Thermal Kinetics Phase Field Model for the Metals' Solidification - Mathematic Derivation of the Dendrite Growth Phase Field Variable Diffusion Model

Abstract

Phase field equations for simulation of dendritic growth have a history of nearly twenty years. The existing phase field equations are directly derived through the Ginzburg-Landau equations. However, though widely used, the physical meaning of each variable in the equations is not clear. So the domestic and foreign researchers have made a lot of mistakes and interpretation. In this paper, with the solid fraction as a phase field variables in the field, based on thermodynamics and heat transfer theory, author gives a rigorous scientific phase variable diffusion model of the pure metal solidification and its derivation process.