Circularly inhomogeneous fluids. Percus–Yevick hard disks: osmotic coefficients and tripletcorrelations

Abstract

For fluids in a circularly symmetric external field, it is shown that the two-dimensionalOrnstein–Zernike (OZ) convolution integral becomes a simple algebraic equation using therotationally invariant basis in two dimensions. Applying the usual closure relations, the fullinhomogeneous pair correlation functions become available. The method is here applied toa bulk uniform fluid of hard disks, using the pair Percus–Yevick (PY) closure, but at thetriplet level in the hierarchy of distribution functions. Consequently, the obtained pairdistribution function and the osmotic coefficient are better than the pervious results.