Abstract.The purpose of the paper is to set up a model for the non-isothermal transition between incompressible phases. The scheme involves an order parameter as a phase field. Because of the incompressibility the phase field is identified with the volume fraction occupied by one of the phases. As a whole, the phases are regarded as a reacting mixture. The paper develops the analysis of the thermodynamic restrictions and provides a set of relations for the constitutive equations. The free energy is shown to play the role of a potential which provides the entropy and enters the diffusion flux and the mass growth of the transition. This in turn determines the evolution equation for the phase field. As an application, Clapeyron's equation is shown to follow for the temperature-pressure relation at equilibrium between the phases.

Received: May 30, 2007

AMS Subject Classification: 74N25, 74A50, 80A22

Key Words and Phrases: phase field, incompressible phases, evolution equation

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 39
Issue: 4