  We use lattice Boltzmann simulations to study the effect of shear on the
phase ordering of a two-dimensional binary fluid. The shear is imposed by
generalising the lattice Boltzmann algorithm to include Lees-Edwards boundary
conditions. We show how the interplay between the ordering effects of the
spinodal decomposition and the disordering tendencies of the shear, which
depends on the shear rate and the fluid viscosity, can lead to a state of
dynamic equilibrium where domains are continually broken up and re-formed.
