Unified Approach to Evolution Equations for Non-isothermal Phase Transitions (original) (raw)

The purpose of the paper is to set up a scheme which embodies and generalizes a wide class of phase-transition models and, moreover, provides a direct approach which avoids ad-hoc assumptions. The starting view is that if the order parameter is a concentration then it satisfies an appropriate balance equation which is then a constraint expressed by a partial differential equation. The diffusion flux and the mass supply, as well as any constitutive function, are allowed to depend on the gradients up to third order. The body is allowed to be deformable and this places a mathematical problem about the representation of the total time derivative of higher-order gradients. The temperature field is allowed to depend on space and time variables. No additional fields are introduced. Consistent with the non-locality of the model, the thermodynamic analysis is based on a statement of the second law where the entropy flux is unknown and has to be determined. Non-locality, entropy flux and evol...