Lattice Boltzmann simulations of phase separation in chemically reactive   binary fluids
  We use a lattice Boltzmann method to study pattern formation in chemically reactive binary fluids in the regime where hydrodynamic effects are important. The coupled equations solved by the method are a Cahn-Hilliard equation, modified by the inclusion of a reactive source term, and the Navier-Stokes equations for conservation of mass and momentum. The coupling is two-fold, resulting from the advection of the order-parameter by the velocity field and the effect of fluid composition on pressure. We study the the evolution of the system following a critical quench for a linear and for a quadratic reaction source term. Comparison is made between the high and low viscosity regimes to identify the influence of hydrodynamic flows. In both cases hydrodynamics is found to influence the pathways available for domain growth and the eventual steady-states. 
K.Furtado, J.M.Yeomans