Density functional theory for spherical drops

Abstract

We have applied Sullivan's model to study the interfacial properties of a spherical drop embedded in a one-component fluid using the mean field approximation. We have examined the effect of drop size (expressed by the equimolar radius Re) on the density profile, pressure tensor, pressure difference Delta p across the interface, surface tension, Tolman's length, and density, pressure, and normal component of pressure tensor at the centre of the drop. Delta p is found to be an ill defined quantity in the sense that it can be defined in various ways, whose results coincide for large drops. The surface tension is a non-monotonic function of Re; it increases slowly from its flat interface value as Re decreases until a maximum value is attained, then it decreases rapidly. For small supersaturations, the drops are under tension and compression while at large supersaturations they are only under tension. The results of this theory are compared qualitatively with previous molecular dynamics simulations and theoretical calculations for drops.