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This paper proposes a simple and accurate lattice Boltzmann model forsimulating thermocapillary flows, which is able to deal with thermophysicalparameters contrasts. In this model, two lattice Boltzmann equations areutilized to solve the conservative Allen-Cahn equation and the incompressibleNavier-Stokes equations, while another lattice Boltzmann equation is used forsolving the temperature field, where the collision term is delicately designedsuch that the influence of the thermophysical parameters contrasts isincorporated. In contrast to previous lattice Boltzmann model forthermocapillary flows, the most distinct feature of the current model is thatthe forcing term used in the present thermal lattice Boltzmann equation is notneeded to calculate space derivatives of the heat capacitance or the orderparameter, making the scheme much simpler and also possible to retain the mainmerits of the lattice Boltzmann method. The developed model is firstlyvalidated by considering the thermocapillary flows in a heated microchannelwith two superimposed planar fluids. It is then used to simulatethermocapillary migration of a two-dimensional deformable droplet, and itsaccuracy is once again consistent with the theoretical prediction when theMarangoni number approaches zero. Finally, we numerically study the motion oftwo recalcitrant bubbles in a two-dimensional channel where the relationshipbetween surface tension and temperature is assumed to be a parabolic function.It is found that owing to the competing between the inertia and thermaleffects, the bubbles are able to move against the liquid's bulk motion andtowards areas with low surface tension.

Phase-field based lattice Boltzmann model for simulating thermocapillary flows