Generalised van der Waals theory of fluids. Vapour-liquid equilibria in simple binary mixtures

By accounting for both short and long range correlation effects to the lowest nontrivial order in density, a correction to the mean field approximation is developed within the generalised van der Waals free energy density functional theory. For bulk fluids the theory yields an analytic pressure explicit equation of state (up to a simple one-dimensional quadrature) that remains cubic in the density (or volume). The encouraging results obtained for pure simple fluids are largely found to carry over to the mixture case. In particular, the vapour-liquid coexistence regime of the phase diagram for a binary mixture has been verified by comparison with statistical mechanical simulation results as well as predictions of the song-Mason-Ihm and Peng-Robinson equations of state, and experimental observations. The importance of normalising for shifts in theoretical determinations of the critical surface is discussed.