Structure and stress in spherical microstructures

Abstract

An integral theory and gradient theory of inhomogeneous fluid are used to predict the structure of spherical interfaces. The nonlinear integral and differential equations of the theories are solved by using state-of-the-art finite element techniques, coupled with Newton’s method. The numerical method, discussed at some length, is suggested as a potential tool for solving other nonlinear problems of fluid statistical mechanics. Results of integral and gradient theories are compared and found to be in qualitative agreement and, on the strength of this agreement, gradient theory is used to describe and analyze the structure and stress in microscopic spherical drops. Predictions from gradient theory indicate a breakdown of the Young–Laplace equation for drops smaller than about ten molecules wide. However, contrary to the usual estimate of the curvature dependence of surface tension, the surface tension of even very small drops (say, three or four molecules wide) is found to deviate little from the tension of a planar interface.