Ind. Eng. Chem. Res. 1998, 37, 2073-2077
2073
Shear-Induced Agglomeration of Particulate Suspensions† Srinivas Chimmili,‡ Deepak Doraiswamy,*,§ and Rakesh K. Gupta‡ Department of Chemical Engineering, West Virginia University, P.O. Box 6102, Morgantown, West Virginia 26506, and DuPont Central R&D, Experimental Station, Building 302, Room 315D, Wilmington, Delaware 19880
The “demixing” of an initially well-dispersed suspension of particulates arising from shearinduced, interparticle collisions in laminar flow was examined with the help of a transparent, cone-and-plate device. Experiments were conducted on a model system consisting of narrowsize distribution, noncolloidal, glass spheres suspended in aqueous corn syrup with added surfactant. The rate of agglomerate growth was measured as a function of time for different constant shear rates and suspension compositions. Data revealed a rapid buildup of particulate size at short times but a leveling off at extended times of shear due to the influence of hydrodynamic shear forces that determine the equilibrium agglomerate size. All the observations could be qualitatively explained by a simple agglomeration analysis that is developed here, and agglomerate growth could be quantitatively represented using an equation resulting from this theoretical analysis. Introduction The phenomenon of agglomeration of fine particles has been studied for a long time because processes such as sintering, pelletizing; and briquetting lead to desired products in the ceramics, mineral processing, and pharmaceutical industries. Fine powders are sometimes converted to larger entities because this conversion improves material handling characteristics (Pietsch, 1991 and 1996). However, when the goal is size reduction and particulate dispersion, as in the blending of solids with liquids, agglomeration is clearly undesirable. The problem is compounded by the fact that the very act of dispersing a solid powder in a liquid leads to particle-particle collisions that can result in coalescence if a binding mechanism develops; commonly encountered binding mechanisms include molecular forces, capillary forces, liquid bridges, and mechanical interlocking (Capes, 1976). Note that agglomerate size does not increase indefinitely; as the aggregates become larger, an equilibrium is reached between the binding forces and the forces of separation. Although colloid stability has been investigated extensively in the past, the agglomeration of noncolloidal particles, especially agglomeration kinetics under the influence of a shear field, has received much less attention (Hansen and Ottino, 1996). Current understanding of both coagulation and coalescence has been reviewed by Chesters (1991). In the present work, the main objective was to experimentally examine shearinduced agglomeration of a model, noncolloidal system with a view toward developing a fundamental understanding of the kinetics of size enlargement. Non* To whom correspondence should be addressed. E-mail:
[email protected]. Tel: (302) 695-9040. FAX: (302) 695-1717. † Dedicated to Professor L. K. Doraiswamy on his 70th birthday. D.D. would like, on this occasion, to express his warmest regards for his father, whose strength of character, scholarship, sensitivity, and good humor have always been a source of inspiration to him. ‡ Department of Chemical Engineering, West Virginia University. § DuPont Central R&D.
colloidal particles were selected for two reasons: (i) agglomerate growth can be followed by optical microscopy, and (ii) colloidal particles also grow and cross into the noncolloidal domain. For ease of data analysis, it is desirable to have compact, spherical agglomerates, which can be accomplished if liquid bridges are the binding mechanism. This phenomenon is known as spherical agglomeration (Farnand et al., 1961) and it takes place on the addition of a measured amount of bridging liquid that preferentially wets the solid surface, but is either immiscible with the suspending liquid or only sparingly soluble in it (Rosen, 1989). If the amount of bridging liquid is very small, voluminous flocs are obtained, whereas large amounts of bridging liquid yield a paste. Typically, 1.5 mL of surfactant led to droplet formation in the matrix fluid. The concentration of glass beads in suspension ranged from 0.05 to 0.4% by volume. Less concentrated suspensions took an inordinately long time to agglomerate (see eq 4), whereas more concentrated ones were such that it was difficult to distinguish individual agglomerates for the purpose of size determination. The initial, welldispersed suspension was prepared by first suspending 10 vol % glass beads in corn syrup in the presence of intense agitation. The solids concentration was then reduced by the addition of measured amounts of corn syrup and surfactant. Finally, the desired amount of deionized water was introduced to lower the shear viscosity. A 0.08-m-diameter, transparent, coaxial, cone-andplate device was fabricated locally using poly(methyl methacrylate) to shear the glass bead suspension at a constant shear rate (Chimmili, 1996). The cone, which had an angle of 4°, was the upper member and it was rotated with an electric motor. The maximum shear rate employed was ∼30 s-1; the use of higher shear rates, similar to a high suspending liquid viscosity, produced little agglomeration. Equipment limitations did not permit in situ determination of agglomerate size. Consequently, samples were sheared for different lengths of time up to 2 h. The rotation was periodically stopped, the cone removed, and a drop of the suspension withdrawn with the help of a 0.005-m diameter glass tube and placed on a glass slide with a circular cover glass. This glass slide was observed with a Fisher Stereomaster zoom microscope with a magnification range of 32× to 160× and with a field of view of ∼0.0018 m. A Minolta X-700 camera mounted on the microscope photo tube, in conjunction with a transmitted light source, was employed to take pictures of the sheared samples; all the photographs were taken at a constant magnification. Size calibration was done by photographing a glass slide with evenly spaced lines of known separation etched on it. The consequences of flow during removal of the upper plate of the shearing apparatus and during
Ind. Eng. Chem. Res., Vol. 37, No. 6, 1998 2075
Figure 1. Initial growth of agglomerates on shearing a suspension containing 0.4% glass beads at 3.4 s-1. The suspending liquid contains 10 vol % water and 1 mL surfactant per milliliter of glass beads.
sample removal were negligible because this flow is of very short duration, and the additional strain imposed on the suspension is small. Essentially equiaxed (i.e., nonelongated) agglomerates with a size distribution appeared on the pictures as black particles on a white background. Image analysis software (Image-Pro Plus) was utilized to measure the number average area of the particles. This measurement was set equal to πr2 to get the equivalent radius r of the agglomerates that appears in eq 8.
Figure 2. Influence of shear rate on agglomerate growth.
Results and Discussion The essential physics contained in the theoretical analysis presented here is that particulate agglomeration in laminar flow is the direct result of interparticle collisions resulting from a velocity gradient, and this is a phenomenon that is opposed by hydrodynamic forces. To qualitatively confirm the analysis, one needs to show that an initially well-dispersed suspension demixes on being sheared at a uniform shear rate. Indeed, it was found in our shearing experiments that the equivalent particle radius could easily double over the time period of 1 h. Typical experimental data, presented as ln R versus time, are shown in Figure 1 for short times and a low value of the shear rate. The data all lie on a straight line, confirming the validity of eq 4; the calculated value of is 0.165. In all other instances also, semilogarithmic plots of R as a function of time were internally consistent, straight lines. Note that if shearing is continued at these low shear rates, the agglomerates become so large that they ultimately settle because they can no longer remain in suspension. In general, as eqs 4 and 8 reveal, agglomerate growth rate should initially depend on the shear rate, the volume fraction of particulates, and the concentration of the bridging liquid. The suspending liquid viscosity influences not only the growth rate at longer times but also the equilibrium agglomerate size. The effect of these four variables was examined in a systematic manner. The influence of shear rate on agglomerate growth is shown in Figure 2 for three different shear rates for a suspension with 0.2 vol % glass beads in corn syrup containing 10% water and 1 mL of surfactant per milliliter of solids. As expected, the equilibrium ag-
Figure 3. Influence of volume fraction of glass beads on agglomerate growth.
glomerate size decreases as the shear rate increases. Furthermore, eq 8 fits the experimental data very well, and parameter values reveal that the sticking factor also decreases as the shear rate increases. This decrease occurs because the probability of a collision leading to particle bonding depends on the time of interparticle contact during the collision (Chesters, 1991). Increasing the shear rate while increasing the frequency of contact reduces the contact time and, consequently, lowers . The effect of changing the amount of glass beads in suspension while keeping the suspending liquid viscosity unaltered is portrayed in Figure 3 for three different volume fractions of glass beads. The ratio of surfactant volume-to-amount of glass beads is held fixed in order to keep the value of unchanged. Thus, the total amount of added surfactant changes as the solids
2076 Ind. Eng. Chem. Res., Vol. 37, No. 6, 1998
Figure 4. Influence of suspending liquid viscosity on agglomerate growth.
volume fraction is changed. In each of the three cases, the suspension was sheared at a fixed shear rate of 17.3 s-1. Equation 8 again fits the data quite well, and varying the amount of glass beads in suspension varies neither the equilibrium agglomerate size nor the sticking probability. The latter quantity is unchanged because the contact time does not change because the shear rate is fixed. Because is unchanged, initial agglomerate growth is faster for the more concentrated suspension due to an increase in the number of particleparticle collisions, in accord with eq 4. The equilibrium agglomerate size is independent of solids volume fraction because this fraction depends on a balance between the hydrodynamic forces and agglomerate strength, neither of which depend on the amount of glass beads. The result of changing the suspending liquid viscosity by changing the amount of added deionized water is shown in Figure 4. The shear rate is again 17.3 s-1, the same as in Figure 3. Both and the equilibrium agglomerate size increase with decreasing viscosity (higher water content), the former because of the ease with which the suspending liquid is squeezed out from between the colliding particles (Chesters, 1991) and the latter because of a reduction in the hydrodynamic forces. Finally, Figure 5 displays the effect of surfactant concentration on agglomerate growth. An increase in the amount of added surfactant should increase agglomerate strength and also make the particles more sticky. Both these expectations are realized as the equilibrium agglomerate size as well as increase with increasing surfactant concentration. Concluding Remarks The simple analysis of shear-induced demixing of an initially well-dispersed suspension in laminar flow appears to be verified by the uniform shearing experiments conducted as part of this research. This result is true for limited ranges of particulate volume fraction and shear rate. All the observations are consistent with expectations based on the physics of the phenomenon. Although the theory involves two parameters that have
Figure 5. Influence of amount of added surfactant on agglomerate growth.
to be determined by experiment, future work is aimed at obtaining their values from first principles. Work in progress involves extending the analysis to the technologically important situation of flow of suspensions in pipelines. Here the spatial variation of the shear rate gives rise to the additional phenomenon of migration of particles toward regions of lower shear rate. Acknowledgment Funding for this research was provided, in part, by the DuPont Company. Literature Cited Brown, D. L.; Glatz, C. E. Aggregate Breakage in Protein Precipitation. Chem. Eng. Sci. 1987, 42, 1831-1839. Capes, C. E. Basic Research in Particle Technology and Some Novel Applications. Can. J. Chem. Eng. 1976, 54, 3-12. Chesters, A. K. The Modelling of Coalescence Processes in FluidLiquid Dispersions: A Review of Current Understanding. Trans. I. Chem. E, Part I 1991, 69, 259-270. Chimmili, S. Shear Induced Agglomeration of Particulate Suspensions. MS Thesis, Chemical Engineering, West Virginia University, Morgantown, WV, 1996. Doraiswamy, D.; Gupta, R. K.; Chimmili, S. Particle Agglomeration and Migration Effects in Laminar Flow Systems. Preprints First AIChE/PPS Joint Topical Conference on Processing, Structure and Properties of Polymeric Materials, Chicago, IL, 1996; pp 92-94. Farnand, J. R.; Smith, H. M.; Puddington, I. E. Spherical Agglomeration of Solids in Liquid Suspension. Can. J. Chem. Eng. 1961, 39, 94-97. Hansen, S.; Ottino, J. M. Aggregation and Cluster Size Evolution in Nonhomogeneous Flows. J. Colloid Interface Sci. 1996, 179, 89-103. Hogg, R. Flocculation Phenomena in Fine Particle Dispersions. Adv. Ceramics 1987, 21: Ceramic Powder Science, 467-481. Kao, S. V.; Mason, S. G. Dispersion of Particles by Shear. Nature 1975, 253, 619-621. Kirkham, J. S. Particle Agglomeration in Non-Aqueous Suspending Media by a Dispersed Water Phase. MS Thesis, Chemical Engineering, West Virginia University, Morgantown, WV, 1979.
Ind. Eng. Chem. Res., Vol. 37, No. 6, 1998 2077 Levich, V. G. Physicochemical Hydrodynamics; Prentice Hall: Englewood Cliffs, NJ, 1962; p 207. Manas-Zloczower, I. Dispersive Mixing of Solid Additives. In Mixing and Compounding of Polymers; Manas-Zloczower, I., Tadmor, Z., Eds.; Hanser: Munich, Germany, 1994; pp 55-83. Pietsch, W. Successfully Use Agglomeration for Size Enlargement. Chem. Eng. Prog. 1966, 92, 29-45. Pietsch, W. Size Enlargement by Agglomeration; Wiley: Chichester, U.K., 1991. Powell, R. L.; Mason, S. G. Dispersion by Laminar Flow. AIChE J. 1982, 28, 286-293.
Rosen, M. J. Surfactants and Interfacial Phenomena; Wiley: New York, 1989; pp 352-353. Sparks, B. D.; Meadus, F. W. Spherical Agglomeration in a Conical Drum. Can. J. Chem. Eng. 1977, 55, 502-505.
Received for review September 10, 1997 Revised manuscript received January 26, 1998 Accepted January 27, 1998 IE9706368
