A Mass Conservative Lattice Boltzmann Model for Two-Phase Flows with Moving Contact Lines at High Density Ratio (Communications in Computational Physics, 2019)
In this paper, a mass conservative lattice Boltzmann model (LBM) is proposed to simulate the two-phase flows with moving contact lines at high density ratio.The proposed model consists of a phase field lattice Boltzmann equation (LBE) forsolving the conservative Allen-Cahn (A-C) equation, and a pressure evolution LBEfor solving the incompressible Navier-Stokes equations. In addition, a modified wallboundary treatment scheme is developed to ensure the mass conservation. The wetting dynamics are treated by incorporating the cubic wall energy in the expression ofthe total free energy. The current model is characterized by mass conservation, propertreatment of wetting boundary and high density ratio. We applied the model on a series of numerical tests including equilibrium droplets on wetting surfaces, co-currentflow and a droplet moving by gravity along inclined wetting surfaces. Theoreticalanalysis and experiments were conducted for model validation. The numerical resultsshow good performances on mass conservation even with a density contrast up to1000. Furthermore, the results show that the moving contact line can be successfullyrecovered, which proves that this model is applicable on the study of moving contactline issue and further related applications.
Keywords: Lattice Boltzmann model; two-phase flow; moving contact line; high density ratio.