A Boundary-Layer Theory for the Dynamics and Thermodynamics of Phase-Interfaces

Abstract

Existing continuum physical theories of phase boundaries model these as mass, momentum, energy and entropy carrying non-material singular surfaces. The physical interpretation of these surface fields is not well understood and leads in fact to misleading results. Real phase interfaces are thin boundary-layers across which all bulk fields experience smooth though rapid changes when crossing from one phase to the other. This is modelled in a new boundary-layer theory for curved phase boundaries. Comparison with the theory of singular surfaces allows physical interpretation of the surface fields in terms of mean values of bulk fields, but it also requires satisfaction of dynamical consistency conditions for tangential momentum and surface stress. These yield new results for the curvature dependence of surface tension, for phase-change processes and the dynamics of nucleation. A stability analysis proves the impossibility of certain nuclei. Some descriptive applications to ice formation in nature and to the phenomena of undercooling and superheating corroborate the new results