The lattice Boltzmann method for the thermocapillary flow in a cavity under microgravity condition

In this paper an LBGK model for thermocapillary flow in microgravity is proposed. In the model two distribution functions are used for the velocity and temperature fields, respectively. Through the Chapman–Enskog expansion, the macroscopic equations for the thermocapillary flow can be recovered from the LBGK model. The boundary conditions for the thermocapillary flow are treated using the non-equilibrium extrapolation scheme. The model is validated by simulating the thermocapillary flow in a two-dimensional (2D) square cavity with a single free surface and differentially heated side walls.