Nonequilibrium Steady States in Sheared Binary Fluids

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 ${L}_{x}\ensuremath{\sim}{\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{\ensuremath{\gamma}}}^{\ensuremath{-}2/3}$ and ${L}_{y}\ensuremath{\sim}{\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{\ensuremath{\gamma}}}^{\ensuremath{-}3/4}$. We discuss the relative roles of diffusivity and hydrodynamics in attaining steady state.