The need for inertia in nonequilibrium steady states of sheared binary fluids

TL;DR

This study numerically investigates phase separation in sheared binary fluids, revealing that inertia leads to steady states with finite domain sizes, while inertia-less systems exhibit indefinite coarsening.

Contribution

It introduces a novel simulation method for sheared binary fluids and clarifies the role of inertia in stabilizing nonequilibrium steady states.

Findings

Inertial systems reach steady states with finite domain sizes.

Inertia-less systems show indefinite coarsening.

Analytical support explains the influence of inertia on steady states.

Abstract

We study numerically phase separation in a binary fluid subject to an applied shear flow in two dimensions, with full hydrodynamics. To do so, we introduce a mixed finite-differencing/spectral simulation technique, with a transformation to render trivial the implementation of Lees-Edwards sheared periodic boundary conditions. For systems with inertia, we reproduce the nonequilibrium steady states reported in a recent lattice Boltzmann study. The domain coarsening that would occur in zero shear is arrested by the applied shear flow, which restores a finite domain size set by the inverse shear rate. For inertialess systems, in contrast, we find no evidence of nonequilibrium steady states free of finite size effects: coarsening persists indefinitely until the typical domain size attains the system size, as in zero shear. We present an analytical argument that supports this observation, and that furthermore provides a possible explanation for a hitherto puzzling property of the nonequilibrium steady states with inertia.