The bulk viscosity of suspensions

Abstract

The bulk viscosity of a suspension is defined analogous to that for a pure fluid as the constant of proportionality relating the deviation of the trace of the macroscopic stress from its equilibrium value to the average rate of expansion. In a suspension the equilibrium macroscopic stress is the sum of the thermodynamic pressure of the fluid and the osmotic pressure of the suspended particles. Rigid particles suspended in an expanding fluid cause a disturbance flow that contributes to the total mechanical pressure in the system, thereby changing the effective bulk viscosity. Expressions are derived to compute the effective bulk viscosity for all concentrations and all expansion rates for a system of rigid particles suspended in a uniformly expanding fluid. The expansion flow drives the suspension microstructure out of equilibrium and the thermal motion of the particles tries to restore the equilibrium. The Péclet number, defined as the expansion rate made dimensionless with the Brownian time scale, governs the departure of the microstructure from equilibrium. The contribution to bulk viscosity is determined to second order in volume fraction of particles for all compression rates (all negative Péclet numbers). A “compression thickening” of the suspension is observed at large compression rates.