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 $L_x\sim {\dot{\gamma }}^{-2\mathrm{/}3}$ and $L_y\sim {\dot{\gamma }}^{-3\mathrm{/}4}$. We discuss the relative roles of diffusivity and hydrodynamics in attaining steady state.