A Model for Non-Equilibrium Thermodynamic Processes Involving Phase Changes

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Abstract
In this paper we consider a mathematical model for the freezing of a binary alloy and generalize the model to represent any non-equilibrium thermodynamic process involving phase changes with diffusion but without convection. We assume that the fluxes in the diffusion process are linear in the corresponding gradients and that the phenomenological coefficients obey Onsager's reciprocal relations. We quote a theorem of Brezis which guarantees the existence of a weak solution for our model. In an appendix we indicate the relation of certain properties of our model to the requirements of classical thermodynamics.

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