Summary
A quantitative theory developed herein for the rheology of concentrated colloidal dispersions accounts for the nature and effect of potential, as well as hydrodynamic, interactions. A configuration-space consemation equation for the pair density P2 provides a fundamental basis for calculating the nonequilibrium microstructure under shear, including three-body couplings due to the pairwise additive interparticle potential. The resulting many-body forces depend on the three-particle distribution function, necessitating an additional equation to completely specify P2. A nonequilibrium closure based on the hypernetted chain (HNC) equilibrium closure relates these forces to the interparticle force and pair distribution function completing the formulation. A computational algorithm exploiting Fast Fourier Transforms solves the resulting integro-differential equations for weak flows, yielding the perturbed pair density as a function of the volume fraction o and the inter-particle potential. Calculation of the stresses is then straightforward.
First, we present the low-shear limiting viscosity as a function of o for hard, soft, and charged spheres without hydrodynamic interactions and demonstrate satisfactory agreement with the limited results available from computer simulations and experiment. Second, we incorporate rescaled hydrodynamic mobilities and the viscous stress, based on extant results for the short-time self-diffusion coefficient and the high frequency limiting viscosity, tb account for hydrodynamic interactions. The corresponding predictions of the low shear viscosity for hard spheres lie within 20% of extensive experimental data for 0 < o < 0.60.