A lattice Boltzmann scheme able to model the hydrodynamics of phase separation and two-phase flow is described. Thermodynamic consistency is ensured by introducing a non-ideal pressure tensor directly into the collision operator. We also show how an external chemical potential can be used to supplement standard boundary conditions in order to investigate the effect of wetting on phase separation and fluid flow in confined geometries. The approach has the additional advantage of reducing many of the unphysical discretisation problems common to previous lattice Boltzmann methods.

11 pages, revtex, 4 Postscript figures, uuencoded