Solution of the Percus-Yevick equation in the coexistence region of a simple fluid

There has been much recent interest in the behavior of integral-equation theories for the distribution functions of a fluid near the critical point and in the two-phase region. For most systems, implementation of these theories necessitates numerical solution of the integral equations. However, for two examples, the adhesive hard sphere fluid in the Percus-Yevick approximation and the hard sphere plus Yukawa tail model in the mean spherical approximation, analytical solutions of the Ornstein-Zernike equation are available. In this work we consider the comparison of results obtained via numerical methods with the analytical solution of the Percus-Yevick equation for the adhesive hard sphere fluid. This complements a recent study by us of the mean spherical approximation for the hard sphere plus Yukawa tail fluid. This allows us to examine carefully how errors arise in the numerical solutions. We examine the accuracy of numerical calculations of the critical exponents as well as the interpretation of solutions obtained in the coexistence region. We discuss the implications of this work for applications to more realistic potentials where only numerical solutions are available.Paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.