Viscosity and Diffusion of Concentrated Hard-Sphere-Like Colloidal Suspensions

Abstract

We present explicit theoretical results for the viscosity and diffusion coefficient of concentrated hard-sphere-like colloidal suspensions. Our results are based on two relevant physical processes that take place on two widely separated time scales. At short times, τ _B ∼ t ≪ τ _P , with the Brownian time τ _B ∼ 1 ns and the Péclet time τ _B ∼ 1 ms, the dominant process is the so-called cage-diffusion. The colloidal particles are locked up in cages and the difficulty to escape out of one cage and into the next is related to the deformability of the cage. This process has a collective character reflected in the fact that each particle inside a cage is at the same time a wall particle of a neighboring cage and the escape rate is determined by the short-time collective diffusion coefficient for which we present an explicit expression. At long times, t ≪ τ _P , the dominant process is a coupled relaxation mechanism as described by the mode-coupling theory, via two slowly decaying modes associated with conserved single-particle or collective dynamical variables. We present closed expressions for the long-time wavenumber dependent self and collective diffusion coefficients and for the Newtonian and frequency dependent viscosity and compare them with a variety of experimental and computational results.