Extension of scaled particle theory to inhomogeneous hard particle fluids. II. Theory and simulation of fluid structure surrounding a cavity that intersects a hard wall

Integral equations describing the structure of a hard sphere fluid surrounding a cavity that intersects a hard wall are derived from scaled particle theory (SPT). The new expressions are solved exactly for specific cavity radii and the predictions are compared to simulation-generated results, showing excellent agreement. Additional simulation studies are conducted for cavity radii that fall outside the range of exact solution. For all cavity sizes, an enhancement of the local density of hard spheres over that of the hard wall contact value is seen for positions near the point of intersection of the cavity and the hard wall. The local density in front of the cavity and away from the hard wall is depleted at small cavity sizes, but eventually approaches the density profile created by a cavity placed within a bulk hard sphere fluid at larger cavity radii. The exact solutions and simulation results are also used to understand why a minimum appears in the inhomogeneous SPT function (G) over bar(lambda,h) [D. W. Siderius and D. S. Corti, preceding paper, Phys. Rev. E 71, 036141 (2005)].