A Molecular Hydrodynamic Theory of Supercooled Liquids and Colloidal Suspensions under Shear

Abstract

We extend the conventional mode-coupling theory of supercooled liquids to systems under stationary shear flow. Starting from generalized fluctuating hydrodynamics, a nonlinear equation for the intermediate scattering function is constructed. We evaluate the solution numerically for a model of a two dimensional colloidal suspension and find that the structural relaxation time decreases as $\dotγ^{-ν}$ with an exponent $ν\leq 1$, where $\dotγ$ is the shear rate. The results are in qualitative agreement with recent molecular dynamics simulations. We discuss the physical implications of the results.