Lattice Boltzmann simulation of the thermocapillary flow in an annular two liquid layers system with deformable interface

A hybrid model, coupling a finite difference method with a multiple-relaxation-time lattice Boltzmann method, integrating continuum surface force model and phase-field method, for axisymmetric two-phase thermocapillary flow with a deformable interface is developed. Thermocapillary flow, originating from an unbalanced surface tension along the interface of two immiscible liquids in an annular cavity with a horizontal temperature gradient, is simulated numerically. The dynamic behavior of the interface is captured using the phase-field method, and no a priori assumption is made regarding the interface shape and deformation. The continuum surface force model is adopted to add the unbalanced surface tension. The flow field is simulated by multiple-relaxation-time lattice Boltzmann method and both phase-field equation and the energy equation are solved by finite difference method. The dependence of fluid convection and interface deformation on the ratio of physical properties between the two liquid layers is investigated.