Supercooled Liquids Under Shear: Theory and Simulation

TL;DR

This paper develops a generalized mode-coupling theory and performs simulations to study how shear flow affects supercooled liquids, revealing shear-induced acceleration of relaxation and viscosity reduction.

Contribution

It introduces a theoretical framework combining fluctuating hydrodynamics with shear flow and validates it through numerical simulations near the glass transition.

Findings

Shear significantly reduces structural relaxation time.

Shear viscosity decreases with shear rate as a power law.

Dynamics remain nearly isotropic despite shear flow.

Abstract

We analyze the behavior of supercooled fluids under shear both theoretically and numerically. Theoretically, we generalize the mode-coupling theory of supercooled fluids to systems under stationary shear flow. Our starting point is the set of generalized fluctuating hydrodynamic equations with a convection term. A nonlinear integro-differential equation for the intermediate scattering function is constructed. This theory is applied to a two-dimensional colloidal suspension. The shear rate dependence of the intermediate scattering function and the shear viscosity is analyzed. We have also performed extensive numerical simulations of a two-dimensional binary liquid with soft-core interactions near, but above, the glass transition temperature. Both theoretical and numerical results show: (i) A drastic reduction of the structural relaxation time and the shear viscosity due to shear. Both the structural relaxation time and the viscosity decrease as $\dot{\gamma}^{-\nu}$ with an exponent $\nu \leq 1$, where $\dot{\gamma}$ is the shear rate. (ii) Almost isotropic dynamics regardless of the strength of the anisotropic shear flow.