Multiphase Thermomechanics with Interfacial Structure. 2. Evolution of an Isothermal Interface
Paper 1 [1988 g] of this series began an investigation whose goal is a thermomechanics of two-phase continua based on Gibbs’s notion of a sharp phase-interface endowed with thermomechanical structure. In that paper a balance law, balance of capillary forces, was introduced and then applied in conjunction with suitable statements of the first two laws of thermodynamics; the chief results are thermodynamic restrictions on constitutive equations, exact and approximate free-boundary conditions at the interface, and a hierarchy of free-boundary problems. The simplest versions of these problems (the Mullins-Sekerka problems) are essentially the classical Stefan problem with the free-boundary condition u = 0 for the temperature replaced by the condition u = h K, where K is the curvature of the free-boundary and h > 0 is a material constant. This dependence on curvature renders the problem difficult, and apart from numerical studies involving linearization stability, there are almost no supporting theoretical results.
KeywordsInterfacial Energy Capillary Force Interfacial Structure Polar Diagram Steady Motion
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