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Dynamic simulation of suspensions of non-Brownian hard spheres

Published online by Cambridge University Press:  26 April 2006

D. I. Dratler  and
W. R. Schowalter
D. I. Dratler
Affiliation:
Department of Chemical Engineering, University of Illinois, Urbana, IL 61801, USA Present address: Exxon Production Research Company, P.O. Box 2189, Houston, TX 77252-2189, USA.
W. R. Schowalter
Affiliation:
Department of Chemical Engineering, University of Illinois, Urbana, IL 61801, USA
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Abstract

In this work, we investigate the suitability of models based solely on continuum hydrodynamics for Stokesian Dynamics simulations of sheared suspensions of non-Brownian hard spheres. The suspensions of interest consist of monolayers of uniform rigid spheres subjected to a linear shear field. Areal fractions ranged from ϕa = 0.2 to 0.6. For these suspensions, two sets of Stokesian Dynamics simulations were performed. For the first set, particle interactions were assumed to be strictly hydrodynamic in nature. These simulations are analogous to those of Brady & Bossis (1985) and Chang & Powell (1993). For the second set of simulations, particles were subjected to both hydrodynamic and short-range repulsive forces. The repulsion serves as a qualitative model of non-hydrodynamic effects important when particle separation distances are small. Results from both sets of simulations were found to be within the range of established experimental data for viscosities of suspensions. However, simulations employing the pure hydrodynamic model lead to very small separation distances between particles. These small separations give rise to particle overlaps that could not be eliminated by time-step refinement. The instantaneous number of overlaps increased with density and typically exceeded the number of particles at the highest densities considered. More critically, for very dense suspensions the simulations failed to approach a long-time asymptotic state. For simulations employing a short-range repulsive force, these problems were eliminated. The repulsion had the effect of preventing extremely small separations, thereby eliminating particle overlaps. At high concentrations, viscosities computed using the two methods are significantly different. This suggests that the dynamics of particles near contact have a significant impact on bulk properties. Furthermore, the results suggest that a critical aspect of the physics important at small particle separation distances is missing from the pure hydrodynamic model, making it unusable for computing microstructures of dense suspensions. In contrast, simulations employing a short-range repulsive force appear to produce more realistic microstructures, and can be performed even at very high densities.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 325 , 25 October 1996 , pp. 53 - 77
Copyright
© 1996 Cambridge University Press

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References

Allen, M. P. & Tildesley, D. J. 1987 Computer Simulation of Liquids. Clarendon Press.
Batchelor, G. K. 1970 The stress system in a suspension of force-free particles. J. Fluid Mech. 41, 545–570.Google Scholar
Bonnecaze, R. T. & Brady, J. F. 1992 Dynamic simulation of an electrorheological fluid. J. Chem. Phys. 96, 2183–2202.Google Scholar
Bossis, G. & Brady, J. F. 1984 Dynamic simulation of sheared suspensions. I. General method. J. Chem. Phys. 80, 5141–5154.Google Scholar
Bossis, G. & Brady, J. F. 1989 The rheology of Brownian suspensions. J. Chem Phys. 91, 1866–1874.Google Scholar
Brady, J. F. & Bossis, G. 1985 The rheology of concentrated suspensions of spheres in simple shear flow by numerical simulation. J. Fluid Mech. 155, 105–129.Google Scholar
Brady, J. F. & Bossis, G. 1988 Stokesian Dynamics. Ann. Rev. Fluid Mech. 20, 111–157.Google Scholar
Brady, J. F., Phillips, R. J., Lester, J. C. & Bossis, G. 1988 Dynamic simulation of hydrodynamically interacting suspensions. J. Fluid Mech. 195, 257–280.Google Scholar
Chang, C. & Powell, R. L. 1993 Dynamic simulation of bimodal suspensions of hydrodynamically interacting spherical particles. J. Fluid Mech. 253, 1–25.Google Scholar
Chang, C. & Powell, R. L. 1994 The rheology of bimodal hard-sphere dispersions. Phys. Fluids 6, 1628–1636.Google Scholar
Conte, S. D. & Boor, C. de 1980 Elementary Numerical Analysis: An Algorithmic Approach. McGraw-Hill.
Dratler, D. I., Schowalter, W. R. & Hoffman, R. L. 1996 Dynamic simulation of shear thickening in concentrated colloidal suspensions. J. Fluid Mech. (submitted).Google Scholar
Durlofsky, L. J. & Brady, J. F. 1989 Dynamic simulation of bounded suspensions of hydrodynamically interacting particles. J. Fluid Mech. 200, 39–67.Google Scholar
Durlofsky, L., Brady, J. F. & Bossis, G. 1987 Dynamic simulation of hydrodynamically interacting particles. J. Fluid Mech. 180, 21–49.Google Scholar
Heyes, D. M. & Melrose, J. R. 1993 Brownian dynamics simulations of model hard-sphere suspensions. J. Non-Newtonian Fluid Mech. 46, 1–28.Google Scholar
Lewis, T. B. & Nielsen, L. E. 1968 Viscosity of dispersed and aggregated suspensions of spheres. Trans. Soc. Rheol. 12, 421–443.Google Scholar
Phung, T. & Brady, J. F. 1991 Microstructured fluids: structure, diffusion and rheology of colloidal dispersions. In Slow Dynamics of Condensed Matter (ed. K. Kawasaki, M. Tokuyama & T. Kawakatsu). AIP.
Russel, W. B., Saville, D. A. & Schowalter, W. R. 1989 Colloidal Dispersions. Cambridge University Press.
Sengen, M. Z. & Probstein, R. F. 1989 High-shear-limit viscosity and the maximum packing fraction in concentrated monomodal suspensions. PhysicoChem. Hydrodyn. 11, 229–241.Google Scholar
Thomas, D. G. 1965 Transport characteristics of suspension: VIII. A note on the viscosity of Newtonian suspensions of uniform spherical particles. J. Colloid Sci. 20, 267–277.Google Scholar