  This paper proposes a simple and accurate lattice Boltzmann model for
simulating thermocapillary flows, which is able to deal with thermophysical
parameters contrasts. In this model, two lattice Boltzmann equations are
utilized to solve the conservative Allen-Cahn equation and the incompressible
Navier-Stokes equations, while another lattice Boltzmann equation is used for
solving the temperature field, where the collision term is delicately designed
such that the influence of the thermophysical parameters contrasts is
incorporated. In contrast to previous lattice Boltzmann model for
thermocapillary flows, the most distinct feature of the current model is that
the forcing term used in the present thermal lattice Boltzmann equation is not
needed to calculate space derivatives of the heat capacitance or the order
parameter, making the scheme much simpler and also possible to retain the main
merits of the lattice Boltzmann method. The developed model is firstly
validated by considering the thermocapillary flows in a heated microchannel
with two superimposed planar fluids. It is then used to simulate
thermocapillary migration of a two-dimensional deformable droplet, and its
accuracy is once again consistent with the theoretical prediction when the
Marangoni number approaches zero. Finally, we numerically study the motion of
two recalcitrant bubbles in a two-dimensional channel where the relationship
between surface tension and temperature is assumed to be a parabolic function.
It is found that owing to the competing between the inertia and thermal
effects, the bubbles are able to move against the liquid's bulk motion and
towards areas with low surface tension.
