On the continuum mechanics of the motion of a phase interface

Abstract: "A recent series of papers [G, AG, GS] began an investigation whose goal is a thermomechanics of two-phase continua based on Gibbs's [sic] notion of a sharp phase-interface endowed with thermomechanical structure. In [G] a new 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. [AG] applied this theory to perfect conductors, in which the underlying equations reduce to a single evolution equation for the interface. [G] and [AG] were limited to rigid systems; [GS] extends the theory to include bodies that deform as they solidify or melt. These theories involve several new concepts, examples being: the creation of new material points; work intrinsic to a moving interface; the formulation of conservation laws for a moving interface. Here I shall discuss some of the new ideas involved in [GS]."