On the VDW1 mixing rules applied to conformal binary mixtures at infinite dilution

Abstract

Henry's constant (HC) for a binary mixture, infinitely dilute in one of the components, is modelled according to the one-fluid conformal solution theory. This theory expresses linearly in closed form the HC in terms of certain thermodynamic properties of the pure solvent component, with coefficients that require knowledge of appropriate mixing rules for their evaluation. The VDW1 mixing rules produce good agreement with simulation data for many mixtures as characterized by size and well-depth ratios of the components; however, the agreement is poor for small values of these ratios. In this paper, a self-consistent approach to improving the performance of the VDW1 rules is presented and illustrated. Comparison with simulation data shows some improvement over the VDW1 rules in the exceptional regions, but some deterioration for large size ratios. One interesting by-product of this exercise is the discovery of an expression for the crosssection virial coefficient in terms of the corresponding pure component second virial coefficients (together with their temperature derivatives), valid for all two-parameter conformal potentials.