Quadratic mixing rules for equations of state. Origins and relationships to the virial expansion

Hall, K.R., Iglesias-Silva, G.A. and Mansoori, G.A., 1993. Quadratic mixing rules for equations of state. Origins and relationships to the virial expansion. Fluid Phase Equilibria, 91: 67-76. Quadratic mixing rules, originally proposed by van der Waals, are used extensively in mixture calculations involving equations of state. Several ways exist to derive such mixing rules from the principles of statistical mechanics or merely classical thermodynamic arguments. In this report we relate the quadratic mixing rules to the rigorous mixing rules for virial coefficients of mixtures. The virial equation of state having a precise basis in statistical mechanics provides theoretical guidance for formulations of equations of state. In addition, the mixture combining rules for the virial coefficients are rigorous. The thesis of this paper is that, if multibody interactions occur in certain ways, the mixing rules for all virial coefficients become identical to the quadratic mixing rule for the second virial coefficient. This implies that quadratic mixing rules should be universal for coefficients (or their combinations) of equations of state.