Statistical mechanics of fluids at spherical structureless walls

Abstract

Statistical mechanical theories of spherical fluid interfaces are discussed in the context of fluids in contact with structureless walls. The thermodynamic route to the surface tension leads to a formula involving gradients of the external field, which is especially suited to the study of fluid-wall systems. The surface tension is found to be determined by the curvature dependence of the density in the region of the wall. For hard walls, potential distribution theory is used to obtain the exact relationship between the statistical mechanical surface tension expression and the grand potential. The accuracy of simple scaled particle theory calculations of the surface tension is estimated from predictions for the equation of state of pair potential fluids with hard core plus attractive tail interactions. Problems with the mechanical route to the curvature dependence of the surface tension are discussed. The planar wall and results for lower dimensionality are included in appendices.