The phase field method—From fundamentals to practical applications in crystal growth

In this paper, the phase-field method is described and used to model ice crystal growth that is studied in Chemical Engineering in the freezing or freeze-drying process. Two mains partial differential equations are developed on the entire domain consisting of the liquid phase, the solid one, and the interface: (i) The Allen Cahn equation that describes the evolution of the phase field and (ii) the energy balance. In this paper, we explain how to preserve the thermodynamic consistency of the system to model quantitatively ice crystal growth, in particular concerning the choice of the free energy density. Several constitutive equations are used to model the specific properties of ice and water. Simulations are performed in 2D domain using Euler discretization for time to solve the system equations. A complete discussion is made concerning the “best way” to choose the main parameters for the simulation with respect to several physical properties like the interfacial tension of ice/liquid water or the equilibrium stability conditions. Finally, freezing simulations are presented and the potential of the phase field method in Chemical Engineering is discussed.