Molecular hydrodynamic theory of supercooled liquids and colloidal suspensions under shear

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 (gamma)over dot(-nu) with an exponent nuless than or equal to1, where (gamma)over dot is the shear rate. The results are in qualitative agreement with recent molecular dynamics simulations. We discuss the physical implications of the results.