Chapter 7 - Simple Fluid Mixtures

Abstract

We begin by deriving the entropy of ideal mixing of gases. The effect of intermolecular interactions on properties of simple fluid mixtures are revealed by the excess properties which are defined as deviations from ideal mixing. We note that pair-potentials needed for simple fluid mixtures are often obtained from mixing rules among which are found the Lorentz–Berthelot rules for Lennard-Jones parameters between species in terms of the single species' parameters. The one-fluid equations of state for mixtures are also obtained by mixing rules for, e.g., the a,b-parameters of the vdW equation of state. Regular solution theory is based on the assumption that the total molecular density remains constant as the composition of a binary mixture varies. The mean-field interaction energy can then be calculated for fixed T and variable composition and the conditions for a composition phase separation are readily obtained. The GvdW equations of state arise from “many-fluid” representations. While mean field binding energies are obtained as vdW one-fluid theories there is a choice of binary and linear mixing rules for the mixture excluded volume. The latter is simpler and generally preferred. The results of test calculations suggest that mixture binding energies are underestimated in the mean field approximation. This is usually the case but more so for mixtures, due to the presence of “composition correlation” which is illustrated.