The rheology of concentrated suspensions of spheres in simple shear flow by numerical simulation

Abstract

The newly developed simulation method known as Stokesian dynamics is used to investigate the rheological behaviour of concentrated suspensions. Both the detailed microstructure (e.g. pair-distribution function) and the macroscopic properties are determined for a suspension of identical rigid spherical particles in a simple shear flow. The suspended particles interact through both hydrodynamic and non-hydrodynamic forces. For suspensions with purely hydrodynamic forces, the increase in the suspension viscosity with volume fraction ϕ is shown to be caused by particle clustering. The cluster formation results from the lubrication forces, and the simulations of a monolayer of spheres show a scaling law for the cluster size: l c ∼ [1 − (ϕ/ϕ m ) ½ ] −1 , where ϕ m is the maximum volume fraction that can shear homogeneously. The simulation results suggest that the suspension viscosity becomes infinite at the percolation-like threshold ϕ m owing to the formation of an infinite cluster. The predicted simulation viscosities are in very good agreement with experiment. A suspension with short-range repulsive interparticle forces is also studied, and is seen to have a non-Newtonian rheology. Normal-stress differences arise owing to the anisotropic local structure created by the interparticle forces. The repulsive forces also reduce particle clustering, and as a result the suspension is shear-thickening.