Lattice Boltzmann simulations of segregating binary fluid mixtures in shear flow

We apply lattice Boltzmann method to study the phase separation of a two-dimensional binary fluid mixture in shear flow. The algorithm can simulate systems described by the Navier-Stokes and convection-diffusion equations. We propose a new scheme for imposing the shear flow which has the advantage of preserving mass and momentum conservation on the boundary walls without introducing slip velocities. We study how the steady Velocity profile is reached. Our main results show the presence of two typical length scales in the phase separation process, corresponding to domains with two different thicknesses.