Ornstein–Zernike Relation and Percus–Yevick Approximation for Fluid Mixtures

A transformation of the Ornstein–Zernike relation for fluid mixtures is derived which involves the direct and indirect correlation functions only over the ranges within which the former are nonzero. Also, two closed expressions for the compressibility pressure in the Percus–Yevick (PY) approximation for mixtures are presented. The analytic solution of the PY approximation for mixtures of hard spheres follows immediately, and it is expected that the results should be of use in numerical calculations for systems with short-range forces, where the direct correlation functions normally tend rapidly to zero with increasing particle separation.