Numerical study on thermocapillary flows of power-law fluids with the lattice Boltzmann method

In this paper, we numerically simulate the thermocapillary motion of a two-phase non-Newtonian power-law fluid by using a phase-field-based lattice Boltzmann (LB) model. In this model, a total of three LB evolution equations are used to solve the macroscopic equations. One of them is used to solve the Allen-Cahn equation for describing the phase interface variation, one is used to solve the incompressible Navier-Stokes equation for describing the non-Newtonian power-law fluid dynamics. In addition, the last LB equation is used to solve the temperature field, where the collision terms are modified and improved to take into account the effect of thermodynamic parameter comparisons. In particular, we consider a parabolic relation rather than a linear one between the interfacial tension and the temperature in this study. Furthermore, two numerical cases were used to validate this LB model: the thermocapillary flow of two superposed planar fluids and the flow of power-law fluid between two parallel plates. It shows that the numerical solutions computed by this model agree well with the theoretical solutions, thus proving the accuracy and feasibility of this LB model. Afterward, we used this method to simulate the thermocapillary motion of bubbles in a microchannel filled with power-law fluids, and the results show that the model is accurate in studying two-phase power-law fluids. In addition, we consider the differences in flow patterns between Newtonian and non-Newtonian fluids and discuss the effects of factors such as viscosity ratios, temperature gradients, inlet velocities, and power-law index on the thermocapillary migration of bubbles. The results show that the above-mentioned factors have a great influence on the position, velocity, and equilibrium flow field of the bubbles.