particles and the shielding of fine particles by coarse particles should be considered. Brownlie (1981) further transformed the Shields curve into a function of dimensionless D* (expressed as Eq. 4.9), i.e. Hc ¼ f ðD Þ, which also has been widely applied. Then, it was suggested that the Shields number can be calculated using Eq. 4.10 for noncohesive sediment, which is represented by the solid line in Fig. 4.11.   qs  q g 1=3 D ¼ D q v2

ð4:9Þ 0:9

þ 0:06  107:7D Hc ðD Þ ¼ 0:22D0:9 

ð4:10Þ

where qs is the density of the sediment particles, q is the density of water, and g is the acceleration of gravity. The Shields curve and the equation proposed by Brownlie et al. (1981) are interconvertible, see Eq. 4.11. That is, the Shields number can be expressed as both a function of particle Reynolds number and a function of dimensionless particle size.

Fig. 4.11 A transformation of Shields curve by Brownlie (1981), data from Vanoni (1965)

4.2 Incipient Motion of Bio-sediment

225

sc U2 q ¼ ðcs  cÞD ðqs  qÞgD U 2 D2 qv2 Re2 ¼ 2 ¼ v ðqs  qÞgD3 D3

Hc ¼

ð4:11Þ

Currently, many equations have been proposed for the incipient motion of noncohesive sediment, but the different criteria of incipient motion should be of special concern when applied. For example, Chu (1993) transformed the incipient criteria proposed by various investigators into the Shields number and found that the values range from 0.0231 to 0.0716.

4.2.1.2

Cohesive Sediment

For cohesive sediment, the condition for incipient motion is affected not only by the shielding effect of the laminar sub-layer but also by the effect of cohesion among fine particles. Thus, the incipient motion is not in the form of individual particles but rather the movement of clusters (Han and He 1997). The incipient velocity is another common expression for incipient motion. Dou (1960), Wuhan Institute of Hydraulic and Electric Engineering (WIHEE 1960), Tang (1963), and Sha (1965) have derived equations for incipient motion of various sediment sizes all considering the effects of cohesive force, as listed in Table 4.2. Here, a brief description on the consideration of cohesive force in Dou’s (1960) and Tang’s (1963) equations is presented. A layer of thin film water would cover the surface of sediment particles that are immersed in water, and thus, an interface forms when two particles contact each other, which results in a cohesive force on the molecular scale. The thin film of water is different from ordinary/free water first in terms of pressure transmission, i.e. the pressure transmits along a straight line, and no pressure appears in the perpendicular direction. This feature of the thin film of water requests an additional downward water pressure (cohesive force), FC, for calculation, see Eq. 4.16, which can be directly expressed as Eq. 4.17 if the positive pressure between particles is 0. According to the different conditions of incipient motion, Dou (1960) assumed that the positive pressure between particles is the effective gravity to derive the incipient velocity for sliding, and Tang (1963) assumed the positive pressure between particles to be 0 in the derivation of the incipient velocity for rolling. These two assumptions will be further applied in the following sections. FC ¼ qgðh þ ha ÞAi

ð4:16Þ

FC ¼ nD

ð4:17Þ

D

mi mi þ 1



3:2 cs cc gD þ




c0sM

c0s ai qD

10 1=2

r
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  5=3 þ 194D ðf cos h  sin hÞ 1520 D x4=3

i

 h m1

1=2  h 0:14
þh 17:6 cs cc D þ 0:000000605 10 D D0:72

Uc ¼ R1=5

Uc ¼

Sha (1965)



 ¼ cs cc 6:25 þ 41:6 hha þ 111 þ 740 hha hDa2d

Uc ¼

Uc2 gD

Formula

Dou (1960) WIHEE (1960) Tang (1963)

Author

(4.15)

(4.14)

(4.13)

(4.12)

Formula number



4:7ðh=DÞ0:06 Flume data Natural river 6 c0s is the dry bulk density of sediment deposit; c0sM is the maximum dry bulk density; and ai = 2.9  10−4 g/cm All lengths in m; x is the settling velocity of particles, f is the friction coefficient (=1.42D1/8), h is the inclination of riverbed mi ¼

ha is the atmospheric pressure measured by the height of water column; d is the thickness of water molecules (=3  10−8 cm); h is the water depth –

Remarks

Table 4.2 Equations of incipient velocity (Uc) considering the cohesion among sediment particles (Chien and Wan 1999, with permission from ASCE)

226 4 Bedload Transport of Bio-sediment

4.2 Incipient Motion of Bio-sediment

227

where h is the water depth; ha is the atmospheric pressure measured by the height of water column; Ai is the interface area between two particles; and n is the resisting moment per unit area resulting from the cohesion.

4.2.2

Incipient Motion of Bio-sediment

In recent years, the importance of biogenic sediment stabilization (mainly due to biofilms) has been increasingly noted (Andersen 2001; Andersen et al. 2005; Gerbersdorf et al. 2008; Stal 2003). Biofilm growth often forms a relatively smooth and stable sediment surface (Paterson 1989) and generates an additional binding force among particles (Righetti and Lucarelli 2007). These phenomena change the structure and morphology of exposed sediment particles leading to a higher incipient motion threshold, i.e. both the cohesion among particles and biofilm-induced adhesion must be overcome for incipient motion. The incipient shear stresses (or velocities) for sediment particles with and without biofilm growth are generally compared to estimate the extent to which biofilms affect the incipient motion of sediment (Cheng 2016). The influences of biofilms on sediment incipient motion have been mainly studied in marine areas through field data collection and observation (Grant and Gust 1987; Tolhurst et al. 2008), especially in the intertidal zone, and an enhancement of sediment stability has been mostly observed. Few studies have been done in freshwater systems, which mainly focused on the characteristics of the biofilm itself or the interaction between biofilms and flow (Battin et al. 2003; Besemer et al. 2007). Overall, knowledge on the biofilm effects mainly comes from correlation studies between the sedimentological and biological factors (de Brouwer et al. 2000). Biofilm growth can significantly enhance the biostabilization, with biofilm-infused bed sediment requiring more energy for erosion than original sediment (Fang et al. 2015). To establish a predictive equation of the incipient velocity of bio-sediment, the relation between biofilm properties and sediment particles on which biofilm grows must be considered, and the established theories should be utilized to calculate the adhesive forces among particles. In this sub-section, the conditions for incipient motion of bio-sediment are evaluated using a circulating flume, and then, the incipient velocity equations are further derived using dimensional analysis and force analysis for both sliding and rolling conditions in the next sub-section (Shang 2011; Fang et al. 2014).

4.2.2.1

Experimental Setup and Procedure

(1) Experimental setup The experiments on incipient motion for bio-sediment were done in the recirculating flume at Tsinghua University of 14 m long and 0.5 m wide, with a fixed bed

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4 Bedload Transport of Bio-sediment

Fig. 4.12 Plan view of a the experimental flume and b the testing area, and c side view of sediment recess (unit: m)

slope of 0.85‰, see Fig. 4.12a. Two sediment recesses that were 0.24 m long, 0.12 m wide, and 0.04 m deep (Fig. 4.12c), were set symmetrically along the centerline at x = 10.05 m from the entrance (Fig. 4.12b), to compare the different incipient motion processes for sediment with and without biofilms under the same flow condition. The discharge was controlled by a regulator and measured by an electromagnetic flow meter. Sediment collected from the Guanting Reservoir was used in these experiments, which is similar to the sediment of the rheological experiments in Sect. 4.1.2. The sediment was classified into two groups, i.e. finer than 0.05 mm (Sample 1#) and 0.05–0.1 mm (Sample 2#), with median diameters, D50, of 0.035 and 0.077 mm, respectively. Both the characteristic sizes with and without dispersing are listed in Table 4.3. According to the classification standard in Chien and Wan (1999), Sample 1# is characterized as silt, and Sample 2# is characterized as sand. The flocculation intensity, F1, of sediment samples usually is calculated using the equation of Liang and Zhang (1994), i.e.

Table 4.3 Characteristic particle sizes of the sediment samples for incipient motion (unit: lm) Cumulative frequency (%)

Sample 1# (finer than 0.05 mm) Dispersed Undispersed F1

Sample 2# (0.05–0.1 mm) Dispersed Undispersed

F1

10 30 50 70 90

7.8 15 35 56 82

6.7 57 77 97 133

2.51 1.06 1.01 1.00 1.00

10 29 45 59 82

1.31 1.86 1.29 1.06 1.00

16.9 60 78 97 133

4.2 Incipient Motion of Bio-sediment

229

F1 ¼

Df D

ð4:18Þ

where Df is the characteristic particle size of flocs and D is the corresponding value in the dispersion state. As listed in Table 4.3, the median diameters are 35 and 45 lm for Sample 1# with and without dispersing, respectively, which corresponds to a flocculation intensity of 1.29, indicating a more obvious flocculation than for Sample 2# (F1 = 1.01). Water from the lotus pond of Tsinghua University was used for biofilm cultivation with additional nutrients (i.e. bio-sediment), for more details refer to Sect. 2.1.2.1. Meanwhile, sediment without biofilm also was prepared through immersing in deionized water for the same period (i.e. original sediment), to clarify the biofilm effects on the incipient motion of sediment. The procedure for biofilm cultivation is as follows. First, sediment samples were mixed with water and loaded into the sediment recesses (Fig. 4.12c) to stand for one day. The surface was scraped after the sediment sample is basically dense and stable. Then, the sediment recesses were separately placed into two tanks for independent cultivation with deionized water or experimental/nutrient solution. In each tank, eight samples were immersed for each particle size group and cultivated for 1–8 weeks, resulting in bio-sediment with biofilm growth of 1–8 weeks for the flume experiments of incipient motion. The water temperature was 15 ± 1 °C, and the laboratory was kept at a relatively uniform temperature that is suitable for microbial activities. Similarly, the experimental water in the tanks was refreshed every day. (2) Experimental procedure Biofilm growth and its strength are dynamic processes that vary with time. Thus, the incipient velocity was measured once per week to estimate its temporal variation. Each week, two recesses of sediment samples of the same size group, which were separately immersed in the deionized water and the nutrient solution, were placed into the flume to compare the incipient motion processes of original sediment and bio-sediment. Two methods have been used to establish a threshold for the incipient motion of sediment (Dey 1999), which are based on the sediment flux (Shields 1936) and bed sediment motion (Kramer 1935). Here, the critical threshold for incipient motion was defined as occurring when “weak transport” commenced (sparse sediment motion), i.e. when 20 or more particles were simultaneously in motion across the bed surface. The criteria were the same for sediment with and without biofilm. After the sediment preparation, clean water was added to the flume. Given the flume width of 0.5 m, the water depth was set as approximately 0.1 m to achieve a width–depth ratio of about 5, thus guaranteeing a two-dimensional steady flow. Water-level point gauges were used to measure the water depth. The Reynolds number, Re, remained above 10,000, and the Froude number, Fr, was consistently less than 1. During each experiment, the flow discharge was slowly increased until reaching the incipient velocity. A propeller velocity meter (LGY-II, Nanjing Hydraulic Research Institute, Nanjing, China) was used to measure the mean

230

4 Bedload Transport of Bio-sediment

velocity of the cross sections, with the probe fixed at a relative water depth of 0.6. Because the flow was fully turbulent, the mean velocity is a reliable parameter to reflect the condition of incipient motion. The spatiotemporal heterogeneity of biofilms and their mechanical properties, as well as the complex relation between the biofilm strength and the sediment resistance to erosion, are all important factors affecting the incipient motion of bio-sediment. It is worth noting that there is a layer of biofilm covering the bio-sediment bed surface. As the flow velocity increases, the surficial biofilm is destroyed first, and then, the bio-sediment particles are exposed to the flow. Thus, the destruction of the surficial biofilm is a prerequisite for incipient motion of bio-sediment, but not the indicator. Considering the complex structure of bio-sediment, the flow discharge should be increased slowly, especially after the surficial biofilm is detached from the bed surface, to eliminate the interference of the covering layer of biofilm on the observation of sediment incipient motion.

4.2.2.2

Description of Incipient Motion

For sediment particles immersed in the nutrient solution, the cultivated biofilm gradually covered the surface, and the surface color changed as follows: yellowish brown ! dark brown ! finally black brown (after six weeks of cultivation, see Fig. 4.13a), which is similar to the observation in Sect. 2.1.2.2 (i.e. soil-yellow ! much deeper ! gray black). The protozoa and metazoa were visible in the nutrient solution after two weeks, mostly copepods and flagellates, which are the main consumers of microbes and organic matter. These organisms form an integrated ecosystem together with bacteria and algae. In contrast, sediment samples immersed in the deionized water were almost unchanged, except that the color gradually deepened into gray after four weeks. This color change may be the result of redox reactions caused by a non-sterile environment, which is consistent with the phenomena in natural aquatic environments. The development of biofilms stabilizes sediment against entrainment. Macroscopically, biofilms cover the sediment bed surface like a blanket, called biofilm mats. A biofilm mat should first be eroded by the flow, thus, providing a certain armoring effect for the sediment particles underneath. After the destruction of the surficial biofilm, some biofilm still exists among the sediment particles, which presents as a filamentous biofilm network. Thus, sediment particles can be bound together by the biofilm leading to a higher entrainment threshold. A filamentous biofilm network is obvious and intensive for the first five weeks and then gradually decreases due to the maturation and aging of the biofilm. Evidently, as the biofilm grows thicker, the strength of the lower biofilm layer weakens as the microbes near the sediment surface are unable to obtain adequate nutrients and convert into inactive substances. Under the same flow condition, the erosion status for sediment with and without biofilms are significantly different. The incipient velocity of bio-sediment is larger than that of the original sediment, i.e. it is much more difficult for bio-sediment to

4.2 Incipient Motion of Bio-sediment

231

Sediment with biofilm

Sediment without biofilm (a)

Sediment with biofilm

Sediment without biofilm (b)

Fig. 4.13 Sediment samples with and without biofilm a before and b after the experiment of incipient motion

be eroded. The bio-sediment surface is still relatively smooth after a flume experiment, while there are clear gullies and severe erosion on the original sediment surface, as shown in Fig. 4.13b. Meanwhile, it was observed that the original sediment starts to move earlier than the bio-sediment. When the bio-sediment starts to move at a higher flow velocity, however, the original sediment particles have already moved massively, i.e. the surface has been scoured by the flow along with the phenomenon of sediment coarsening on the bed surface.

232

4.2.2.3

4 Bedload Transport of Bio-sediment

Variation of Incipient Velocity

The variation of the incipient velocity for the original sediment, which changes slightly with time, is shown in Fig. 4.14 and listed in Table 4.4. For sediment groups of finer than 0.05 mm and 0.05–0.10 mm, the average incipient mean velocity (1–8 weeks) was 0.240 and 0.185 m/s, respectively, corresponding to a shear velocity of 0.012 and 0.009 m/s. These measured mean velocities were in good agreement with the values calculated using Tang’s (1963) equation (i.e. 0.25 and 0.20 m/s, respectively). Table 4.4 also lists the measured results of incipient motion for bio-sediment, indicating that biofilms contributed to the sediment stability and led to a higher

Fig. 4.14 Temporal variation of incipient velocity for the original sediment and bio-sediment (Fang et al. 2014)

Table 4.4 Incipient motion criteria for (a) the original sediment and (b) bio-sediment (Fang et al. 2014) Sediment sample

Time (week)

(a) Original sediment 500, the Shields number of the modified Shields curve becomes almost constant at about 0.045, which is quite close to the value of 0.041 calculated by the equation suggested by Tang (1963). As in the foregoing analysis, the adhesive forces are affected by the substrate on which the biofilm grows. Comparing the curve only considering cohesion and that considering both cohesion and adhesion, it can be further concluded that the adhesion effect can be important in the region of 0.2 < Re* < 1.0, while the gravity and cohesion dominate for a larger Re* and a smaller Re*, respectively.

4.2.3.3

Discussion on Incipient Motion

To thoroughly study the applicability of incipient velocity equations, it is necessary to systematically analyze the relevant factors. The incipient motion conditions for sediment are a function of the characteristics of sediment particles (e.g. density, size, and shape), fluid (e.g. density and viscosity), and flow conditions (e.g. mean velocity and shear stress). The gravity force, FG, cohesive force, FC, and adhesive force, FA, are responsible for preventing particle movement, while the forces generated by the flow promote movement, i.e. FG ¼ ðqs  qÞa3 gD3 / D3 FC ¼ nD / D FA ¼ CA  D2 / Db2 þ 2 The roles of these three resistance forces change with particle size, as shown in Fig. 4.23a, where the adhesive force corresponds to a biofilm growth of 4 weeks. The slopes of these three curves indicate that: gravity > adhesion > cohesion, i.e.

4.2 Incipient Motion of Bio-sediment

247

Fig. 4.23 a Theoretical effects of particle size on the resistance forces calculated using Eqs. 4.17, 4.19, and 4.21 (Fang et al. 2014); and b variations of the contributions of these three resistance forces with the particle size

the gravity changes the fastest as the particle size changes. Meanwhile, the variations of their contributions in resisting incipient motion with the particle size are shown in Fig. 4.23b. For the particles coarser than 0.2 mm, the gravity force gradually takes the dominant role in the resistance against particle movement, and it can be several orders of magnitude larger than the cohesive and adhesive forces. For the particles finer than 0.01 mm, however, the gravity force can be ignored, and the cohesive force plays the most important role. If 0.01 mm < D < 0.2 mm, the adhesive and cohesive forces occupy the dominant position. These variations are consistent with the observations in Figs. 4.17 and 4.21. The drag force and lift force generated by water flow can be expressed as functions of shear stress, which changes with the average velocity and sediment substrate. Figure 4.24 shows the calculated shear stress for a range of particle sizes under different average velocities using the logarithmic velocity distribution formula (see Eq. 4.35). The conditions for calculation are: rectangular section, no bedforms, and width of water surface = 50 cm, water depth = 10 cm, and q = 1.0 g/cm3. Because of the viscous sub-layer, the shear stress exerted on the bed

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4 Bedload Transport of Bio-sediment

Fig. 4.24 Calculated shear stress for different particle sizes under different mean velocities using Eq. 4.35 (U represents the mean velocity in the cross section) (Fang et al. 2014)

does not change significantly until the particles exceed approximately 0.3 mm. For the same mean velocity, the shear stress increases with the increasing roughness when the particles protrude into the turbulent region. This is the reason why the smooth surface of matted biofilm can reduce the forces produced by water flow and provide an initial protection for sediment before the failure of biofilm mats. After the failure of biofilm mats, particles with biofilm adhesion continue the resistance. Thus, the presence of biofilms enhances the stability of the sediment bed due to several reasons. First, biofilm covers the sediment bed as a biofilm mat (reducing the shear stress), which provides a certain armoring effect for the underlying sediment particles. Meanwhile, biofilms in the deep sediment layer provide as a filamentous biofilm network which fills the pores and bonds sediment particles together (adhesion), and further enhancing sediment stability after the surficial biofilm is destroyed. Table 4.6 lists the change of the incipient shear stress, sc, resulting from biofilms from the literature. The incipient shear stress of bio-sediment can be up to about 20 times as large as that of the original sediment (without biofilm) in marine areas, while it is about three times higher in freshwater pffiffiffiffiffiffiffiffiffi environments. According to the relation of Uc ¼ sc =q, the critical shear velocity of bio-sediment is, thus, about 4.7–1.7 times and 1.7 times that of the original sediment in marine and freshwater environments, respectively.

4.3

Bedload Transport of Bio-sediment

Bed sediment is potentially subjected to transport and redistribution after the incipient motion, and bedload and suspended load are the two main components of sediment transport. For bedload transport, there are usually three modes of particle motion, i.e. sliding, rolling, and saltating. van Rijn (1984a) suggested a simple expression for bedload concentration of noncohesive sediment as a function of flow

0.01–0.08

0.120, 0.316

0.257 (noncohesive) 0.007 (cohesive) –

Prince Edward Island, Canada Venice Lagoon

Intertidal zone

Tampa Bay, Florida Eaton Estuary, Scotland, England Texel, Netherlands Bristol, England

0.189

Cohesive sediment

Sampling site

Original sediment size (mm)

Existing information Surface layer Surface layer (10 mm)

–

Mussel aquaculture farm Field sampling and annular flume

Field sampling

Surface layer Surface layer (2 mm) Surface layer

Object of study

Field sampling and flume experiments Cultured in seawater

Sample

1.53 times 2.06 times 1.15 times 1.15 times 1.74 times in summer and 1.03 times in winter (average values)

2.44 times

–

– Filamentous cyanobacteria Micro-aquatic plants Zosteraceae U. rigida Shellfish remains

–

2.9 times

21.7 times and 9.6 times

10–15 times that of original sediment 7 times

Incipient shear stress sc

–

Diatom and cyanobacteria Microcoleus vaginatus Nitzschia

Diatom

Purple sulfur bacteria

Microbial species

Table 4.6 Relevant studies of incipient motion under the influence of biofilm

(continued)

Walker and Grant (2009) Amos et al. (2004)

Stal (2003)

Yallop et al. (1994)

Grant and Gust (1987) Tolhurst et al. (2008)

References

4.3 Bedload Transport of Bio-sediment 249

Sampling site

Lauffen Reservoir, Germany Glass bead

Seven lakes

Oldman River, Canada

Original sediment size (mm)