Here I will describe a theory for predicting the effect of interparticle interactions on the macroscopic properties of concentrated colloidal dispersions. The main focus will be on the calculation of the low-shear viscosity. An applied shear flow distorts the positions of the particles from their equilibrium configuration. Ensemble averages of hydrodynamic and interparticle forces over this new distribution then provide predictions for the suspension properties.

A configuration-space conservation equation for the pair density P_2 provides a fundamental basis for calculating the nonequilibrium microstructure; however, it requires including three-body couplings. The resulting many-body forces depend on the three-particle distribution function, necessitating an additional equation to completely specify P_2. Nonequilibrium PY and HNC closures relate the many-body forces to the pair density and conditional averages account for hydrodynamic interactions. The results are predictions of the nonequilibrium structure and low-shear viscosity as a function of volume fraction for various repulsive potentials. Different approximations for the hydrodynamic interactions ranging from complete neglect to mean-field and lubrication approximations allow calculation of the contributions to the viscosity of both interparticle and hydrodynamic forces. The approach described here can be extended to arbitrary interparticle interactions, polydisperse systems, and large shear rates.