Nonequilibrium steady states in sheared binary fluids

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 Lx approximately gamma (-2/3) and Ly approximately gamma(-3/4). We discuss the relative roles of diffusivity and hydrodynamics in attaining steady state.