Modelling of dendritic growth and bubble formation

A two-dimensional lattice Boltzmann method (LBM)-cellular automaton (CA) model is developed for the simulation of dendritic growth and bubble formation during alloy solidification. In the model, a kinetic LBM, which describes flow dynamics through the evolution of distribution functions of moving pseudo-particles, is adopted to numerically solve the gas-liquid two-phase flow based on the Shan-Chen multiphase scheme. The kinetics of dendritic growth is determined according to a local solute equilibrium approach. The present model takes into account the effect of liquid-solid phase transformation on the nucleation and growth of bubbles. The interaction mechanism between dendrites and bubbles is also embedded in the model. The wettability of a bubble on a smooth solid surface is simulated. The simulated contact angles with various interaction coefficients agree well with the data calculated from an empirical formula derived from the Young's equation. The proposed model is applied to simulate dendritic growth and bubble formation under directional solidification conditions. The simulated results are compared with those observed experimentally during solidification of a transparent organic material. The simulation results reveal some dynamic features of bubble nucleation, growth, and motion, as well as the interaction between the dendritic growth and bubble formation during solidification.