ANALYTICAL SOLUTION OF THE ORNSTEIN-ZERNIKE EQUATION FOR MIXTURES

Solution of the Ornstein-Zernike equation under the Percus-Yevick or the mean spherical approximation is presented analytically in a matrix form. The new solution is an extension of the general Ornstein-Zernike solution suggested recently for pure fluids. The development is based on further application of the Hilbert transform and multiple-dimensional space analysis. In addition to the potential matrix, only a hard core correlation function matrix and its inverse are involved in the expression. The solution achieved in this work is explicit and is applicable to any arbitrary potential functions with an additive hard core. The first-order solution for two Yukawa mixtures has been compared with the full solution reported in the literature to serve as an example.