Fluids inside a pore—an integral-equation approach

Abstract

Integral equations for density profiles of fluids inside a slit pore and a spherical pore are derived using an Ornstein-Zernike system of equations. For a hard-sphere fluid we specialize to a Percus-Yevick (PY) closure and a hypernetted-chain (HNC) closure, and also consider the BBGKY hierarchy with a kind of superposition-approximation (SA) closure. The bulk correlation needed in the OZ system of equations is obtained from the PY approximation. These approximations, which will be referred to as the PY/PY and the HNC/PY approximations and the BBGKY-SA scheme, are applied to a pure hard-sphere fluid. It is shown that the BBGKY-SA equation is the same as the HNC equation used with a simple approximation for bulk direct correlation functions. The density profiles, partition coefficients, and solvation forces for the hard-sphere fluids inside a slit and a spherical pore are calculated and compared with simulation results. It turns out that the PY/PY approximation gives us a better overall agreement with simulations than either the HNC/PY approximation or the BBGKY-SA scheme in the slit-pore system. However, the PY/PY approximation yields some unphysical results for high concentrations and certain values of the ratio of spherical-pore diameter to hard-sphere diameter, while the HNC/PY approximation is the best among the three approximations in the spherical-pore system when compared with simulation results. A non-local density-functional form of closure, introduced by Blum and Stell for the flat-wall problem, is also discussed, but not assessed numerically.