SETTLING RATES AND SEDIMENT VOLUMES OF FLOCCULATED KAOLIN SUSPENSIONS ALAN S. MICHAELS AND JUSTIN C. BOLGERI Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge 39, Mass.
This study investigated the settling rates and sediment volumes
of
aqueous,
flocculated kaolin suspensions as
functions of kaolin concentration, container dimensions, and chemical composition of the aqueous phase.
Equations
which correlated the data were derived, based on a structural model which assumed that in a flocculated suspension, the basic flow units are small clusters of particles (plus enclosed water) called flocs.
These flocs retain their
identity under the mild forces experienced in gravity settling. A t l o w shear rates, the flocs group into clusters o f flocs, called aggregates.
The aggregates may form networks
which extend t o the walls of the container and give the suspension its plastic and structural properties,
HE KINETICS of sedimentation of particulate solids in liquid T m e d i a and the structural and rheological characteristics of the resulting sediments are of great importance to a broad segment of the chemicals processing and process metallurgical industries. Although sedimentation phenomena have been subjects of research for many decades, and much insight has been gained into the hydrodynamics of sedimentation processes, relatively little is yet known of the role of particleparticle attractive forces in settling and sediment consolidation. T h e object of this investigation, therefore, was to study the sedimentation behavior of aqueous suspensions of a solid (kaolin) whose surface characteristics are well enough understood to allow analysis and interpretation of sedimentation data in terms of particle-particle interactions. Most previous studies of settling rates have pertained to suspensions of dispersed, nonattracting particles, rather than to flocculated suspensions. I n general, these have been attempts to extend Stokes’ law to cover nonspherical particles (7, 3, 20), to allow for the effect of particle concentration upon settling rate (70, 77, 77, 20), or to calculate the wall effect for settling in containers of finite size (77). T h e first general study of flocculated suspensions was by Coe and Clevenger ( 4 ) ,who described the various concentration zones which exist within a settling suspension, and who observed that the upward flow of displaced supernatant was a special case of pore flow. Wadsworth and Cutler (22) studied the effects of flocculating agents upon the settling rates of kaolin suspensions. Smellie and La Mer (72, 79) also studying flocculated kaolin suspensions, sbggested that settling rates could be correlated using the Darcy filtration equation to predict the flow rate of displaced supernatant, and proposed a n 1 Present Address, AVCO Research and Advanced Development Division, Wilmington, Mass.
24
I&EC FUNDAMENTALS
extrapolation procedure to estimate the ultimate volume of the settled bed. Gaudin, Fuerstenau, and Mitchell (6-8) used x-ray adsorption techniques to measure the local kaolin concentrations in settling beds as a function of time and position. The density profiles so obtained indicated that the displaced supernatant fluid leaves the bed through pores of comparatively large diameter during the early stages of settling and later is expelled via much smaller tubules in the compressive phase of sediment consolidation. These authors also noted that settling rates increased as container height increased. The studies cited above represent important contributions to the understanding of relative movement of solid and liquid during settling and consolidation in flocculated suspensions, but the part played by suspension microstructure in these phenomena remains obscure. Examination of a highly purified, well characterized solid, suspended in a solution phase of controlled composition, appeared to offer promise of analysis in terms of its microstructural features. The clay mineral kaolinite, in aqueous suspension, was selected for this purpose. Kaolinite, a hydrous aluminum silicate of composition A1203 2 S i 0 2 . 2 H ~ 0 ,occurs in the form of thin, roughly hexagonal platelets, of length-to-thickness ratio of about 10. Under normal conditions, in aqueous suspension, the particles carry a negative charge, distributed over the basal surfaces; this charge arises, it is believed, by occasional substitution of aluminum for silicon in the clay crystal lattice, this charge deficiency being satisfied by retention of foreign cations (commonly hydrogen, aluminum, calcium, magnesium, or sodium) on these surfaces. These ions are mobile in aqueous media, and are responsible for the ”cation exchange capacity” of the clay, which is of the order of 1 to 2 meq. per 100 grams of solid. Under acidic conditions (pH 6), alumina exposed a t the edges of the plates apparently binds hydrogen ions, and assumes a positive charge (78); this causes electrostatic attraction between edges and faces, with the formation of highly expanded “card-house’’ flocs. Under alkaline conditions, the edges become neutral or negatively charged, and the particles deflocculate, provided the electrolyte concentration in solution is low. At high electrolyte concentrations (at both high and low pH) electrostatic repulsion (or attraction) between particles is reduced because of double-layer compression or ion shielding of the surface charges. Under these conditions, residual valence forces a t the particle surface cause the pa1 ticles to adhere to one another along their basal surfaces, forming “card-pack” flocs. More complete treatments of the surface chemistry of kaolin and of the factors controlling particle interaction forces are given by Brindley ( 2 ) , Michaels (75), Street and Buchanan (27), and others (73, 78, 22). The ability to control and to predict the magnitude and geometry of particle interactions in kaolin suspensions thus renders it an ideal substance for systematic investigation.
0 Figure 1.
The
tl
1
c2
Figure 2. Three general types of settling plots
Floc-aggregate structural model
Procedure
forces and collisions experienced in gravity settling. Because the flocs are originally formed under conditions of severe agitation in the Waring Blendor, the most probable floc shape is a sphere, the shape most capable of resisting deformation by surface forces. Further, it has been shown (74, 76) that flocs tend to approach a uniform size in any shear field. This size increases as clay concentration increases or as shear rate decreases. At low shear rates the flocs tend to group into clusters of flocs, herein designated as aggregates. These aggregates may join together to form extended networks (as in Figure I ) , which extend to the walls of the container and give the suspension its plastic and structural properties. Settling Rate in Dilute Suspensions. Settling rates were determined by plotting the height, Z , of the interfacial plane between the slurry and the supernatant as a function of time. There were three general types of plots, as shown in Figure 2. For very dilute suspensions ( $ K < 0.007 for untreated kaolin)
T h e kaolin used in this study was a well crystallized, acidbleached product of rather narrow particle size distribution [90 weight % between 0.2- and 2-micron equivalent diameter (g)] provided by the Georgia Kaolin Co., and designated PD-10. T h e cation exchange capacity of this material was found to be approximately 1.0 meq. per 100 grams. As received, the solid was found to contain approximately 0.5 mmole of readily extractable aluminum (as alumina) per 100 grams. Sedimentation data were obtained in a 25' =t 0.5' C. constant temperature room, using vertical glass cylinders which ranged from 500-ml. graduates u p to tubes 120 cm. long and 6.5 cm. in I.D. T o investigate the effects of changes in the chemical content of the ambient fluid, five flocculated slurries were studied in detail. SLURRYA. Cntreated kaolin, p H 4. This was PD-10 grade kaolinite, mixed with distilled water in a Waring Blendor. At a kaolin volume fraction. d K > 0.03, the p H of slurry A was 4.0. SLURRY B. Untreated kaolin, p H 6. This was identical to slurry A except that the p H was raised to 6.0 by the addition of Y a O H . SALT-LVASHED SLURRIES C A ~ D. D The Georgia Kaolin Co. uses a n acid-wash procedure (9)to remove iron oxides and other impurities from the kaolinite. This procedure. however, also dissolves considerable quantities of lattice aluminum, which is subsequently precipitated and deposited upon the platelet faces as positively charged colloidal alumina. By reducing the number of negative charge sites on the platelet faces, this alumina weakens the edge-to-face attractive forces which give rise to the card-house flocs in acid slurries. I t is possible to remove most of this surface alumina by repeated extraction of the kaolinite with 111; S a C l a t p H 3, according to the procedure described by Martin (73). Slurry C was salt-\vashed twice this way. and then adjusted to a p H of 4.5 and a chloride ion concentration of 0.001S. Slurry D was identical to slurry C except that the slurry p H was adjusted to 6.5 ivith h-aOH. CARD-PACK SLURRYE. I n contrast to the card-house flocced slurries A, B, C. and D, slurry E had a platelet face to platelet face card-pack structure. Slurry E was prepared by raising the p H of slurry A to 9.0 with K a O H , and then adding enough XaCl to bring the C1 concentration in the supernatant to 0.06A\r.
I
I
01
1000
80C
2 wU
600
LT
W
I-
-z U
0 I-
-
400
W
3:
6 2
200
Results a n d Discussion
The Model. T h e model used to interpret the data was based on the premise that in a flocculated suspension, the basic flow units are not the primary particles, but are small clusters of particles (plus enclosed water), herein called flocs. These flocs have a certain amount of mechanical strength and so are able to retain their identity under the very mild surface shear
0 0
10
20
30
TIME, MINUTES
Figure 3.
Dilute settling plots
Slurry B (1000 ml. = 32.0 cm.)
VOL.
1
NO. 1
FEBRUARY
1962
25
LYaCI, pH9 33 8
the straight-line plot of Figure 2, a, is obtained. Data taken with slurry B over this concentration range are shown in Figure 3. These dilute settling rates decrease rapidly as clay concentration increases, but are independent of the dimensions of the settling tube as long as the tube I.D. is large compared to the average aggregate diameter. Direct observation, using a 45X microscope mounted against the glass tube wall, showed that the aggregates a t these dilute concentrations settled as roughly spherical, individual units, rather than as chains or networks. While the aggregates were not uniform in size, the size range was fairly narrow for untreated kaolin, where the horizontal diameters ranged from about 50 to 400 microns. FACTORS DETERMINING AGGREGATE S I Z E . The siie Of the aggregates is not a fundamental property of a flocculated suspension, but is a dynamic property which depends upon the rates a t which aggregates grow by collision and are broken down by viscous shear forces. The data of Table I permit some deductions regarding the effect of mixing intenrity upon aggregate size. “Inverted” means that the settling tube was turned end over end by hand 8 to 10 times to start the settling run. “Blended” means that the sample was mixed for 1 minute in a Waring Blendor just before being poured into the settling tube. The settling rates for the blended suspensions are higher than for the inverted suspensions for all four systems ; therefore strong mixing must produce large aggregates. Yet the spread in aggregate sizes must also increase as mixing intensity increases. If all aggregates were of the same size and density, then all would settle a t the same rate and the interface would be sharp and the supernatant fluid would be clear. Strong agitation in the blender produces large aggregates which settle quickly but also produces many small aggregates which remain behind in the cloudy supernatant. Table I also shows that settling rates are reproducible for each of the cases of inversion of the settling tube, that the aggregates can recover their former size after severe agitation in the blender, and that the low-pH slurry, having the strongest cohesive forces, is affected least by changes in the mixing conditions. Hence, the major factors determining aggregate size are the internal cohesive forces holding the aggregates together and the method of agitation used to start the run. If one uses a standard mixing procedure (in this work, the standard procedure consisted of inverting the tube 8 to 10 times), then for any slurry the aggregates should approach a fairly uniform, reproducible average equivalent spherical diameter, dA. SETTLING RATEE Q U A T I O N . The Richardson and Zaki (77) equation for the group settling rate for uniform, spherical particles can be written
50 7
Q = Vs~e485
3
% z
.. U 3
ci
1
C
0.005
0.01
& density zone and a n upper nonuniform region in the final settled bed. Table 111 shows DETERMINATION OF FLOC CONCESTRATION. how measurements of the slopes of the straight-line regions of the settling plots of Figures 11 and 12 may be used to convert kaolin volume concentration, $ K , into floc concentration, @ P . T h e procedure illustrated in Table 111 may be used to construct a plot of +P us. dK for each slurry. A less accurate but less time-consuming procedure is to measure Z , for only two initial heights (Zo1and Zo*)a t each concentration, and then to calculate $= from Equation 30 in the form
-
Figure 13 shows the complete curves of d F us. $,, with the points either taken from Table I11 or calculated by Equation
Table 111. Slurry A A A A
D
Calculation of Floc Concentration by Equation 30
Figure 11 11 11
12 12
+K
m (Slope)
6,
CFK?
Cm. 0.8 1.0 1.2
0.62m 10.3 9.80 8.80
13.3
1.7
12.8
1.3
8.25 7.90
0,00210 0,00410 0,00877 0,0190 0,0157
16.7
VOL. 1
NO. 1
15.8
14.2
+F>
CFR$K 0.0216 0,0402 0.0772 0.157 0.125
FEBRUARY 1962
31
-
-
31. I n the latter cases, the two initial heights used a t each 60 cm. and Z02 30 cm. concentration were Z,, Each curve in Figure 13 is concave to the $K axis, indicating , increases (floc density decreases) as $ K decreases for all that ,C five slurries, most probably because floc size decreases as clay concentration decreases, as observed by Reich and Vold (76). T h e relative heights of the curves differ, showing that floc volume and floc water content are functions of liquid phase composition. The order of the curves agrees with the order for the same five slurries in Table 11. DETERMINATION OF $ A . According to the floc-aggregate structural model shown in Figure 1, water can be removed from a bed settling under normal gravity by two mechanisms. (In a centrifuge, additional water may be expelled as the flocs deform and compress.) During the early stages of settling, interaggregate water is expelled as the aggregates deform and move closer together. The second, and much slower, mechanism involves the squeezing out of intra-aggregate water as the flocs within the aggregate crowd closer together. The x-ray density data of Gaudin and Fuerstenau illustrate both these mechanisms in Figure 6, e a n d f , which show a n upper decreasing density zone: a central uniform density plateau, and a bottom increasing density region. The original aggregates are crowding closer together in the upper region and are being compressed in the bottom region. T h e uniform density zone in between corresponds to a region wherein the volume fraction of the original aggregates is just equal to unity. The aggregate density, p a , and the original aggregate volume concentration, dA, could be calculated from the fraction of incident radiation which is transmitted through the uniform density zone of Figure 6 , f . A less accurate, but more universal, method is based on the observation that the density profile shown in Figure 6, f,occurs a t the time of the “second break” in the settling plot, a t t = t 2 in Figure 2. If one assumes that the area under the actual profile of Figure 6, f, can be approximated by a squared off rectangular profile of height Zz and width corresponding to p a , then the original aggregate volume is ir/4D2,Z~,and the aggregate volume coefficient is
T h e results of a large number of measurements of Z Z as a function of Z, and $ F indicate that Equation 32 overestimates ,C , for short columns, Z, < 50 to 70 cm. The results for taller columns, however, were found to be independent of either Z, or $ p , and to agree with the previous value of CAP = 3.64 for slurry A from Equation 28. Nine tests with slurry A a t 2, > 70 cm. gave a n average value of CAP = 3.78 with a standard deviation of 0.15. Table I V shows similar results for slurries B, C! D, and E.
From these data, CaF,the ratio of the aggregate to the floc volume concentration, is approximately 3.8 for all five slurry systems studied. Unless the aggregates are both confined and strongly compressed, the flocs always seem to cluster in such a way that the floc fraction within a n aggregate is -1/3.8 = 0.26. This means that for $ F < 0.26, approximately, the aggregates are composed of about 3 volume parts of water to one part of floc, independent of floc concentration or liquid phase composition. For $ F > 0.26, the aggregate volume concentration is unity and there can be no free-fall settling. The slow subsidence of the interface which does occur a t high concentrations (Figure 2, c) is due to the slow squeezing out of intra-aggregate water as the bed consolidates.
Conclusions For a flocculated suspension, the floc rather than the primary particle is the fundamental structural unit in low shear processes such as gravity sedimentation. The settling rates and sediment volumes observed could be explained by considering the flocs to be rigid spheres which tend to cluster together into weak aggregates. Aggregates grow by collision, break down by shear forces, and are able to form the extended networks which give the suspension its structural properties. Each of the properties studied in this work, including settling rates, sediment volume, and aggregate size, was a function of just two variables: floc volume concentration and the strength of the attractive force between flocs.
Nomenclature b
c..
= ordinate intercept of straight line of Equation 30, cm. = ratio of volume concentration of component i to component j CAF =
+A/+F;
CAK=
+A/+X;
CFK =
+F/+K
= average (equivalent) aggregate diameter, microns d, = average pore diameter, Equation 27, microns Do = diameter of container tube, cm. D, = yield diameter, defined by Equation 19, cm. g = local gravitational acceleration, 980 cm./sec2 I = intensity of x-ray transviewer beam k , = shape factor in Kozeny-Carman equation m = slope of straight line predicted by Equation 30 Q = settling rate of slurry-supernatant interface, cm./hr. Q. = initial settling rate, cm.,/hr. QI = maximum settling rate, cm./hr. Q ’ = prime superscript denotes settling rate in infinitely large settling tube s = specific surface area, sq. cm./cc. tl = time at which free-fall settling period ends tz = time defined by Figure 2 L, = tortuosity factor rx = pore hydraulic radius vs = Stokes’ settling velocitv. cm./hr. V S A = Stokes’ veloci6 for single aggregate, cm./hr. z =height of slurry interface, cm. Z , = initial height of slurry column, cm. Z , = final height of settled bed, cm. Z, = yield height defined by Equation 20, cm. Z,1 = yield height at t = t l , Equation 26 ZQ = height of interface a t t = t 2 , Figure 2 AZ = height of control volume in Figure 8 dA
~
Table IV.
Estimate of CAFby Equation 32 +F ZO Z2
Slurry
+K
B
0.0179
0.126
C
0.0200
0.196
D
0.0157
0.125
E
0.0237
0.106
98.5 108.5 84.7 99.1 51.3 69.7 87.8 59.9 81.0
46.1 49.5 68.7 77.7 24.5 30.4 38.6 25.2 33.2
CAF 3.70 3.62 4.01 4.00 3.82 3.48 3.52 3.98 3.87
A = aggregates SUBSCRIPTS.K = kaolin F = flocs f = final condition S = suspension (the slurry taken as a whole) GREEK E
fi fiw
32
l&EC FUNDAMENTALS
= = =
void fraction abbreviation for micron. 1 I.( = lo-* cm. viscosity of water, 0.893 cp. a t 25’ C.
density, grams/cc. PIC = 2.58 compressive strength of aggregate network. dynes ’sq. cm. = yield stress, dynes/sq. cm. For a plastic suspension, T-T~ as shear rate-0 = aggregate volume concentration = floc volume concentration = kaolin volume concentration
P
=
U”
=
Ty Q.4
$‘F $‘K
literature Cited 11) Andreason. A. M. H.. Kolloid Z.48. 175 11929). \
I
(2j Brindley, G. W.,“Ceramic Fabrication Processes.” Chap. 1 , 11’. D. Kingery, ed., Wiley, New York, 1958. (3) Burgers, J. M., Second Report on Viscosity and Plasticity. pp. 113-84, VA 51. Academy of Sciences, Amsterdam, 1938. (4) Coe. H. S.. Clevenger, G. H., Trans. A m . Znst. Mzning Engrs. 55. 356-84 11916). (5) Fuerstinau.’ M. C., Department of Metallurgy, M.I.T., unpublished data, Mav 1960. (6) Gaudin, A. M., Fuerstenau. M. C., Eng. Mining J . 159, 110
(9) Georgia Kaolin Co., Elizabeth. K. J., “Georgia Kaolin Handbook,” Bull. TSBH-10 (1956). “Some Aspects of Fluid Flow,” Chap. (10) Hawkesley, P. G. W., 7, Arnold &.Co., London, 1951. (11) Kynch, G . J., Trans. Faraday S i c . 48, 166 (1952). 112) La Mer. V. K.. Smellie. R. H.. Jr.. Lee. P. K.. J . Colloid Sci. ’ 12, 230 (1957). ’ (13) Martin, R. T., Proc. 5th Conf. on Clays and Clay Material, Natl. Acad. Sci.-Natl. Research Council, Publ. 566, 23 (1958). (14) Mason, S.G., Pulp and Paper M a g . Canada 49, 13, 99 (1948). (15) Michaels, A. S.? “Ceramic Fabrication Processes,” Chap. 2, W. D. Kingery, ed.. Wiley, New York, 1958. (16) Reich, I., Vold, R. D., J . Phys. Chem. 63, 1497 (1957). (17) Richardson, 3. F., Zaki, \V. Tu’., Trans. Znst. Chem. Engrs. 32, 35 (1954). (18) Schofield, R. K., Samson, H. R., Discussions Faradqy Soc. 18, 135 (1954). (19) Smellie, R.H., LaMer, V. K., J . ColloidSci. 11, 704 (1956). (20) Steinour, H. A., IND.ENG.CHEM.36, 618, 840, 901 (1944). (21) Street, N., Buchanan, A. S., Australian J . Chem. 9, 4 (1956). (22) Wadsworth, M. E., Cutler, I. B., Mining Eng. 8, 830 (1956). ,
RECEIVED for review November 6, 1961 ACCEPTED December 15, 1961
/\ 1- ,0-5- A \ /.
(7) Gaudin, A. M., Fuerstenau, M. C., Preprint, Intern. Mining Proc. Congr. London, April 1960. (8) Gaudin. A. M., Fuerstenau, M. C., Mitchell, S. R., Mining Eng. 77, 613-6 (1959).
I
Division of Industrial and Engineering Chemistry, ACS, Symposium on Dynamics of Multiphase Systems, University of Delaware, Newark, Del., December 1961.
FULLY DEVELOPED TURBULENT PIPE FLOW OF A GAS-SOLID SUSPENSION S
Velocity and concentration distributions of solid particles were colculoted for the case o f low solid-to-gas mass ratios, small particles, and negligible gravity effect.
When
these conditions ore sctisfied, the solid particles slip a t the woll and lag behind the stream ot the center of the pipe.
Dependence of the particle velocity distribution on the concentration distribution is to be exoected.
from studies of motion of a single solid particle in the turbulent field of a fluid, studies of dynamics of a gas-solid suspension as a whole have either excluded turbulence (3, 72) or have been completely empirical (70, 77, 79). Studies on the gas dynamics (72) and compressible potential motion ( 3 ) have shown that rigorous forniulation of general turbulent compressible motion of a gas-solid suspension over a solid boundary will be very complicated indeed. A solution is not even available for the statistical .lormulation of simple turbulent pipe flow, where the turbulence is nonhomogeneous ( 7 ) . Even when one assumes a n isotropic turbulent field, solution of the problem of motion of a single particle is a t best academic (6). T h e present study proposes a n extension of the present semiempirical method of treating turbulent flow through circular
A
PART
. L.
S 0 0 , University of Illinois, Urbana, Ill.
pipes-namely, the 1/7th velocity law (7 7)-to the case of a gas-solid suspension. Data are utilized on distributed mass flow of solids in pipe flow a t air velocities from 50 to 100 feet per second, solid particles consisting of 100- to 200-micron diameter glass beads, and solid-to-air mass ratios of 0.05 to 0.15 (77). I n the range under consideration, compressibility of the fluid phase and the effect of gravity on the density distribution of solid particles are negligible. Concentrations of solid particles are small. such that the velocity distribution of the gas stream is not significantly affected by the solid particles. I t is sometimes tempting to suppose that the heterogeneous mixture of solid particles and fluid may behave as a homogeneous fluid, the dense particles playing the role of the heavy component of a homogeneous mixture. This assumption would greatly facilitate the development of a theory but is almost never true in practical situations, for it would require that the suspended particles be extremely small. I n fact, for particles as large as those of real interest, the solid-fluid mixture has to be treated as heterogeneous. Then, because the solid particles have greater density than the fluid, the concentration of particles is not uniform over a horizontal pipe, the average velocity of the particles near the wall is not zero even though the velocity of the fluid is zero a t the wall, the concentration of particles is velocity-dependent, and the excess of particle velocity over fluid velocity is positive near the wall and negative in the core of fluid, A realistic theory of the motion of solid-fluid suspensions must account for these facts. VOL. 1
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FEBRUARY 1962
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