Dynamic simulation of bimodal suspensions of hydrodynamically interacting spherical particles

Abstract

Stokesian dynamics is used to simulate the dynamics of a monolayer of a suspension of bimodally distributed spherical particles subjected to simple shearing flow. Hydrodynamic forces only are considered. Many-body far-field effects are calculated using the inverse of the grand mobility matrix. Near-field effects are calculated from the exact equations for the interaction between two unequal-sized spheres. Both the detailed microstructure (e.g. pair-distribution function and cluster formation) and the relative viscosity are determined for bimodal suspensions having particle size ratios of 2 and 4. The flow of an ‘infinite’ suspension is simulated by considering 25, 49, 64, and 100 particles to be ‘one’ cell of an infinite periodic array. The effects of both the size ratio and the relative fractions of the different-sized particles are examined. When the area fraction, ϕa, is less than 0.4 the particle size distribution does not affect the calculated viscosity. For ϕa > 0.4, and for a fixed fraction of small spheres, the bimodal suspensions generally have lower viscosities than monodispersed suspensions, with the size of this effect increasing with ϕa. These results compare favourably with experiment when ϕa and the volume fraction, ϕv, are normalized by the maximum packing values in two and three dimensions, respectively. At the microstructural level, viscosity reduction is related to the influence of particle size distribution on the average number of particles in clusters. At a fixed area fraction, the presence of smaller particles tends to reduce average cluster size, particularly at larger ϕa, where significant viscosity reductions are observed. Since the presence of large clusters in monodispersed suspensions has been directly linked to high viscosities, this provides a dynamic mechanism for the viscosity reduction in bimodal suspensions.