Shear-induced diffusivity in supercooled liquids

The Taylor-Aris theory of shear diffusion predicts that the effective diffusivity of a tracer molecule in a sheared liquid is enhanced by a term quadratic in the shear rate. In sheared supercooled liquids, instead, the observed enhancement is linear in the shear rate. This is a fundamental observation for the physics of nonequilibrium liquids. Here, we derive a formula for the effective molecular diffusivity in supercooled liquids under shear flow based on the underlying Smoluchowski equation with shear (Smoluchowski diffusion-convection equation) with an energy barrier due to the crowded energy landscape. The obtained formula recovers the effective diffusivity with a correction term linear in the shear rate, in reasonable agreement with results from numerical simulations of different liquids as well as with earlier experimental results on shear melting of colloidal glass. The theory predictions are compared with molecular simulations of supercooled water and supercooled Lennard-Jones liquids. The comparison suggests that the predicted enhancement of diffusivity is inversely proportional to temperature and directly proportional to the zero shear viscosity.