Nonequilibrium steady states in sheared binary fluids

TL;DR

This study uses lattice Boltzmann simulations to explore steady shearing in binary fluids, revealing finite domain sizes and specific scaling behaviors under shear, with insights into the roles of diffusivity and hydrodynamics.

Contribution

It demonstrates the existence of steady states with finite domain sizes in sheared binary fluids and characterizes their scaling laws, contrasting some theoretical predictions.

Findings

Finite domain lengths are achieved under steady shear.

Scaling laws: Lx ~ γ̇^(-2/3), Ly ~ γ̇^(-3/4).

Hydrodynamics and diffusivity influence steady state attainment.

Abstract

We simulate by lattice Boltzmann the steady shearing of a binary fluid mixture undergoing phase separation with full hydrodynamics in two dimensions. Contrary to some theoretical scenarios, a dynamical steady state is attained with finite domain lengths $L_{x,y}$ in the directions ($x,y)$ of velocity and velocity gradient. Apparent scaling exponents are estimated as $L_{x}\sim\dot{\gamma}^{-2/3}$ and $L_{y}\sim\dot{\gamma}^{-3/4}$. We discuss the relative roles of diffusivity and hydrodynamics in attaining steady state.