Improved three-dimensional multiple-relaxation-time color-gradient lattice Boltzmann finite-difference model for thermocapillary flows

This study is devoted to developing a color-gradient lattice Boltzmann model capable of simulating thermocapillary flows with variable properties. To achieve the purpose, some modified work is conducted. The equilibrium distribution function for density is modified in the developed model. The scheme of multiple-relaxation-time is applied to deal with the single-phase and perturbation collision operators to enhance the algorithm stability, and a simple correction term is incorporated into the single-phase operator. In addition, the finite-difference method is adopted to solve the temperature field. The developed model is first used to simulate the layered two-phase flow in a horizontal channel to test the density ratio that can be achieved without temperature effect. Then two classical thermocapillary flow problems of thermocapillary-driven flow in a heated microchannel and thermocapillary migration of a deformable droplet or bubble are simulated, and the model is proven to successfully simulate the thermocapillary flows with density ratios up to 10.