  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. Our main results concern the presence of two
typical lenght scales in the phase separation process, corresponding to domains
with two different thicknesses. Our simulations at low viscosity confirm
previous results only valid in the limit of infinite viscosity.
