Macroscopic effects of microscopic roughness in suspensions

Abstract

We study a model suspension consisting of a monolayer of identical spheres in a viscous medium without Brownian effects. In the absence of inertia, and under the influence of finite forces, perfectly smooth spheres will never come into contact because of the strength of the lubrication interaction. Indeed, an interaction between two spheres is perfectly reversible. However, this ideal is not achieved in practice: careful experiments with just two spheres show that some irreversible interaction occurs. We treat this interaction as a simple contact between the spheres: we assume that they are microscopically rough and have surface asperities which are too sparse to affect the hydrodynamics of the system, but which prevent the particles from approaching beyond some nominal surface separation. For a dilute suspensions in steady shear flow, a calculation to order c(2) in the particle area concentration shows that roughness actually lowers the viscosity of the suspension relative to its value for smooth spheres; this is because the excluded parts of configuration space are those with very close particles, where the lubrication layers cause high dissipation. Negative normal stress differences are also introduced by the roughness. At higher concentrations we use Stokesian Dynamics to simulate the suspension dynamics. We find that rough- ness increases the viscosity above an area concentration of around 40% and the normal stress differences be- come very sensitive to particle configuration, and fluctuate strongly with time.