Particle Size: Measurement, Interpretation, and Application

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Part icle Size: M e a su r e m e n t ,

In t e r p r e t a t i o n ,

and

Ap p lica t io n

Particle Size: M e a su r e m e n t , In t e r p r e t a t io n , a n d A p p lica t io n Riyad R. Irani and Clayt on F. Callis M o n sa n t o

John

Ch e m ica l

W ile y

&

Com p an y,

So n s,

In c. ,

St .

New

Lo u is,

York

M i sso u r i

•

Lon don

C opyright © 1963 by John W iley & Sons, Inc. All R ights R eserved. T his book or any p a rt thereof m ust n o t be repro­ duced in any form w ithout the w ritten perm ission of the publisher. L ib rary of Congress C atalog C ard N um ber: 63-16018 P rin ted in the U nited S tates of A m erica

Con t e n t s

1

A p p lic a t io n s of

P a r t ic le

Si z e

D i st r i b u t i o n

M e a su r e m e n t s

1

.

Com m e r ci al Ap p l i c at i o n s Inf l u enced b y Par t i cl e Si ze

2

.

Ch e m i cal a n d Physi cal Pr oper t i es Af f ect ed b y Par t i cl e Si ze

9

2

D e f in it ion s

3

Me thods of

Data

D i st r i b u t i o n

F u n ct io n s A p p l i c a b l e

4

17

P r e se n t a t i o n

25

to

Pa r t ic le

Si z e

D i st r i ­

b u t io n s

34

.

Bi n om i al Di st r i b ut i on Law

34

.

The Ga u ssi a n ( No r m al ) Di st r i b ut i on Law

36

.

The Lo g- No r m a l Di st r i b ut i on Law a n d It s Mo d i f i c at i o n s

39

.

Ot h e r Di st r i b ut i on Law s

55

Se d i m e n t a t i o n

58

5

T e ch n iq u e s

.

Rat es of Se d i m en t at i on

58

.

Pr e p ar at i on of Su sp e n si o n f or Se d i m en t at i on

62

.

Gr av i t at i o n al Te ch n i q ue s Base d on Ch a n ge i n Con ce n t r at i on at a Gi v e n Level

.

Gr av i t at i o n al Cu m u l at i ve Te ch n i q ue s

69 76

vii

v iii

.

C o n te n ts Ce n t r i f u gal Techni q ues Base d on Ch a n ge i n Con ce n t r at i on at a Gi v e n Dep t h

83

.

Ce n t r i f u gal Cu m u l at i ve Techni q ues

84

.

Par t i cl e Cl assi f i cat i on

88

6

M i c r o sc o p y

93

7

Si e v i n g

107

8

M i sc e l l a n e o u s T e c h n i q u e s

123

.

A v e r a ge Si ze f r om Per m eam et r y

123

.

A v e r a ge Par t i cl e Si ze f r om Ad so r p t i o n Me t h o d s

128

.

Ch a n ge in El ect r ol yt i c Resist ivit y ( Cou l t er Count er )

134

.

Ca sc a d e Im p act or f or Ai r - b o r n e Par t i cl es

135

.

Li ght Scat t e r i n g as a Me a su r e of Par t i cl e Si ze

138

9

C o m p a r i so n

of

Pa r t ic le

Si z e

D i st r i b u t i o n

Data

from

V a r io u s M e t h o d s

10

Pr oce d u r e

for

C h o o si n g

142

the

Ap p r o p r ia t e

Me thod

of

P a r t i c l e Si z e M e a su r e m e n t

154

In d e x

163

Pre face

I t seems clear to us th a t scientific progress depends on th e develop­ m en t of b e tte r tools and b e tte r m ethods for m easuring properties of m aterials. T h is general statem e n t certain ly applies to th e very im ­ p o rta n t p ro p e rty of finely divided m a tte r, th e p article size distribution. T h ere are m any know n exam ples of th e dependence of th e properties of m aterials on th e ir p article size ch aracteristics. T h is is am plified in C h a p te r 1, where a num ber of com m on applicatio n s of p article size d istrib u tio n m easurem ents are described. H av in g gone through the process of equipping a lab o ra to ry w ith all th e necessary tools for m easuring p article size, it becam e clear to us th a t no single reference w ork existed which would give an a n a ly s t a sim ple choice of th e preferred technique for p article size m easurem ent of a specific m aterial. T h e p resent book was w ritten to fulfill th is need, as well as to aid in the in te rp re ta tio n of the results. T h e su b ject m a tte r is inclusive and sim plified to allow the novice to become fam iliar w ith th e techniques, in te rp re ta tio n , and u tility of p article sizing w ithin a reasonable am o u n t of tim e, y e t sim plification is n o t m ade a t th e expense of a rigorous tre a tm e n t. T h e order of th e chapters is som ew hat a rb itra ry . F o r those w anting to choose rap id ly th e a p p ro p ria te m ethod of p article size m easurem ent, C h ap ters 10, 5, 6 , 7, and 8 should be read in th a t order. T hose in v esti­ g ato rs know ledgeable in p artic le size technology, b u t w anting to verify th a t th ey are proceeding correctly, should find the flow sheets in v

vi

P r e fa c e

C h a p te r 10 and th e com parison of d a ta from v arious techniques in C h a p te r 9 very useful. C h ap ters 2 and 3 on definitions and m ethods of d a ta p resen tatio n are of an in tro d u cto ry n a tu re . R eaders u n fa m ilia r w ith th e su b ject m a tte r should stu d y these ch ap ters first. C h a p te r 4, on th e m ath em atical tre a tm e n t of p artic le size d istrib u tio n , would be of in te re st to those w ishing to delve deeply into th e subject. R. R. I r a n i C . F. C a l l i s S t. L o u is, M o .

March, 1963

Part icle Size: M e a su r e m e n t ,

In t e r p r e t a t i o n ,

and

Ap p lica t io n

chapt er 1

A p p lic a t io n s o f p a r t icle d i st r i b u t i o n

si z e

m e a su r e m e n t s

T he uses for m aterials in a finely divided form are astonishingly common and diverse. A round th e home, such things as flour, salt, sugar, coffee, and face pow der im m ediately come to m ind. O ther household products such as tooth p aste, detergents, polishes, insecticides, drugs, and abrasives also contain a finely divided m aterial as an essential com ponent. M an y ind u strial operations either handle or consume powders or produce a pow der as th e final product. T he cem ent, glass, ccram ic, p ain t, coal, fertilizer, food, paper, drug, dye, cosmetic, and even o ther industries perhaps, should be m entioned. M an y n a tu ra l phenom ena resu lt from th e properties of m a tte r in a finely divided state. One of th e m ost basic physical properties common to all these finely divided substances is th e ir particle size d istribution, th a t is, th e fre­ quency of occurrence of particles of every size present. T he c h arac te r­ istics of a single particle are n o t usually of practical in terest; rath er, the m ean characteristics of a large num ber of particles is the thing th a t can be studied statistically . I t should be em phasized, however, th a t the knowledge of th e size ch aracteristics is of no value unless adequate cor­ relation has been established w ith functional properties of specific in­ terest or w ith processing v ariables th a t can be controlled. M an y investigations of the significance of particle size d a ta are re­ ported in the literatu re. Some of these reports are reviewed in this introductory ch ap ter in order to point out m ore specifically, w ith de­ tailed examples, the im portance of this basic physical property in the 1

2

/

P a r tic le S iz e : M e a s u r e m e n t, I n te r p r e ta tio n , a n d A p p lic a tio n

p re sen t-d ay technology of m an y com m on m aterials. N o a tte m p t h a s been m ade to p resen t an all-com prehensive survey of these a p p lic a ­ tions; in fact, some en tire fields of investigation have been o m itte d , and, u n d e rstan d a b ly , th e in terests of th e au th o rs are em phasized. T h e experiences described in th is c h ap te r should ad eq u ately d e m o n strate th a t when problem s arise in th e handling and use of finely d iv id ed m aterials, one of th e first things th a t should be investig ated is th e p article size d istrib u tio n , because m ore often th a n n o t th is is a co n ­ trolling factor. T h e c h ap te r is divided into tw o p a rts. T h e first p a r t deals w ith applicatio n s of com m ercial interest, w hereas th e second p a rt describes properties of p a rtic u la te m a tte r th a t are affected by p article size. C O M M E R C IA L

Se g r e g a t i o n

of

A P P L IC A T IO N S

Pow de re d

IN F L U EN C ED

BY

P A RT ICL E

SI Z E

M ix t u r e s

U niform m ixtures of chem ically different pow ders will be stab le as regards segregation only if the pow ders are of sim ilar p artic le size d is­ trib u tio n s. T h is is a significant p ra c tica l problem in th e fertilizer in ­ d u stry , w here th e “ b len d er” is required by law in m ost areas n o t only to deliver th e q u a n tity of each p la n t food co n stitu en t claim ed, b u t also to g u aran tee th e lo t to th e purch aser as a uniform m ixture. T h e p ri­ m a ry m echanism of segregation in bulk fertilizers involves th e differing tendencies of p articles of v ary in g size and shape to roll down an in ­ cline. Segregation occurs as th e blended fertilizer is piled in to a tru c k or bin if m a te ria ls of w idely v ary in g p article sizes are present. F lo w

Co n d it io n in g

D ra m a tic changes in th e physical properties of poor-flow ing pow ­ dered an d g ra n u la r m a te ria ls can often be effected by th e ad d itio n of sm all am ounts of finely divided pow ders. T h e a d d itiv e is generally referred to as a flow -conditioning agent. An optim um conditioner level exists ( 1) for each co n d itio n er-m aterial system beyond which flow m ay no t change significantly or m ay become poorer. F lo w ab ility a t th is level m a y be q u ite different for different conditioners. E ffective conditioning agents m u st adhere strongly to th e su rface of the m a te ria l being conditioned and are m uch sm aller in size. M icro ­ scopic exam inations ( 2 ,3 ) of conditioned m aterial show th a t p a rtic le s of th e m a te ria l are uniform ly coated w ith p articles of th e conditioner. F igure 1-1 d em o n strates th e covering pow er of diatom aceous e a rth a t th e 2 % level in a m ixed fertilizer w ith an average p article size of 150 m icrons. T h e im p o rtan ce of th e rela tiv e p artic le sizes of co n d itio n er

A p p lic a tio n s o f V a rtic le S iz e D is tr ib u tio n M e a s u r e m e n ts

/

3

F IG . 1-1, 15 0-m icron p a rticles o f m ixed fe rtilizer b efo re (le f t ) and a fte r (rig h t) a d d itio n of 2% d ia to m a ce o u s ea rth .

and m aterial is obvious from calculations of the num ber of particles of conditioner per particle of m aterial. F o r exam ple, w ith 1-m icron con­ d itioner and 20-m icron m aterial, this num ber is eighty. F o r 2 -micron conditioner and th e sam e m aterial, th e num ber drops to ten. T he o p ti­ m um concentration of flow conditioner is explainable ( 1) in term s of satu ratio n of th e m aterial being conditioned, followed by form ation of flocks of conditioner p articles th a t re ta rd over-all flow. T he flow properties of a pow der can also be im proved in m an y eases by m ixing in coarser, free-flowing m aterials. T he am ount of coarser m aterial needed to im prove flow is generally exceedingly high, up to 10007» the original powder. In these m ixtures, th e fines of the m a­ terial being conditioned adhere to the surface of the large particles of flow-im proving agent (4). I t is interesting to note th a t this effect has been used (1 ,5 ) as a basis of flow tests for m easuring the flow ability of powders. Ca k e

In h ib it io n

T he m echanism of caking has been fairly well established because of the considerable atten tio n devoted to th e problem by the fertilizer, salt, sugar and related industries (6-13). T he presence of m oisture, w hether in the sam ple or artificially introduced, is necessary for cak ­ ing to tak e place. T he form ation of a sa tu ra te d solution on th e particle

4

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P a r tic le S iz e : M e a s u r e m e n t, I n te r p r e ta tio n , a n d A p p lic a tio n

Nu m b e r aver age part icle si ze of t r i cal ci um phosphat e, m i c r on s

F I G . 1-2. C a k in g o f m ille d sa lt w h en m ix ed w ith 1% tr ic a lciu m p h o sp h a te o f d iffe ren t p a rticle s iz e . R e p r o ­ d u c ed from In d . E n g . C h e m ., 51, 1288 (1 9 5 9 ).

surfaces followed by ev ap o ratio n of m oisture from th e solution leaves a residue th a t bridges and binds together th e original particles. T h e general considerations discussed for th e flow -conditioning agents also ap p ly to an tic ak in g agents. T h e p artic le sizes of both th e m a te ria l and th e an tic ak in g ag en t are im p o rtan t. H a rd e sty and K u m ag ai (7) have shown th a t th e m ore finely divided a m ixed fertilizer th e m ore severe th e caking, w hether an an tic ak in g ag en t is p resen t or not. T h ey also re p o rt th a t larg e-p article conditioners are relativ ely ineffective. Ira n i, C allis, and L iu (1) m easured th e caking of sam ples of m illed s a lt m ixed w ith equal w eights of tricalciu m ph o sp h ate sam ples of different average p article sizes b u t ap p ro x im ately eq u ally broad size distrib u tio n s. T h e y found th a t th e finer th e p article size of th e condi­ tioner, th e less severe w as th e caking of th e salt. T h is correlation is reproduced in Fig. 1-2. O ther studies on fertilizers (12) have show n th a t th e presence of a conditioner does n o t p rev en t form ation of c ry stallite shells on p artic le surfaces b u t, in m ost cases, these shells a re contained beneath th e conditioner coating. Pr op e r t ie s o f

Ka o lin it e

R eg u lar v a ria tio n in specific surface area, exchange cap acity , h e a t of w etting, lin ear d ry in g shrinkage, and p erm eab ility tim e of w a te r leaching w ith p article size for k ao lin ite is rep o rted by H a rm a n a n d F rau lin i (14). N um erical values of these pro p erties for v arious size fractions are reported in T a b le 1-1.

Applications of Particle Size Distribution Measurements

/

5

T ABLE 1 -1 Pr o p e r t i e s o f Ka o l i n i t e ( 1 4 ) o f Dif f e r e n t Pa r t i cle Si z e s

Size (microns)

Specific Surface (sq. m /gm )

0.05-0.10 0.10-0.25 0.25-0.5 0.5-1 2-4 5-10 10-20

30.2 12.9 6.6 3.0 0.7 0.3 0.15

D u st

Base Perm eability Exchange Tim e to Leach C apacity through Layer, (m illiequiv./ 10 ml of W ater 100 gm) (sec) 9.50 5.43 3.88 3.76 3.58 2.60 2.40

750.0 474.0 452.0 200.0 15.0 4.4 2.7

H eat of W etting (cal/gm ) —

1.89 1.42 1.38 1.15 0.99 0.95

Linear D rying Shrinkage (% dry length) —

3.70 2.69 2.35 2.19 1.89 1.45

E x p l o si o n s

F in e p articles of v arious substances, w hen suspended in air, are explosive u n d er certain conditions. D u sts v a ry w idely in th e ir in ­ flam m ability because of differences in com position, co ncentration, and p article size (15). An increase in th e in flam m ability of a given d u st w ith increase in fineness has been observed from m easurem ents of pressures generated on explosion (16) an d from changes in inflam m a­ b ility on th e ad d itio n of know n percentages of in e rt d u st such as fu lle r’s e arth (17). Su r f a c e

C o v e r a ge

of

P i gm e n t s

P igm ents are exam ined ro u tin ely for th e presence of large particles o r aggregates w hich m ay adversely affect tex tu re, gloss, and opac­ ity (18). M o st of th e w ell-produced m icronized pigm ents co n tain no p articles over 2 -3 m icrons in size (19). T h e op acity of a p a in t is q u a li­ ta tiv e ly found to be inversely p ro p o rtio n al to th e p article size of the pigm ent w hen th e p articles are larg er th a n th e w ave length of lig h t (20). P a rtic le s sm aller th a n th e w avelength of lig h t s c a tte r ra th e r th a n reflect th e light, w ith a possible resu ltin g decrease in o p acity . A m inim um of w hite reflectance is desirable for th e densest b la ck pigm ents, and therefore th e tendency is to reduce th e particles of black pigm ents to sizes sm aller th a n th e w avelength of light. A decrease in th e p article size of calcium carb o n ate extender pig­ m en ts has been found to im prove th e surface coverage, also know n as hid in g power, and gloss of a p a in t film ( 21), p resum ably from im ­

6

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P a rtic le S iz e : M e a s u r e m e n t, I n te r p r e ta tio n , a n d A p p lic a tio n

provem ent in th e dispersion of the hiding pigm ent by th e very fine calcuim carbonate. T he shape of the particles of a pigm ent is a p p aren tly of considerable significance in th e d u ra b ility of p a in t films. P a in ts prepared from acicu lar-ty p e zinc-oxide fillers have been shown to w eather b e tte r th an those com pounded from other form s of the oxide of sim ilar p u rity (22). T he significance of surface coverage in flow conditioning of solids has been m entioned earlier. O ther exam ples w here surface coverage is im p o rtan t include face powder, chalk, carbon for au to tires, and fillers for paper. A b r a si v e n e ss o f

Dental

P o l i sh i n g

A ge n t s

D entifrices contain several ingredients, one of which is an abrasive solid whose function is rem oving debris and stains from the teeth and polishing th e too th surface (23). T he abrasive used in tooth powders should be of such a particle size th a t d u st will not be generated on handling, and y e t sm all enough not to be g ritty in th e m outh. Studies of th e influence of particle size of powders on th e ir abrasiveness have been reported for calcium carbonate (24) and dicalcium phosphate (25). T he abrasiveness of calcium carbonate pow ders w as found to increase regularly w ith the respective w eight average particle diam e­ ters (24). E pstein and T a in te r (25) also concluded th a t th e particle size of a pow der is a reliable indication of its abrasiveness and suggest the use of slopes of curves relating m edian particle sizes to determ ined abrasiveness for com paring the abrasive power of different m aterials. According to this criterion, precipitated calcium carbonate is about six tim es as abrasive as dicalcium phosphate. T he abrasive ch arac­ teristics, however, are m arkedly influenced by other factors such as shape of particles, surface roughness differences, and th e presence of im purities in the p reparation. E m pirical correlations of abrasiveness and particle size m ay v a ry for different m aterials and for different p rep aratio n s of the sam e chemical. A t m o sp h e r i c

Co n t a m in a t io n

P a rticle size studies of the n atu re of the p a rtic u la te m a tte r in smog­ laden city atm ospheres have shown th a t the m aterial responsible for m uch of the decrease of visibility consists of particles having diam eters of ab o u t the w avelength of light (26). In the C ity of Los Angeles, this m aterial consists largely of hygroscopic droplets. T he hum an nose filters o u t alm ost all particles over 10 m icrons in size and ab o u t 95% of all particles g reater th an 5 m icrons from dust-

A p p lic a tio n s o f P a rtic le S ize D is tr ib u tio n M e a s u r e m e n ts

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7

polluted a ir (27). Silica p articles ab o u t 0.5 m icron in size seem to be p articu larly active in producing silicosis. P articles below 0.1 m icron m ay be too sm all to be retained by the lungs (28), and particles below 5 m icrons in size can pass from the lungs to th e blood and m ay reach th e lym phatic system . These findings are of extrem e im portance, of course, in the design of filters to rem ove the particles from polluted a ir and prevent physiological dam age. D ustiness of a pow dered m aterial, a m ajo r nuisance in bulk handling and a source of a ir contam ination, cannot be predicted solely on the basis of particle size inform ation (29). A very im p o rtan t factor is the “stickiness” of the pow der or how well th e particles adhere to one another. W ith m aterials of broad size distributions, th e very fine p a r­ ticles m ay coat the larger particles and hence not show up as d u st (see flow conditioning). A ndreasen et al. (29) state th a t for a given m aterial rem oval of fines below 10 m icrons lowers the d u stability. Be h a v io r

of

D r u gs

T he p article sizes of drugs such as penicillin and streptom ycin are rigidly controlled during m anufacture (30). A sm all particle size allows more rapid resuspension into th e m edium following separation on storage and perm its th e use of sm all needles for injection. A lower lim it, however, is imposed when local poisoning results from a toorap id rate of dissolution into the lym phatic fluids. Ef f i c ie n c y

of

Bi o c i d e s

Sm ith and Goodhue (31) review ed the subject of the relation of particle size to efficiency of insecticides and concluded th a t toxicity tests show the sm aller particles of solid insecticides to be, in general, the m ore effective. N o such clear generalizations could be draw n for oil emulsions. M etcalf and Hess (32) found in airplane dusting of P aris green th a t the effectiveness was g reatly reduced if the particle size was so sm all th a t the d u st d rifted aw ay from th e tre a tm e n t area. Loss in toxicity was not evident in increasing from 10- to 20- up to 50-micron m aterial, and a considerable im provem ent in the am ount of d u st reach ­ ing the desired area was achieved w ith th e large particles. H euberger and H orsfall (33) report th a t th e fungicidal and protec­ tive values of cuprous oxides v a ry inversely w ith the particle size. Uptake

of

N u t r ie n t s b y

Pla n t s

T he particle size of phosphate rock has been shown to be a significant variable in the yield and phosphorus u p tak e of a lfalfa and buckw heat p lan ts (34). R esults on yields of alfa lfa w ith varying treatm en ts with

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P a rtic le S iz e : M e a s u r e m e n t, I n te r p r e ta tio n , a n d A p p lic a tio n T ABLE 1 - 2 Ef f e ct o f Fin e n e ss o f G r i n d i n g o f Ph o sp h a t e Rock on Y i e l d s o f A l f a l f a ( 3 4 )

Yield in Grams * for Phosphate Rock Added

Crop Number

Elapsed Time (days)

Control, \TA JNO Phosphate Rock Added

-1 0 0 + 150 Mesh

-1 5 0 + 325 Mesh

-1 0 0 Mesh

-3 2 5 Mesh

1 2 3 4 5

61 24 22 32 72

34 35 38 35 29

65 50 55 42 72

68 54 58 44 75

75 56 60 48 82

78 59 62 49 86

° Each mesh size represents the accumulated averages of six sources of phos­ phate rock.

fractions of the sam e phosphate rock are reproduced in T ab le 1-2. Com plete distribution d a ta on th e - 1 0 0 - and -3 2 5 -m e sh fractions could possibly explain the sim ilarity of response of these two fractions. T he fineness of the rock, however, was no t as im p o rtan t as its source in determ ining its agronom ic effectiveness. Se t t i n g T i m e

of

Ce m e n t

As pointed o u t earlier, chem ical reactiv ity in general increases with decreasing particle size because of the g reater surface available per u n it w eight in finer m aterial. T he decrease in th e tim e required for concrete to set w ith increasing fineness of th e particles has been cited as a good exam ple of such an application of particle size inform ation. Speed of construction and strength of the concrete are favored by fine m aterial, b u t a compromise level is used to give adequate w orking tim e, a desirable ra te of h e at evolution, and a m inim um of shrinking and cracking. Q u a lit y

of

Ba k e d

Goods

P a rticle size is one of the principal features discrim inating flours th a t are suitable for cake m aking from those th a t will form a good bread dough (35). In addition, com m ercial flours m ust have a certain balance of protein and starch. Flours from different sources v a ry in th eir protein content, and th e p ro tein -to -starch ra tio in a given flour

A p p lic a tio n s o f P a r tic le S iz e D is tr ib u tio n M e a s u r e m e n ts

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9

varies w ith th e size of th e particle. G racza (36) sep arated flour sam ples by a ir e lu tria tio n into tw o fractions of v ary in g size d istrib u ­ tions an d correlated th e com position of th e fractions w ith th e sh a rp ­ ness of sep aratio n betw een th e d istrib u tio n curves. Below a value of 32 m icrons, th e finer fractio n s were rich er in p rotein th a n the coarse fractio n s; w hereas above th is value th e reverse was found. T hus, G racza shows th a t it is possible to achieve a uniform level of p rotein through p roper blending of the different size fractions.

C H E M IC A L

AND

A F F ECT ED

B u l k i n e ss a n d

P H Y SI C A L BY

P RO P ERT IES

P A RT ICL E

SI Z E

Pa ck in g

B ulkiness of a pow der, defined as th e reciprocal of th e a p p a re n t den sity , p ( l — ^ ), w here p is tru e den sity and f th e void fraction, has been found to increase w ith decreasing p article size (37). Q u a n tita tiv e relationships are given by R oller (38) for a n h y d rite, gypsum , P o rtla n d cem ent, an d chrom e yellow pow ders. F rom th e results shown in Fig. 1-3, th e concept of a critical size, above which bulkiness is co n sta n t w ith size, w as developed. T h e critical size ranges from 14 to 29 m icrons for these powders. M easu rem en t of b u lk d ensity und er specified conditions has been described as an em pirical m eans of determ ining average p a rtic le size (3 9 ). T h e b u lk den sity will v a ry w ith th e v ib ra tio n to which the pow der is subjected, and also w ith th e u n ifo rm ity of th e particles, since voids in th e stru c tu re of regular p articles m ay be occupied by sm aller p articles. F u rn a s (40) has experim entally determ ined th e voids in m ix-

FIG. 1-3. Bulking properties of various powders.

10

/

P a r tic le S iz e : M e a s u r e m e n t, I n te r p r e ta tio n , a n d A p p lic a tio n

F I G . 1-4. R e la tio n b e tw e e n v o id s an d aize c o m p o s itio n in tw o -c o m p o n e n t s y s te m s o f b ro k en so lid s w h en th e v o id s o f s in g le c o m p o n e n ts are 0.5.

tures of tw o sized fractio n s and found th a t th e voids w ent through a m inim um for some in term ed iate m ixture, as illu stra te d in Fig. 1-4. In addition, th e voids were less th e lower th e size ra tio betw een the fractions. Pr op e r t ie s o f

Su sp e n si o n s

A decrease in a p p a re n t fluidity of suspensions w ith decrease in p a r­ ticle size has been reported for zinc-oxide pigm ents in oil (41) an d for glass spheres suspended in zinc brom ide dissolved in aqueous glyc­ erol (42). T h e a p p a re n t fluidity, how ever, of suspensions of glass spheres in a nonaqueous m ixture of ethylene tetrab ro m id e and d ie th y l­ ene glycol w as found to be in dependent of p artic le d iam eter (42). Sweeney and G eckler q u a lita tiv e ly explain these a p p aren tly conflicting observations in th e following w ay. E ach p article is surrounded by an adsorbed la y e r of fluid which increases its effective size. T h e resulting increase in th e volum e co n centration of particles is th e larg est for th e sm all particles, and varies from fluid to fluid. B y using selected blends of p artic le sizes (glass spheres) of closely sized fractions, Sweeney and G eckler (42) w ere able to show th a t the fluidity of a suspension is dependent on th e bulk density of th e solids. T his effect has been tre a te d by o th er investigators (43). T h e sedim entation of sm all p articles suspended in liquids or gases

A p p lic a tio n s o f P a r tic le S iz e D is tr ib u tio n M e a s u r e m e n ts

/

11

is th e basis for determ ining the size d istrib u tio n of p a rtic u la te m a tte r and is also used to sep arate pow dered m aterial into various size fra c ­ tions. S to k es’ law is used to relate th e ra te of fall to th e p article size. A lthough s tric tly applicable only to spherical p articles, th e relation holds very well for p articles which differ appreciab ly from sphericity. D av ies (44) has published an excellent article on th e settlin g of sus­ pended particles. T h e scatterin g of light by fine particles is responsible for n a tu ra l phenom ena such as th e blue color of the sky, th e b rillian t colors of m any sunsets, and th e h azy appearan ce of th e atm osphere. T he th eo ry of th e scatterin g of lig h t by fine particles was first devel­ oped by R ayleigh (45) an d la te r extended by M ie (46). F lo w

of

Pow de rs

Flow experim ents (47) w ith circu lar orifices have shown th a t, for each orifice, flow w ould n o t occur u n til a m inim um p article size was exceeded. B eyond th e m inim um p article size, th e ra te of outflow first increased, th en w ent through a m axim um , and for th e larger m aterial decreased w ith increase in p article size. T he size of th e orifices used v aried from y32 to 1 in. and th e finely divided m aterials were closely sized fractions of glass spheres in th e range of 28-470 m icrons. T he decrease in outflow w ith increase in p article size is in agreem ent w ith a stu d y in th e sam e size range by B ingham and W ikoff (48). F ra n k lin and Jo h an so n (49) em pirically related th e m ass flow ra te from orifices of m aterials (in th e range of 0.03 to 0.3 in.) w ith signifi­ c a n t v ariab les as follows: w

_____________________ p b X D l 93______________ (6.288M3 + 23.16) (D p + 1.889) - 44.90

w here W is th e m ass ra te of flow in p o u n d s/m in u te, pB the d en sity of m aterial in p o u n d s/cu b ic foot, D 0 th e d iam eter of th e orifice in inches, D p th e d iam eter of th e p article in inches, and n 3 th e ta n g e n t of th e in te rn a l k inetic angle of repose. In these studies, th e bed height was g re a ter th a n one colum n diam eter, and the p article-to-orifice ra tio and th e orifice-to-colum n d iam eter exceeded certain m inim um values. T he colum ns used ranged from 1.8 to 8.8 in., th e orifice diam eters from 0.2 to 2.3 in., and th e p article density from 7.3 to 676 lb /c u ft. E m pirical correlations on th e flow of sand (50) and c a ta ly s t pellets (51) have also been reported. M a gn e t ic

Pr op e r t ie s

Selwood (52) has review ed a num ber of investigations of the m ag­ netic p roperties of finely divided m aterials in which th e principal

IS

/

P a r tic le S iz e : M e a s u r e m e n t, I n t e r p r e ta t i o n , a n d A p p lic a tio n

em phasis was on p article size. T hese include studies of g rap h ite (53), th e m agnetic changes th a t occur in carbon d uring g rap h itizatio n (54), q u a rtz (55), an d nickel in supported c a ta ly sts (56, 57). B h atn ag er e t al. (58) found th a t, in general, th e m agnetic su scep tib ility of pow dered m etals is independent of p artic le size. Problem s of oxidation, con tam in atio n , or change of m icrocrystalline stru c tu re th a t m a y affect the su scep tib ility are difficult to avoid in finely divided m etals. So l u b i l i t y

and

Ra t e

of

So l u t i o n

T he ra te of dissolution of sm all p articles is g re a ter th a n th a t of large ones because th e ra te of dissolution of p a rtic u la te m a tte r is dependent on th e specific surface in co n tact w ith th e liquid m edium (59). S olubility has also been observed to be dependent on p article size. Several au th o rs (60) have studied th is phenom enon. K n a p p (61), how ­ ever, w as th e first to allow for an y facto r which w ould p rev en t th e p articles from a tta in in g an indefinitely high v alue of supersolubility w ith extrem ely sm all size. H e p o stu lated th e existence of an electrical charge on th e particles and re la ted th e so lubility of a n y given size particle, S r, to th e solubility of a very large p article, S, by th e ex­ pression: RTF. M

Sr S

2 — =
g

s.

60

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^

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Sedimentation in isobutyl alcohol, sample No. 18

30

170*: £

Sedimentation in isobutyl alcohol, sample No. 3

.

\

200

230 I 270 2 325 00 400

- V 04

\

\

\

\ 20

-

\

\ 10 0.2

j, 1-1___ L 1

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J__ I I I 1 10 20 40 60 80 Percent by weight greater than

j_ X 95

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F IG . 9-9. T h e co m pa riso n b etw e en w o v c n -sie v e a n a ly sis and th e m o re a cc u ra te m e th o d s on a n h y d ro u s m o n o ca lciu m p h o sp h a te. M icro sco p y d a ta co n v er ted to w e ig h t are rep resen te d b y th e d ash ed lines.

Wichscr and Shellcnbcrgcr’s intcrcomparison (17) of sieving, liquid sedim entation (Andreascn pipet), and air flotation (Roller Air Analyzer (18)) on flour is illustrated in Fig. 9-10. I t was concluded th a t sieving is applicable above 37 microns, air flotation below 80 microns, and the Andreascn pipet below 50 microns. W ork a t the Oak Ridge N ational L aboratory (19) on thorium oxide in the particle size range of 0 .2-20 microns established th a t centrifugal sedim entation data correlate well with results obtained by g rav ita­ tional sedim entation methods (Andreasen pipet, turbidim etric, and activation analysis) for the portion of sample composed of particulate m atter greater than 2 microns in size. The results on one representative sample are shown in Fig. 9-11. In the m ajority of tests made, thorium oxide was found to exhibit no significant difference in particle size distribution when the sedim entation tests were made in different dis­ persing media. This was not always the case, however, and indeed when 0.005M H 2S 0 4 was utilized as the dispersing medium, the measured particle size distribution differed considerably from th a t when either xylene or 0.005M N a 4P 20 7 was utilized. In the size range below 10 microns, it has been repeatedly shown (20) that, if proper dispersion is achieved, centrifugal sedim entation utiliz­ ing the layer technique (see C hapter 5) and the electron microscope

Pe rcent by w eight great er t han

F I G . 9-10. C o m p a riso n o f p a rticle size d istrib u tio n cu rv e s fo r w h ea t flour b y sie v in g , air flo ta tio n (R o lle r A n a ly z e r ), and se d im e n ta tio n (A n d rea sen p ip e t). S e e F . W . W ich ser an d J . A . S h ellen b erg er, C e re a l C h e m ., 25, 155 (1 9 4 8 ). 2 0 .0

s

i

1

1

1

1

1

l

1

1

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|

1

1 0 .0 —

a

X

o

ArO

5 .0 —

—

—

J V o

2 .0 —

—

A ■ *!0

_

1 .0 -

-

• Centrifugal sedimentation in xylene; * o Gravitational Andreasen pipet in xylene, *■ Gravitational Andreasen pipet in 0.001 M N a ^ O z ; ■ Gravitational sedimentation using activation analysis in 0.05M N a < P .

0 .4

0 .2

0 .1

—

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1

1 2

5

1

1

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20 40 60 80 90 Percent by weight greater than

I

I

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98 99

F I G . 9-11. P a rtic le size d istrib u tio n o f th oriu m o x id e . C o m p a ri­ son o f cen trifu g a l an d g r a v ita tio n a l m e th o d s u sin g v a rio u s d is ­ p ersin g m ed ia . S e e O. M e n is, H . P . H o u se , and C . M . B o y d , O RN L-Z3.'i& , C h em istr y -G en er a l.

161

152

/

P a r tic le S iz e : M e a s u r e m e n t, I n te r p r e ta tio n , a n d A p p lic a tio n

F I G . 9-12. iD te rco m p a riso n o f e lec tro n m icro sco p y an d cen trifu ­ gal se d im e n ta tio n on silic a .

d ata (counted and sized electronically) gave identical particle size distributions. This is illustrated in Fig. 9-12 for measurements on silica powder. Agreement between light microscopy and centrifugal sedim entation has also been noted by W hitby (21). Batel (22) made a thorough investigation of sieving, air separation, sedim entation, and the Blaine perm eam eter (23). He concluded th a t sieving is strongly affected by the sieving motion, especially when a large fraction is present below 60 microns. Air separation using the B.A.H.C.O. Classifier (see reference 104 in C hapter 5) was found to be useful in the 30-100-micron range. The Blaine perm eam eter was found to give characteristic numbers th a t did not correspond to particle size by itself. If the particles are properly dispersed, it was concluded th a t sedim entation (Andreasen pipet) is useful in the 1-60-micron range. A critical comparison (24) of the Andreasen pipet and sedim entation balance (Recording Sedibal) methods showed the latter to be more precise and to require less manpower for operation.

C o m p a ris o n o f P a r tic le S ize D is tr ib u tio n D a t a

/

153

Sum m ary

I t has been established th a t if microscopy, gravitational sedim enta­ tion using a balance, centrifugal sedimentation using the layer tech­ nique, and sieving are utilized in their proper particle size ranges (dis­ cussed in the next ch ap ter), equivalent particle size distributions are obtained, independent of technique. The work of various investigators suggests th a t the more specialized particle size distribution techniques should only be utilized after they have been checked against the es­ tablished methods. In the next chapter, on recommended methods, the utilization of the established techniques for particle size distribution measurements are discussed in greater detail. REFEREN CES

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24.

D . P . A m es, R . R . Ira ni, and C . F . C a llis, J . P h y s . C h e m ., 63, 531 (1 9 5 9 ). J. F . H e iss and J. J . C o u ll, J . C h e m . E n g . P ro g r., 4 8 , 133 (1 9 5 2 ). R . R . Ira n i, u n p u b lish ed resu lts, M o n sa n to C h em ic a l C o ., S t. L o u is 66, M o . J . G . R a b a tin and R . H . G a le, A n a l. C h e m ., 28, 1314 (1 9 5 6 ). S . G . M a g u ire and G . W . P h e lp s, J . A m . C e r a m . S o c ., 40, 403 (1 9 5 7 ). S . W . M a rtin , C e ra m . A b s tr ., 21, 92 (1 9 4 2 ). D . G . S a m m a ro n e and H . S . Sa un d ers, A m . C e ra m . S o c . B u ll., 36, 340 (1 9 5 7 ). A . I. M ich a els, T . L . W ea v e r, and R . C . N e ls o n , A S T M B u ll. N o . 247, p. 140 (1 9 6 0 ). J. C . B a r n e tt an d R . R . Ira n i, u n p u b lish ed resu lts, M o n sa n to C h em ica l C o ., S t. L o u is 66, M o . F . B . H u tto and D . W . D a v is , O ffic. D ig . F e d e r a tio n P a in t V a rn ish P ro d . C lu b s, 3 1 ,4 2 9 (1 9 5 9 ). D . H . M a tth e w s, J . A p p l. C h e m ., 7 , 610 (1 9 5 7 ). R . B . A n derso n and P . H . E m m e tt, J . A p p l. P h y s ., 19, 367 (1 9 4 8 ). R . R . Irani and W . S. F o n g , C e re a l C h e m ., 38, 67 (1 9 6 1 ). R . R . Ira n i, A n a l. C h e m ., 32, 1162 (1 9 6 0 ). E . S . P a lik , A n a l. C h e m ., 33, 956 (1 9 6 1 ). R . R . Irani and C . F . C a llis, A n a l. C h e m ., 31, 2026 (1 9 5 9 ). F . W . W ich ser and J. A . S he llen b erg er, C e re a l C h e m ., 25, 155 (1 9 4 8 ). P a r tic le S iz e A n a ly s is o f M e ta l P o w d e rs, M e ta ls D isin te g r a tin g C o m p a n y , E liz a b e th , N . J., 1946. O. M e n is, H . P . H o u se , and C . M . B o y d , O R N L -2 3 4 5 , C h em istry -G en era l, O ffice o f T e c h n ic a l S erv ice s, U . S. D e p t, o f C o m m erce, W a sh in g to n 25, D . C. R . R . Ira n i and E . F . K a e lb le , A n a l. C h e m ., 3 3 , 1168 (1 9 6 1 ). K . T . W h itb y , H e a tin g , P ip in g a n d A ir C o n d itio n in g , 61, 449 (1 9 5 5 ). W . B a te l, C h e m . In g . T e c h ., 29, 581 (1 9 5 7 ). T h e B la in e P e r m e a m e te r is offered b y P re cisio n S cien tific C o ., C h ica g o , 111. D . B a ch m a n and H . G ersten b erg , C h e m . I n d . T e c h ., 29, 589 (1 9 5 7 ).

c h a p te r

10

Procedure for choosing the appropriate method of particle size measurement

Analysts frequently face the problem of having to decide which particle size method is the most applicable to their problem. Figures 10-1 to 10-6 are aids to the analyst in m aking his decision. The reader can refer back to the appropriate chapter for more details on each method. A few examples of how the procedure would work for two powders with all particles below 100 microns are given below. A research engineer is assigned the problem of designing cyclones to remove or isolate the finer particles in different powdered m aterials. Therefore, he is interested in weight-size distributions of the powders with a precision of ± 3 % a t any specified size. He finds th a t none of the products involved are held on a 140-mesh woven sieve. F or one pow­ dered product he is interested in, more than 60% of the m aterial passes through a 325-mesh woven sieve. W ith micromesh sieves, he finds th a t only 10% of the powder passes through the 20-micron sieve. Therefore, he adopts R o-T ap sieving of calibrated micromesh sieves with the aid of a flow-conditioning agent (see C hapter 7). Another product with the same size characteristics is very hygro­ scopic, for example, ammonium perchlorate, and sieving is alm ost im­ possible. F or this product he uses liquid sedim entation in an organic fluid th a t disperses ammonium perchlorate but does not dissolve it. A pigment m anufacturer has to supply powders with no particles over 10 microns. He is interested in a routine plant method good to ± 5 % for controlling the product. The weight-size distribution of one pigment with a weight-median size of 2-3 microns can be readily 154

C h o o sin g th e A p p r o p r ia te M e th o d o f P a r tic le S iz e M e a s u r e m e n t

/

155

measured with a M ine Safety Appliance Co. layer sedim entation cen­ trifuge, using an appropriate dispersing fluid. Another pigment is sig­ nificantly finer in size and has a weight median size of 0.1-0.5 micron. For this latter pigment he probably has to invest in an electron micro­ scope, if this is possible. Counting the electron photomicrographs m an­ ually to obtain number-size distribution is feasible but tedious. If money is available, he will buy an autom atic counting and sizing device such as Cinema Television’s (London) Flying Spot Particle Resolver. If the pigments are nonporous and have a smooth surface and only an average particle size is desired, the pigm ent m anufacturer should seriously consider gaseous or liquid adsorption for surface area meas­ urement. The adoption of one specific method in preference to another m ust be based on such things as precision and accuracy required, cost of equipment, tim e per analysis, and caliber of personnel running the experiments. Finally, it should be emphasized th a t we should measure the size attribu te th a t is m ost directly correlated with the characteristic of interest and then keep the expression of size in those terms, unless comparisons outside the system are required. Table 10-1 shows the dimensions on which different m easurem ent techniques are directly dependent. TABLE 10-1 Dim ensional Effects of Different M easurem ent Techniques0

D is tr ib u tio n M o m e n t (P o w er o f D is tr ib u tio n V aria b le) D istr ib u tio n W eig h tin g B y n um ber B y area B y v o lu m e *

S iz e M icro sco p y — S ie v in g

A rea

V o lu m e

L ig h t sc a tte r in g

C o u lter C o u n ter

T u r b id ity A ll se d im e n ta tio n

— —

m eth o d s and classifiers

• A d a p ted from a p r iv a te co m m u n ica tio n w ith P rofessor K . T . W h itb y , U n i­ v e r sity o f M in n e so ta .

OJ

s

Particle

Size:

M ea su rem en t,

In terp reta tio n ,

and

A p p lic a tio n

F IG . 10-1.

Choosing

Cont from Fig. 10-1

I

1___________

the Appropriate

Method

o] Particle

Size M easurement

F IG . 10-2.

Oi s

158 Size, m icrons

W oven sieves

Layer liquid centrifugal sedim entation Accurat e Part icle Size Distribution

Calibrat ed elect roform ed sieves

Liquid gravitational sedim entation Light m icroscope Electron m icroscope Autom atic counting and sizing of photomicrographs or sam ple direction

Elutriation Rapid "Average" Size

Adsorption ( for nonporous part icles) Perm eabilit y =

"Average" Size

X-ray diffraction Light scatt ering Turbid imetry

--------------------------------------------------------------------------------------------------------------------------------------------------------------- >-

F I G . 10-3.

Choosing

I I

Cont . from Fig. 10-1

the Appropriate

Est im at e solids cont ent

0.1

1.0

10

100

Size, m icrons

W oven sieves

+ w Calibrat ed elect roform ed sieves '7 V ' Liqu id gravit at ional sedim ent at ion

'

Elect ron m icroscope Aut om at ic count ing and sizing of phot om icrographs Light scat t ering, if only average size is desired and appropriat e elect rolyt e is found

F I G . 10-4.

Measurement

Light m icroscope

Size

Layer liquid cent rifugal sedim ent at ion

_

of Particle

D ilue to 5-10% solids cont ent for sieving. For ot her t echniques, dilut e to about 0 .1 - 0 .5 % . Preferably, dilut e w ith sam e fluid and dissolved solids a s in slurry

Method

0.01

160

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P a r tic le S iz e : M e a s u r e m e n t, I n te r p r e ta tio n , a n d A p p lic a tio n

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