Consistency conditions and equation of state for additive hard-sphere fluid mixtures

A number of consistency conditions for the contact values $gij(σij)$ of the pair correlation function of species i and j in an additive hard-sphere fluid mixture are discussed. It is shown that most of the theoretically-based expressions, as well as other more empirical in character, existing for these functions, fail to satisfy at least one of the conditions. It is suggested that one could improve the performance of the expressions for $gij(σij)$ and the equation of state by using the consistency conditions. This is illustrated by modifying the Boublı́k–Mansoori–Carnahan–Starling–Leland expressions for $gij(σij),$ which results in better predictions for these functions as well as for the compressibility factor and the fourth and fifth virial coefficients.