A geometrical theory of capillarity with applications to the Stefan problem

The definition of Van der Waals forces and their effect in the immediate proximity of the solid-liquid interface is the conceptual framework for the formulation of a new approach to the analysis of the interfacial phenomena. For a static interface the theory gives the classical results of Laplace while for moving interfaces and high values of the curvature it departs sensibly from it showing, in agreement with the results of Tolman and of Kirkwood et al., a clear dependence of the surface tension from the curvature of the interface. We derive, moreover, an explicit equation for the supercooling effect and, starting from the energy balance, an equation of evolution for the interface curvature. Some qualitative results, obtained from this equation with the aid of an energy method, are interpreted and discussed.