Regularized phase-field model for description of dynamics of “solid-fluid” system

The presented work is devoted to the development of a mathematical model of the phase field type (with diffuse interface) for description of the dynamics of the “solid-fluid” system. The main balance relations are formulated using Euler description. Using the Coleman–Noll procedure, constraints are derived in the form of constitutive relations based on the second law of thermodynamics. A distinctive feature of the model is its preliminary quasi-hydrodynamic regularization.