Dynamic simulation of suspensions of non-Brownian hard spheres

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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.

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