Lattice Boltzmann Simulations for Anisotropic Crystal Growth of a Binary Mixture
Phase field models are powerful tools to simulate the interfaces evolution in glass melt solidification mechanism, including crystallization phenomena. The purpose of this work is the numerical implementation of a phase field model for solidification of a dilute binary mixture by using the Lattice Boltzmann equations. The proposed Boltzmann method is based on the BGK approximation for kinetic equations relative to the phase field, supersaturation and temperature. In order to simulate the anisotropic term in the phase field equation, the equilibrium distribution function is a modification of the one used in the standard method for the advectiondiffusion equation. Simulations are carried out for anisotropic crystal growth for various thermal conditions, i.e., for several values of undercooling and different values of Lewis number.