Dense Suspension Rheology

This year's research on the behavior of concentrated suspensions has focused on the connection between viscous suspensions and granular media - from wet to dry - as it pertains to mixing. Here 'mixing' is quantified in its most primitive form - the diffusive motion of the particles. Diffusion is one of the most basic and elemental transport processes and is responsible for the molecular mixing of different chemical species. For a small sub-micron- or nano-sized colloidal particle, the diffusivity is given by the Stokes-Einstein formula relating the diffusivity to the thermal energy times the hydrodynamic mobility. The self-diffusivity decreases as the concentration of nanoparticles increases owing to the crowding effect of near neighbors. As the diffusing species increases in size from a nanoparticle to a several micron-sized colloidal particle, the stirring of the background fluid can give rise to another mechanism of transport - 'shear-induced' diffusion. Here, hydrodynamic interactions among particles promote mixing and the self-diffusivity now scales as the particle size squared times the shear rate. In this regime, the self-diffusivity is an increasing function of concentration since particle-particle 'collisions' are responsible for the diffusive motion. At still large particle size (millimeter or larger), the inertia of the particles becomes important, direct particle-particle collisions dominate, and the self-diffusivity now behaves like that in a dense gas with the diffusivity proportional to the mean-free path times the square root of the 'granular temperature', the latter of which is set by the stirring motion and the energy dissipated upon collision. As in a dense gas, the self-diffusivity now decreases with increasing particle concentration. The physical origin of these various behaviors, the dependence of the self-diffusivity on shear rate and particle concentration and their implications for mixing and particle distributions in inhomogeneous flows is discussed in this report.