Phase-field based lattice Boltzmann method for containerless freezing

In this paper, a lattice Boltzmann model is proposed to simulate solid-liquid phase change phenomena in multiphase systems. The model couples the thermal properties of the solidification front with the dynamics of the liquid droplet interface, which enables the description of the complex interfacial changes during solid-liquid phase change process. The model treats the interfaces of gas, liquid, and solid phases using the phase field order parameter and the solid fraction. The volume expansion or contraction caused by the change of properties such as density during phase change is represented by adding a mass source term to the continuum equation. The proposed model is first validated by the three-phase Stefan problem and the droplet solidification on a cold surface, and the numerical results are in good agreement with the analytical and experimental results. Then it is used to model the solidification problem with bubbles. The results show that the model is able to accurately capture the effect of bubbles on the solidification process, which is in good agreement with previous work. In addition, a parametric study is carried out to examine the dependence of the sessile droplet solidification on different physical and numerical parameters. The results show that the droplet solidification time increases with increasing droplet volume and contact angle.