Steimour Rate of sedimentation suspensions of uniform-size angular particles.pdf

8/13/2019 Steimour Rate of sedimentation suspensions of uniform-size angular particles.pdf

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840 IN D U S T R I A L A N D ENGI NEER I NG HE M I S T Y Vol. 36, No. 9rently amorphous substances, were found on the surface of beadsof vitreous compositions of P205/CaO mole rat io 1.4-1.9; thesecompositions had been made by reaction of rock phosphate withPz05n excess and had been stored in capped bottles in the labora-tory for five years. Autoclaving of pure, finely ground calciummetaphosphate with small amounts of water for a few minutesa t 180 C. and then cooling gave practically complete conversionof metaphosphate to monocalcium phosphate. In boiling diluteacids, complete hydrolysis of calcium metaphosphate to ortho-phosphates requires several hours, and in aqueous extracts atroom temperature the hydrolysis may continue for months IO).In the presence of limestone the hydrolysis of calcium metaphos-phate is followed by formation of dicalcium phosphate, whichwas identified in th e solids obtained by boiling an aqueous slurryof the stoichiometric proportions of pure calcium carbonate andcalcium metaphosphate.

ACKNOWLEDGMENTThe authors acknowledge the encouragement and aid of R. L,Copson, J. W. H. Aldred, E. H. Brown, and other members ofthe TVA Chemical Engineering Staff in obtaining the data andpreparing this paper. They are grateful also for the helpfuladvice of J. F. Schairer and other members of the staff of the Geo-

physical Laboratory, Carriegie Inst itut ion of Washington. Thegenerous cooperation of 8. B. Hendricks, K. I> Jacob, and W. LHill of the-U. S. Department of Agrirul ture is acknowledged.LlTER4TURE CITED

(1) Adams, J. R., and Ross, 1 '. ., IND.ENG.CHEM . ,33, 121-7(2) Bariett, R. L., and McCaughey, W. J., Am. Mineral., 27, 680(3) Bartholomew, R. P., and Jacob, K. D., J . Assoc. Of ic ia i A ~ T(4) Copson, R . L., Pole, G. R., and Baskervill, W. H., IND. E ~ G(5) Curtis, H. A , , Copson, R. L., and Ahrams, A. J., Chem. & Me t

(1941).95 (1942).Chem., 16, 698-611 (1933).C H E M . , 4, 6-32 (1942).Ena.. 44. 140-2 (1937).(6) CurtG,'H. A., Copson, R. L., Abrams,A . J., and Junkins, J X..

(7) Frear, G. L., and Hull, L.H., IND.ENG.C H Z M . , 3,1560 6Ibid.,45, 18-22 (1938).(1941).(8) Hill, W . L., Faust, G .T., and Reynolds, D. S., A m . J . Sci . , 212

(9) Jacob, K. D., and Ross, W. H., J. A g r . Research, 61, 539 bU(10) MacIntire, W . H., Hardin, L. J., and Oldham, F. D. , I ND(11) Tromel, G., Mitt. Kaiser-Wilhelm Inst. Eisenforsch. Dusse l do r f

457 (1944).(1940).ENG.CHEM., 9, 224-34 (1937).14, 5-34 (1932); Stahk u. B k n , 63, 21-30 (1943).

RATE OF SEDIMENTATIONSuspensions of Uniform-Size Angular Particles

Rates of sedimentation are reported for suspensions of closely sized emery par-ticles, both flocculated and nonflocculated. Except for the value of an e x -perimental constant, one rate equation applies to both states, provided theflocculated suspensions are highly concentrated. Comparison w ith previous testson uniform spheres indicates that a portion of the liquid suspension medium iscarried down with the angular emery particles during their fall, whether thesuspensions are flocculated or not. The question as to 3s hether this liquid is boundto the particles or simply stagnant is studied, and evidence is shown to support

HAROLD 3. STEINOURPortland Cement Association,Chicago, 111. the latter view.

N THE first article of this series 15) equations were de-veloped for the sedimentation rates of dispersions of uniformspheres. Under conditionswhere the Stokes law gives the ve-locity of a single isolated sphere, the velocity a t anx concentrationof spheres is given by Equation 24 of the first paper :I

Q = vieeZ10-- .82(1--e)where the function 10-1.82 1-e) is empirical. At values of cbetween 0 . 3 and 0.7, Equation 24 is practically equivalent toEquation 23 16):

3Q = 0.123Va -_1 . 5which was derived, except for the value of the proportionalityconstant, by using the hydraulic radius to denote the size of theflow space around the spheres and by assuming that no addi-tional variable shape factor was needed.In the present article th e sedimentation of angular particles isconsidered, starting with the equations for spheres. The experi-ments on which the study is based embraced both the disperseand flocculated states. Low Reynolds numbers (Table 1V) en-sured viscous flow in the displaced liquid. Particles of very smallsize were used td permit flocculation; they were closely sized inorder to obtain uniform settlement in the disperse or non-flocculated state. Flocculated suspensions in which manysizes are present will be treated in a third article.

SEDIMENTATION TESTS ON EMERY POWDERSA commercial emery powder was fractionated by air separa-tion; two fractions called A and B were used in sedimentationtesta. Their densities were 3.79 and 3.77 grams per cc.,. respec-tively. The appearance of emery A is shown by Figure 1.Size analyses (Table I) were obtained for both roducts by anadaptat ion of the Wagner turbidimeter method 68 ) .The sedimentation tests Rere made in water. At first, intests in which flocculation was to be avoided, no dispersingagent was added, for the fresh powders did not flocculate. How-ever, as a safeguard 0.1274 sodium hexametaphosphate was usedin late r tests. Absence of flocculation was shown by directobservations with a binocular microscope, and by the firmnevsand constant density of the sediments produced by differentinitial concentrations of solid. In all test s in which flocculationwas desired, zinc sulfate was used, chiefly a t 0.12%. All sus-pensions were mixed for 2 minutes with an electrical mixer and,except as noted in the tables, were tested in a cylindrical glassjar about 100 mm. in diameter, filled to a height of 40 to 60 mm.These dimensions were chosen in order t ha t effects of Ta l fric-tion would be negligible at the center of the jar 14). A microm-eter microscope reading to 0.001 mm. was used to follow thechange in level of th e suspended solids. Readings were timedto 1 second. Temperatures were 24 1 C.In all tests on flocculated suspensions the readings were takenon a float placed centrally in the jar (Figure 2) . The float waslike one used by Powers f4), thin disk of Bakelite with athread-like glass stem attached to its upper face. The densitieswere such tha t the float rode a t the plane of separation of thesuqpension and a layer of vvater which was placed on top in


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September, 1944 I N D U S T R I A L A N D E N G I N E E R I N G C H E M I S T R Y 841

Figure 1. Photomicrograph of Emery A (X 500)quantity sufficient to cover the disk. Readings were taken bysighting on the tip of the stem.In suspensions that were not flocculated, wall friction wasnot appreciable; hence, in tests on these suspensions the floatmethad was eventually abandoned and readings were takendirectly on the level at the wall of the vessel. In all cases thesuspensions settled with satisfactorily sharp upper boundaries.

Curves of subsidence of the surface of a suspension againsttime are shown in Figure 3. Their shapes are fairly typical formost of the tests, but a t values of B below 0.65 the nonflocculatedsuspensions gave curves which sagged a little in t he central por-tion (Figure 4). The effect was distinctly noticeable in tes ts onemery A at B = 0.60 and 0.577, and those tests were omitt ed fromfurther study. Liquid content E = 0.577 was the lowest at whicha good mixture could be made.Results of sedimentation tests are shown in Table 11,arrangedin order of increasing dilution. The rates of settlement are forthe initial constant-rate periods.

RATES OF SEDIMENTATION O F NONFLOCCULATEDSUSPENSIONSRate data that conform to Equation 23 of the first paper fallalong a straight line through the origin when [ (1 - E ) ] isplotted against E. In Figure 5 this method of plotting has beenapplied to t he dat a for the nonflocculated suspensions of emeriesA and B.The dashed lines in Figure 5 represent Equation 23 16)asapplied to the systems under study. In determining the values

of Va he average diameters reported in Table I were used. It isevident that the experimental points do not conform to Equation23. However, up to E = 0.75 the data for both emeries are rep-resented by

( e - 0.168)31- & = 0.176 Va--

Ltn equation similar to 23 of the first paper bu t differing, in theterm on the right, both in the magnitude of the initial factor andin the nature of the cubed quantity.The function of e shown by Equation 1 is the same form asthat found by Powers 14) fo r flocculated pastes of portlandcement and water. For those pastes the subtractive term wasconsiderably larger than 0.168 and varied with the cement used.

The manner of its occurrence suggested tha t some of the waterwas not taking part in the general flow of liquid relative to t hesolid particles which occurs during sedimentation. Hence,Powers assumed that a small quantity of water remained witheach falling particle. Symbol wawhich he applied to the sub-tractive term in his equation stood for immobile water; th esame symbol will be used here. Kozeny 11) and Carman3, ) lso found that a term equivalent to w was needed in a

few instances in an equation, similar in principle to 23 lb ) ,which Kozeny 11, 9) derived for laminar flow through granularbeds. The need for the term arose only in a few water perme-ability tests on clays.The three authors cited above concluded that, in tests re-guiring the w, erm, the need probably arose because of liquidwhich in some way became bound to the particles. However,Fair and Hatch (7) who derived an equation like tha t of Kozeny,believed that stagnation prevented some of the liquid from con-tributing to the flow. Such an occurrence would be analogous tothe separation from laminar flow observed by Johansen (9) atsharp-edged orifices in circular pipe.In nonflocculated suspensions any liquid that fails to takepart in the general flow must be in separate increments asso-ciated with the individual solid particles, irrespective of whetherit is bound to the particles or stagnant at angularities in theircontours. If th e amount of such liquid per partic le is inde-

TABLE. SIZEANALYSESOF EMERIES AND B F RO M SEDIMENTATION IN WATER,USING SODIUMHEXAMETAPHOSPHATESDISPERSANTDiameter, Emery A Emery 33 Diameter, Emery A , Emery B,Microns % by W i . % by Wh. Microns %b y Wt. % b y Wt.50 -40 2.0 0.8 10-9 5.2 23.340 -30 1.7 1.6 9-8 0.1 17.630 -20 . 2.2 3.3 8-7 0.1 11.120 -18.5 1.7 1.1 7-43 0.0 2.118.5-17 1.4 1.4 6-5 0.1 0.417 -16 1 9 0.5 5-4 0 0 0 316 -15 3.3 0.3 4-3 0.1 0.016 -14 6.8 0.9 3-0 0.4 0.514 -13 12.6 2 2is -is 22.0 4.212 -11 24.1 3.511 -10 14.4 24.9 Emery EmeryA 3

Sp. surface. calod. &e for spheres s q . cm./oc. 4930 6260Av. diam. crtlcd. from sp. su rf ad , microns 12.2 9.6

Figure 2. Sedimentation Test i n Progress


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42 I N D U S T R I A L A N D E N G I N E E R I N G C H E M I S T R Y Vol. 36, No. 8pendent of the nearness of other particles, thenfor a given powder the to tal amount should be pro-portional to the volume of the powder. Hence, ifY is the proportionality constant, the immobile

(Chrono- % of Read- Eieight, Vol. x 106 Initi al Settled rect Equation 23 (16) for such immobile liquid,a ( l - e) should be subtract,ed from each c in the

Float 55 65. 0 1300 32 48 equation. The limiting velocity, VR, eeds no cor-rection since it is found experimentally and shouldSjde 57 75. 0 3355 53 47 therefore embody the effect of any immobile liquid.The modified equation after some rearrangement is:

TABLE1. SBDIMENTATI~NF EMERIES A N D B IN ~OO-MM.-DIAMETERVBSSELFluid PorosityConon. of Content Rate of Settle- ofRe nlating %J of Fluid Settlement ment, Sediment. liquid per unit of total volume is a 1 - ). To cor-Test NO. &gent, Initial in Total (Cm./Seo.) rp of % of

logical) Mater W t . ing Mm. (6 X 102) (& X 108) Height Vol,Emery A , NonflocoulatedFloat 56 70.0 2155 42 48Float 41 75.0 3390 52 48Side 56 80.0 5410 63 46

Emery .L Flocculated

2 01 08 04 03 0B 0.1212 0.127 0.129 0.128 0.1213 0.0010 0.1211 0.1214 0 . 1 223 0.1221 0.1220 0 .1222 0.1215 0 .1216 0.0017 0.2019 0.1218 0.12

FloatFloatFloatFloatFloatFloatFloatFloatFloatFloatFloatFloatFloatSideSideSideSideSide

En-

51 60.053 62 .5; . 63 .768 85.052 59 . 658 70.042 75.080 .0443 85.057 62.556 65.056 70.042 76.075.0432 75.042 80.042 86.0

tery A . Nonflocculal

50 70.0

56673680693214521520250047009930110813712185219032803270321051307550

ted

R142726354360323646465455546372

i i ,5656555859616462144545464 545454546

( - -aI i - aQ = 0.123 (1 - CY)*V , -

If wi is used in place of a / l + a),aw / ( l - wi), and the equation becomes:

When wi = 0.168 as in Equation 1,0.123/( 16 0.120 .127 0.12I 0.122 0.1224 0.124 0.126 0.12

11 0.129 0.1210 0.12

Emery R . Nonflocculated equals 0.178, and Equation 3 becomw practicallyidentical with Equation 1. Hence the experi-ides 40 6 0. 0 621 27 45Bideb 58 62.5 675 3 4 44Side 40 85 .0 847 38 44 mental results may be regarded as wholly consist-Ride 38 70. 0 1350 44 47Float 37 70 .0 149OC 43 47 ent with the theory that a quantity of liquid pro-portional t o the volume of the emery remains withide 45 75. 0 2055 56 44Side 56 80.0 3140 64 44Side 58 85 .0 4700 72 46 the particles during their fall. For both emeries Aand B the quantity of thie: liquid is indicated toFloat 32 67.5 658 20 59Float 36 70. 0 841 24 61 be 0.202(I - ), or one fifth of th e volume of solid.According to this theory, E - a 1 - is tjhe~ Float 28 75.0 1475 35 61 general expression for the mobile liquid. There-fore, since the linear relation illustrated by Figure5 was previously indicated 1 5 ) t o apply up to

Emery 5 , Flocculated

Vessel 68 mm. i n diameter.& Vessel 63 mm. in diameter.e This value waB omitted from the figures. I t is widely difi'erent from the other value~ Q I - 0.70 and appears to involve an error sufficiently large to warrant rejection.

e,3

0 4 8 12 14 16 18 20Time, Minute r

Figure 3. Sedimentation Curves f o r E m e r y A ate = 0.65 Figure 4. Sedimentation C u r v e s for NonflocculatedSuspensions of Emery A in Plain Water at e = 0.60


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September, 1944 I N D U S T R I A L A N D E N G I N E E R I N G C H E M I S T R Y 843e = 0.70when a was zero, it should apply up to e= 0.75 when CY is 0.2. This agrees satisfactorilywith the data.

STAGNANT LIQUIDThe fact that the two emery powders of differentsize particles have the same value of a helps de-termine whether the immobile liquid is bound ormerely stagnant. If this liquid is stagnant, then

a, he quantity of such liquid per unit volume ofsolid, should be determined b y the shapes of the par-ticles and be independent of particle size, as wasfound. Bu t if the liquid is bound to the particles,the thickness of the layer should probably be aboutthe same for particles of different sizes, and thetotal quantity would not then remain a constantproportion of the volume of solid, 1 - , when thesiae of particle waa changed. It would be morenearly proportional to the exposed surface, thespecific surface in sq. om. per cc. times (1 - ). Onthis latter basis wi should be 1.2 times as large foremery B as for emery A. The da ta in Figure 5conform much bet ter t o the one common value forwb; indeed, as will be shown late r, equality of thew i values is also indicated by a more precise methodof evaluation. However, to obtain more evidence,tests were made on another emery powder of muchlargec particle sise.A relatively large-grained product of fairly-uni-form partic le siae waa obtained by sieving a coarseemery powder on screens having square openings,62 nd 74microns on a side, respectivcly. The prod-uct, emery E, had a density of 3.93 grams per cc.and was tested for sedimentation characteristics indiethyl phthalate (density 1.115 grams per c E . a t22' C., viscosity 0.091 poise at 27.5' C.). No dis-persing agent wae needed. The first sedimenta-

0.10

0.08

In

0.06a

0.04

0.02

0.oc

tion tests were made at 27.5' C., later ones at 23.6' C. Allreadings were taken on the level of the suspension at the wallof th e vessel. Curves of height of suspension against time weresimilar to those for th e finer emeries. The porosities of thesediments were practically constant at 58% of the set tled volume.Rates of settlement obtained a t E = 0.60 were exceptionally lowand are not reported; the fluid content was judged t o be tooclose to i ts lower limit t o permit free orientation of t he particles.

0.0 0.2 0.4 0.6 0.8E

Figure 5. [Q(l-c)] l / a v s . E for Sedimentation of NonflocculatedSuspensionsof Emeries A a n d B

TABLE11. SEDIMENTATIONF EMERYIN DIETHYLHTHALATETests in 6&Mm.-Diam. Jar at97 K O 7 Tes t s in

Fluid~ ~ ~ ~ ~ dettlementTest No. (om./sec.)

Rate of(chrono- vol. x 105logical) (e X 109 (& X 109

1-1 62 .6 3471-2 62.6 3563-1 66.0 4612-2 66.0 4553-1 67.6 6703-2 67.5 5724-1 70.0 7394-3 70.0 7674-4 70 .0 7305- 1 72.5 9266-2 72.6 9260-1 7 6 .0 11816-2 7 5 .0 1198a Rates adjusted to 27.5' C.by multiplying by 1.16 factorbased on tests at e = 0.76).Testamade in 68-mm.-diam.jar.

Teat No.(chrono-logiral)7- 17-27-37- 48- 18-28-33-49-19-29-89-4

10-110-210-310-4i l - 111-211-311-4

92-Mrn.-Diam. Jar at23.6' C.0Fluidcontent Rate ofof fluid settlement'% total (am./aeo.)vol. x 10s6 x 10') 4 105)76.0b 115375.0'~ 1191.75.0'~ 120375.0b 122077.5 157477.6 143077.6 140677 .6 14188 0 .0 18068 0 . 0 186880.0 84880.0 187682.6 229082.6 23108 2 . 6 230082.6 231085.0 289085 0 284086.0 291086.0 2870

The rates obtained at higher values of E are shown in TabTe IfI;thorn determined at 27.5 C. were used in Figure 6.The value of ws ndicated b y Figure 6 s 0.22,a figure distinctlylarger tha n th e value 0.168 ound for emeries A and B. This re-sult is the opposite of what would be expected of bound liquid, ifthe diethyl phthalate is assumed to build about the same thick-ness of adsorption layer as the water. The large particles ofemery E would require much lower values of a and w han dothe particles of A and B if the adsorption layers wereof thesamethickness. It is estimated that the thickness would have to beabout twenty times as great on emery E particles to account ftwth e results obtained. Against the possibility of this occurreaaceris evidence obtained by the writer in tests on portland cementin various liquids, including diethyl phthalate; this evidemmindicates that there is little change in w i upon changing liquids.Furthermore, even th e estimated layer thicknesses for emerieaA and B are so great as to comtitu te strong independent evidenceagainst the existence of the layers. Assuming th at the v o l wof bound liquid is approximately equal to the thickness of layertimes the area of surface exposed to liquid, thicknesses of 0.30and 0.24micron are indicated for emeries A an d B, respectively.[The surface areas were calculated from air permeability data13) which indicated values about 1.4 times those obtained bysedimentation analysis.] Ye t BulMey 9) ound that in flowof oils the thickness of stationary film does not exceed 0.02 o0.03micron; Bastow and Bowden 1) tudied t he flow of var iousliquids and found that liquid 0.1 micron from a solid surfacetakes par t i n the movement.Still further evidence appears in the previous article 16)inwhich Equation 23 was found to be adequate for suspensions ofglass spheres that averaged 13.6 microns in diameter. Thornspheres were only a little larger t$han he particles of emery A


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I N D U S T R I A L A N D E N G I N E E R I N G C H E M I S T R Y Vol. 36, No. 9average diameters reported in Table I. The ur values as origi-nally estimated were adjusted slightly to make the slopesstrictly 1.82; this m a s the basis for th e statement made earlierthat the equality of the w, alues for emeries A and B did notrest solely on the evidence from Figure 5. Figure 7 shows thatwhen these WA values are used, the data conform closely to thestraigh t lines even a t the high dilutions; as corrected forstagnant liquid, they conform to the equation found to hold forspherical particles.The stagnant liquid may not be strictly immobile, for adifference simply in the patterns of the streamlines near thesurfaces of angular and spherical particles could conceivably causethe difference in results. However, since the flow patterns mustbe similar in their more general aspects, the close agreement ofthe theory with the dat a seems to indicate th at any motion in theliquid called stagnant must be relatively small.Miscellaneous data are assembled in Table IV to aid in (om-paring conditions in the suspensions of t he various emery powders,The Reynolds numbers are given only for infinite dilution andare calculated from the formula commonly used for spheres. Theyare not strictly comparable when the particles differ in shape.It should be realized also that a Reynolds number representativeof the general flow will decrease with E 4),ince both the velocitiesand the distances between particles decrease.

0.16

0.14

0.12

0.10. /T=W- 0 0 8e-

0 06

0 04

0 02

0 00

igure 6, [ Q l - e ) ] / e 21s. f o p Sedimentationof Norlflorculated Suspensions of Emery E

and might have been expected t o bind a comparable quantity ofwater, yet now erm was needed.The theory that the wz alues found For the nonflocculated sus-pensions of emery particles are indicative of adsorbed liquid mustbe rejected; the theory that there is stagnant liquid which ac-companies the angular particles in amounts determined by theirshapes is consistent with all data considered thus far. The quan-tity per unit volume of solid is evidently greater for emery E thanfor emeries A and B, but the difference in particle shape whichthis indicates is in accord with the fact that emery E gives sedi-ments of relatively high porosity.

COMPARISON WITH WORK OF OTHERSEquation 4 has been applied to data obtained by Kermaclr,MKendrick, and Ponder 10) on the sedimentation of red bloodcells, discoidal in shape, apparently uniform in size, and notflocculated. The tests were made on the cells of man, rabbit, ox,and sheep. Gaudin (8) averaged the results obtained for thedifferent types of cells, after converting them to percentages ofthe estimated velocities a t infinite dilution, and then comparedthe averages witfi values calculated from several different equa-tions. Table V reproduces part of Gaudins table, including thevalues calculated from the equation of Kermack et al. and thosefrom Gaudins best equation. Values calculated from Equation 4

are shown in comparison. Th e method of applying Equation 4was graphical, and no weight was given to Gaudins 100 rate

RESULTS FOR A L L CONCENTRATIONSUp to this point the concept of stagnant Iiquid has been testedonly with dat a obtained a t concentrations high enough so thatEquation 3 can be applied. The general Equation 24 16) pre-sented at the beginning of this article provides the opportunityto make a more extensive test of t he concept. If the quantity

of stagnant liquid remains a fixed proportion of the volume o fsolid at all concentrations, then Equation 24 should representthe data for the emery if E i s replaced by a quantity represent-ing actual mobile liquid per unit of b t a l volume. This quantityis E - Substitutionin Equation 24 gives:(1 - ), equivalent to (E - w J / 1 - w J I

1 - - cwhere volume of solid plus immobile liquid per unit of1 - WEtotal volume. If the equation represents the data, a straightline having the slope 1.82 should be obtained when loglo&($)*s plotted against (e - w 8 ) / ( 1 - w,), he complement

This method of plo tting was used in Figure 7 which presentsthe dat a for the three preparations of emery. The points shownor emeries A and B at (E - w t ) / ( l - wL) 1 were based on theof (1 - ) / ( l - W l ) .

TABLEv. DATAROM TESTSN EMERIES, B, ANI1 EEmery A B E

iNXONF LOCCULATEDUSPENSIONSStokes velocity V , cm./sec. 0.026 0.016 0,098Reynolds No. a t inhnite di1n.Q 0 . 0033 0.0016 0.0091aW i 0.168 0.168 0.22a 0.202 0.202 0.28a Definedas: particle diam. X liquid density X Stokes velocityb Particle diameter of emery E was taken as 0.0076 om., corresponding t o

I__viscositylimiting velocity indicated by Figure 7.

TABLE. APPLICATIONOF VARIOUSQUATIONS TO DATAOFKERMACK,ENDRICK, AND PONDER10) O N SEDIMENTATOF REDBLOODELLSExptl . Rete of Sedimen-tation, % of ValueEstd.

R~~~~ fo;for Infinite Diln. Theoretical Ra te of SedirnentatiouAverage tests on Kermack , This article,calcd. b various MKendr ick, Eq. 4 with1 - Gaudin 6) cells Ponder Gaudin w = 0.167

Corresponding to Equation of:

0.00250.0060.010.020.040.080 .160.32

979489837 3512913

97-9793-9586-9278-8767-7946-6022-347-22

939693867243Neg. bNeg. b

979593867660358

069 490847263287Calculated in terms of Gaudins average percentages by arbitrarilyaasuming the observed rate a t 1 - 6 = 0.0025 to, be 97% Va n each case.b The equation was derived for low concentrations only.


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September, 1944 I N D U S T R I A L A ND E N G I N E E R I N G C H E M I S T R Y 845

-1.6

-1.8

-2.0

-2.2

-2.4

-2.6

-2.8 0.3 0.4 0.5 0.6 07 0 8 0 9 1.02)Figure 7. Loglo Q [( 1 - Wi)/(e - Wi) I us- E - wi)/( l- WI )for Sedimentation of Nonflocculated Suspensions ofEmeries A, B, and E

since it was not experimental. It is concluded from Table Vtha t the d ata can be represented as well by Equation 4 s by eitherof the others with which comparison is made.SEDIMENTATlON RATES O F FLOCCULATED SUSPENSIONSEmeries A and B were also tested when flocculated. Those

tests made possible a direct comparison of effects in the twostates, but flocculated suspensions of a much finer emery powderwere also tested to extend the basis for determining th e effect ofparticle size. This finer emery (D) was a commercial prepara-tion. The results of a sizeanalysis are shown in Table VI. In the tests for ra te of sedimen-tation the 0.12% solution of zinc sulfate was used as flocculant.The test s were made at 25 C. in the same way as those on emeriesA and B, except that they were discontinued before completionof settlement. The data are presented in Table VII.In Figure 8, [ (1 - ) ] % is plotted against E for the flocculatedsuspensions of emeries A, B, and D. As was true of the dat a forthe nonflocculated suspensions, the points for each product canbe represented by a single straight line, except for a few points a tthe highest values of E . The slopes of the lines were calculatedfrom Equation 3, the best values of w eing determined by trial.On the whole, there is fair agreement with the equation. SinceEquation 3 was derived for nonflocculated suspensions, thisagreement indicates a considerable degree of similarity in thesedimentation of the flocculated and nonflocculated suspensions.Nevertheless, it is evident from Table I1 that the flocculationmaterially reduced the r ate of settlement a t most concentrations.This is reflected in increased values of w L .This effect of flocculation on the rate of settlement in concen-trated suspensions is the opposite of the effect in dilute ones. Incontrast to dilute suspensions, highly concentrated ones maydevelop so continuous a floc structure that all liquid displaced bythe settlement must make its way through th e actual floc texturewhere the resistance is high. Such an assumption helps explain

Its density was 3.38 grams per cc.

why Equation 3 applies as well as it does, for the equation isbased on the premise of flow past the individual particles. Theincrease in W i may mean simply tha t the contacts or virtual con-tacts between particles which are evidently a feature of theflocculated state cause the amount of stagnant liquid per particleto b? somewhat greater than tha t in a dispersion.ABSENCE OF STRUCTURAL RESISTANCE

The floc formation assumed above for concentrated suspensions,is essentially a three-dimensional network extending fairly uni-formly throughout the whole volume of the suspension, butoffering initially almost no mechanical structurd resistance tocollapse under the action of gravity. The assumption of negli-gible s tructural resistance seems necessary because flocculationcauses no change in the numerical factor of Equation 3; supportfor the assumption is provided by determinations of hydrostaticpressure. Tha t the hydrostatic pressure is an index to thenature of th e resistance is readily shown. When particles in aliquid form a completely self-supporting structure, they do not,contribute to this pressure which is therefore determined by thedensity of the liquid in the usual way. Bu t in the absence ofstructural resistance, particles which settle without accelerationlare supported entirely by the liquid, and the hydrostatic pressureis determined by the density of the mixture.No tests for hydrostat ic pressure were made on suspensions ofthe sized emery powders, but fifteen determinations were made onother concentrated flocculated suspensions, most of which wereportland cement pastes in which E was 0.58. Structural resistancewas thought to be more probable in such suspensions than inthose of inert, closely sized particles.The hydrostat ic pressures were determined by pouring t he sus-pensions into a vessel in which a manometer tube, partly filledwith water and stoppered, was supported with its lower end wellabove the bottom of t he vessel. This manometer was a singletube having an enlarged lower end fitted with a fritted glass disk.Each suspension was brought to a level such that the head ofwater in the manometer was a little less than tha t calculated forequilibrium. I n a few minutes after the manometer was un-stoppered, the water rose to a height which remained practicallyconstant for some minutes and then declined at a rate t hat sug-gested development of boundary effects at the tube. However,the maximum heights usually prevailed as long as 5 or more min-utes after th e suspensions were in place, which was long enoughto ensure that the constant rates of sedimentation had been es-

TABLEI. SIZEANALYSISF EMERY FROM SEDIMENTATIIN WATER,USINGSODIUMEXAMETAPHOSPHATES DISPERSADiameter, Diameter, Weight,Microns weght Microns %Diameter,Microns weyt.ht,

50-40 1 5 12-11 0.0 7-6 21.040-30 2.3 11-10 0.3 6-5 14.830-20 2.5 10-9 1.0 5-4 21 220-15 1.1 9-8 1.4 4-3 24 816-12 0. 8 8-7 1.1 3-O5 0 2Sp. surface. calcd. as for sphere sa, sq. cm./cc. 12,950A v . dism., calcd. from sp. surface, microns 4.0 I

I Average parti cle diameter of this portion taken a8 2 microns since rnioro-scopio examination indicated absence of extrem e fines.

TAB LE VII. SEDIMENTATION OF FLOCCULATEI)USPENSIONS OFEMERYFluid FluidContent,, Rate of Content, Ra te ofyoof Fluid Settlement % of Fluid Settl ementTest No. in Tota l (Cm./Sec,j Test No. in Total (Cz.(@.)(Chrono- Vol. X 108 (Chrono- Vol.logical) (e X 10%) (Q X 106) logical) (e X 10%) Q X 109

1 67.6 95 8 75.0 2462 70.0 112 4 77.5 3263 72.5 183 5 80.0 4387 72.7 171 0 85.0 956


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846 I N D US T R I A L A N D E NG I N EE R I N G C H E M I S T R Y Val. 36, No. 9

EFigure 8. [Q( l -e) ] h os e for Sedimentation of Floc-culated Suspensions of Emeries A , B, and

tablished. In general, the equilibrium heights were within * 1-570of those calculated by assuming no structural resistance. Asthe probable experimental error w w stimated to be about theeame magnitude (l.W%),he absence of appreciable structural re-sistance was considered to have been demonstrated.

FLOC SrRUCTUREThe assumption that a rather uniform network of p a r t i cktills all the space in concentrated flocculated suspensions makesn o allowance for any liquid outside the floc space proper. It i spresumed that concentrations for which the data can be rep-resented by Equation 3 are so great th at there is no tendency forthe floe t o occupy less tha n the tota l available volume. How-

evw9 the data might still be in approximate agreement withEquation 3 f the fine structure were broken by pockets of liquidsf elatively large dimemiom. The existence of random iso-lated pockets would not conflict with the apparent requirementthat liquid escaping from the settling mass should pass thrwgh&bo loo meshwork and contact the individual particles. Thepwkets would tend to produce nonuniformity in the flow, butthere would probably be readjustments in floc texture, and thecab of di me nt at io n might not be far from that of a suspensionwbollgp occupied by floc of the same concentration as that in t hedo@ space proper. Accordingly, it is of interest that liquid inpockets could contribute to wa n the same way as liquid stagnantat angularities in the individual particles. Th at is, if liquid inpsokets mounted to wl, per unit of total mixture, this would

leave (E - w p ) / l- w p )as the proportion of the actual fioc spaceoccupied by liquid. This quant ity has the same form as E -w. /(1 - w,)which was previously shown to represent the rnohileliquid when wL esults from stagnant liquid.Liquid in pockets is mentioned merely as a possibility, for t brat e equation is explained more satisfac torily entirely on the basisof the stagnant liquid which, in any case, appears t o be responsiblefor most of wi.The basic assumpiion that there are no channels for liquid toescape without passing through th e floc texture ipi in accord withdirect observations. Powers, in his work on cement pasteu,usually found no evidence of significant breaks or channels in th epaste structure in tes ts in which his d ata were in agreement withhis rate equation; a t higher dilutions, channels and boils couldeasily be seen, but then the rates were higher than those pre-dicted by the equation. These observations have been con-firmed by the writer. Also, many indications of boundary resist-ance which have been obtained in the work on cement pastes areregarded as further evidence of the continuous nature of the flocstructure. I n none of the tests on th e emery suspensions wereany channels seen. However, it is believed that the poinb inFigure 8 that were obtained at high dilution and that trend u pward from the straight lines representing the rest of the d ata doso because the less concentrated suspensions were too dilute toprevent breaks in the s truc ture, breaks too fine to be seen readily.EFFECT OF PARTICLE srm IN FLOCCULATED SUSPFLNSIONS

Particle size affects the value of V ; that it also affects thevalue of w i when the powders are flocculated is suggested byFigure 8. However, judgment as to the generality of t h mrelation should be reserved until additional data are presented inthe third article of this series. The fine emery D, for which IBPis much the largest, had relatively low density and was evidentlyless pure than the other emeries. It was also less uniform inparticle size, on a percentage basis. Th e w, alues for flocculatedsuspensions of the various emery powders follow:Sp. Surface b%Sedimentatio; A4V0rag0 i orFlocculated

Emery sq.Cm./ &r Vicrons Suspension8Method Diameter.

ABD4,9306,25012.950

12.29 . 64 . 00 .2680.2880.360

Among recent investigations of Hocculated suspensions, thornof Egolf and BIcCabe 6), Ward and Kammermeyer l y ) , andWork and Kohler (18)relate to lower concentrations tha n thosedealt with here. The work of Powem 14) on the sedimentationor bleeding of portland cement pastes is apparently the mostextensive previous study of highly concentrated flocculated suepensions with which comparison can be made. Powers9 ra teequation differs in some respects from Equation 3, but the differ-ences can be reconciled, as will be shown in the third article OBthis series.Although the data of Egolf and NcCabe on 16-micron silicaare for more dilute suspensions, they can also be representedlinearly by plotting [ (1 - against e. Apparently, after abreak in slope like that shown for emery A in Figure 8, anotherlinear relation often obtains.

CONCLIJSIONSThe effect of parbicle concentration on rate of sedimentationin nonflocculated suspensions settling under conditions of viscouaflow is not the same for angular particles as i t is for spheres.However, the results for the two kinds of particles can be broughtinto complete agreement by assuming that the angular particleacarry with them a volume of liquid which is a constnnt proportionof the volume of the solid at all concentrations. The quant ity


8/8

September, 1944 I N D U S T R I A L A N D E N G I N E E R I N G C H E M I S T R Y 847per unit volume of solid appears to be a function only of particleshape. For different preparations of emery the indicated quan-tities were 20 and 28% of the volume of solid. Several lines ofevidence are presented to show tha t this liquid is not adsorbedby the particles. Apparently it is simply liquid that has re-mained stagnant at angularities in the particles.Flocculation of concentrated suspensions of the same emerypowders that were tested in the nonflocculated sta te materiallyreduced the rates of sedimentation. However, the same rateequation could be applied with fair success when modified onlyby an increase in wd which, for the nonflocculated suspensions,corrects for the liquid tha t is assumed to be stagnant. It is con-cluded that in highly concentrated flocculated suspensions thereis no opportuni ty for liquid to by-pass floc structure in escapingfrom the mass during sedimentation, but that in general thisliquid must flow past t he individual particles in much the sameway as in a nonflocculated suspension. Two possibilities areseen for the increase in wr: (1) The quant ity of stagnant liquidmay be increased by reason of interparticle contacts caused byflocculation. (2) There may b e isolated pockets of liquid dis-tributed through the mass, pockets whose dimensions are ma-terially greater than those of the meshes in the floc structureitself. How such pockets can produce an increase in wi has beenHhown.

The possibility that structural (nonviscous) resistance pro-duced by the flocculation ma y have been a factor in decreasingthe rates of settlement was investigated by determining hydro-sta ti c pressures in flocculated suspensions of various powders,bu t principally in aqueous pastes of portland cement. It wasfound that there is no appreciable structural resistance duringthe initial stage of t he sedimentation when the constant r ate isestablished.ACKNOWLEDGMENT

The writer was assisted by Richard G. Brusch a nd Herbert WeSchulta in t he experimental work reported in th is artiole.

PRINTING INKS

NOMENCLATUREQ = initial rate of settlement of top surface of a suspension,cm. /sec.V . = rate of fall of an isolated sphere as given by Stokes law,cm./sec.; used also to represent rat e of fall of an iso-lated particle when Reynolds number is such tzat asphere would fall in accordance with Stokea laww, - dimensionless constant used by Powers 14)tu, = dimensionless constant analogous to wia = dimensionless constant denoting volume of fluid per unit

volume of solid, that a pears to remain with angularparticles during their f a 8= proport ion of total volume of suspension occupied by liquid(analogous to porosity in beds of particles)eLITERATURE CITED

Bastow, S. H., and Bowden, F. P., Proc. Roy. SOC. London),Bulkley, R.. Bur. Standards J.Research, 6, 89-112 (1931).Carman, P.C.,.Agr . Sci. , 29,Pt. 2, 262-73 (1939).Carman, P.C . , J.SOC hem. I d . , 57, 225-34T (1938).Carman, P. C. , Trans. Inst . Chem. Engrs. (London), 16, 1138-88Egolf,C.B., and McCabe,W. ., Trans Am. Inst .C h . ngra.,Fair, G. M., and Hatch, L. P.,J. A m . Water WorlcsAssoc., 25,Oaudin, A. M., Principles of Mineral Dressing, 1st dJohansen, F. C., Proc . Roy. Soc. (London),A126, 231-45 (1930).Kermack, W . O . , MKendrick, A. G., and Ponder, Eric, Proc.Koaeny, Josef, Kulturtechnilcer, 35, 478-86 (1932).Kozeny,Josef,Sitzbe-r.A h a . W i s s. V ie n ,IIa, 136,271-306(1927).Lea, F.M.,nd Nurse, R . W., J . Soo. Chem. Id., 8, 277-83TPowers, T. C . , Research Lab., Portland Cement Aasoo., Bull.Steinour, H. H., IND.ENQ.C H ~ M . ,6, 618-24 (1944).Wagner, L. A., Proc. Am. SOC Testing Materialrr, 33, Pt. 11,Ward, H. T., ;nd Kammermeyer, Karl, IND.ENO.CHBY.,32,Work, L.T., nd KoNer, A. S., Tbid., 3.2 329-34 (1940).

A151, 220-33 (1935).

(1938).33, 620-42 (1937).1551-65 (1933).Chap. 8,New York, McGraw-Hill Book Co., 1939.Roy. SOC. dinburgh, 49,170-97 (1929).

(1939).2 (1939).553-70 (1933).62243 (1940).

from Colloidal Dispersions ofSOYBEAN PROTEINLFRED F. SCHMUTZLER ANDDONALD F. OTHMER

Polytechnic In stit ute, Brooklyn, N. Y.

ROTEI N dispersions in diethylene glycola previous article 98). Printing inks mapersions are nondrying on the printing press, but whenprinted films of the inks are exposed to steam, the y harden im-mediately. The y are not sufficiently water resistant for uni-versal use. To eliminate this defect, reactions designed to lowerthe water absorption of proteins were investigated.I n aqueous dispersions, soybean protein will no t precipitateor gel when reacted with formaldehyde 95). Plastics made fromit have relatively high water absorption 1-4). In contrast tosoybean protein, casein and blood albumin gel almost immediatelyupon th e addition of even small amounts of aldehydes to theiraqueous dispersions, an indication tha t the behavior of the formerdiffers considerably from that of the latter. Nevertheless it,

Pwas found th at some features of t he hardening of casein couldbe applied to soybean protein.

In order to improve the hardness and durabil ity of caseinfibers (artificial wool, lanital), in some instances) mall amountsof salt s of heavy metals are added to the spinning solution 10,13, 1.9, 1.6, 20); in others the .dispersed casein is reacted withisocyanates (6, 16, 17, 18), sothiocyanates 1 1 , 16), nd carbondisulfide (6). Although isocyanates may undergo side reactionsin the presence of hydroxyl groups, isothiocyanates and carbondisulfide combine solely with amino and amide groups. Theinitial step is the formation of thiourea derivatives, followedby condensation reactions with aldehydes, with the formationof modified thiourea resins (9, 10, 4). In the reaction of pro-teins with carbon disulfide, hydrogen sulfide is liberated and cancombine with aldehydes, with the formation of thioaldehydes,which are much more reactive than the aldehydes from which

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