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 ̇ \.γ^-ν with an exponent ν<~1, where ̇ \.γ is the shear rate. The results are in qualitative agreement with recent molecular dynamics simulations. We discuss the physical implications of the results.
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Miyazaki et al. (2002) studied this question.