Phase change interactions and singular fronts

Abstract

The balances of mass, linear momentum and energy for a continuum provide jump relations between values of the physical variables on the two sides of a singular surface, either a boundary of the medium or an interior surface. In the case of a mixture, an overlap of interacting continua, there are jump relations for each constituent. While an elementary phase change front across which one phase of a constituent is transformed completely to a different phase can be treated as a single constituent, more general situations have co-existing phases on one side of the front, each with their own density, velocity, stress and internal energy fields, which must be treated as separate constituents. The phase change is now a mass transfer between constituents which becomes a surface production term in the mass balance jump relation for each constituent. In turn this implies surface production contributions to the momentum and energy relations associated with the surface mass transfer, including interaction body force and energy transfer contributions as well as the direct transfer terms. The general jump relations with such surface production contributions are formulated, and are illustrated for a number of situations arising in polythermal ice sheets and wet snow packs.