Lattice Boltzmann modeling of bubble formation and dendritic growth in solidification of binary alloys

The cellular automaton (CA)-lattice Boltzmann (LB) coupled model is extended to three dimensions to study bubble formation and dendritic growth of binary alloys. The coupled model, with implicitly embedding the dendrite-bubble interaction, accounts for the gas precipitation and liquid-gas transition by the LB Shen-Chen scheme. Model validation is performed by simulating the Laplace law and the contact angle, and agreements are well-shown between simulation data and analytical expressions. Simulations of directional solidification is then carried out, reproducing several essential physical phenomena, including the nucleation of bubbles at the liquid/solid interface and the precipitation of small bubbles in the inter-dendritic region, which coincide qualitatively with the in situ experimental observation. There exist cooperative and competitive relationships between the dendritic growth and the bubble formation during solidification. The dendritic growth promotes the bubble nucleation at the initial stage, while a competition rises up at the latter stage. Altering the initial liquid density can obviously change the final microstructure, but hardly significantly influence the macroscopic statistical trends of solidification.