Classical multicomponent fluid structure near solid substrates: Born-Green-Yvon equation versus density-functional theory

We report a study of adsorption of binary mixtures of hard spheres of different sizes on a hard wall by using a version of density-functional theory, the Born-Green-Yvon (BGY) equation and Monte Carlo simulations. Following the BGY approach introduced by Fischer and Methfessel for single-component fluids, the proposed extension uses coarse-grained densities to approximate the contact values of pair distribution function of hard spheres. A procedure for evaluation of the coarse-grained densities, leading to an exact theory in one dimension, is proposed. The density-functional theory employed here, however, uses the Meister-Kroll and Groot approach. Comparisons of theoretical calculations with Monte Carlo simulations, as well as with previous theoretical predictions, have shown that density-functional theory reproduces the pseudo-experimental data accurately, even for extremely large size ratios of molecules of both species. The accuracy of the predictions of the BGY approach is less satisfactory, and for higher bulk fluid densities discrepancies with numerical simulations have been found.