Reduction-consistent multiple-relaxation-time lattice Boltzmann equation method for wall bounded N immiscible incompressible fluids

Abstract

A multiple-relaxation-time (MRT) lattice Boltzmann equation (LBE) method is developed for N-phase (N≥ 2) flow with moving contact lines. In the model, MRT LBE is applied to solve the incompressible Navier-Stokes equation, and another MRT LBE is developed for fluid-fluid interface capturing, where the MRT LBE has the reduction-consistent property and can guarantee the mass conservation of each phase. The wettability of solid in the presence of N (N≥ 2) immiscible fluids can be achieved by a reduction-consistent wettability boundary condition, which can treat different contact angle between the fluids and the solid. A series of benchmark tests such as spreading of droplets and compound droplet on a solid wall, and compound droplet impact on a dry solid wall are conducted to validate the MRT LBEs, and it is shown that the predictions of LBE agree well with the theory/other numerical results.