Nonisothermal phase separation based on a microforce balance

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Our aim in this article is to derive models for nonisothermal phase separation. Starting from the two fundamental laws of thermodynamics, we consider the approach of Gurtin, based on a balance law for microforces, to derive nonisothermal Cahn-Hilliard type equations. These equations extend previous models derived by Alt and Pawlow based on an entropy principle to nonisotropic materials and to systems that are far from equilibrium. We also extend this approach to the Ginzburg-Landau (Allen-Cahn) equation, for which we recover, as particular cases, some models obtained by Fremond with a physically different approach.