Phase field lattice Boltzmann model for two-phase flow coupled with additional interfacial force

Abstract

The phase field model has become increasingly popular due to its underlying physics for describing two-phase interface dynamics. In this case, several lattice Boltzmann multiphase models have been constructed from the perspective of the phase field theory. All these models are composed of two distribution functions: one is used to solve the interface tracking equation and the other is adopted to solve the Navier-Stokes equations. It has been reported that to match the target equation, an additional interfacial force should be included in these models, but the scale of this force is found to be contradictory with the theoretical analysis. To solve this problem, in this paper an improved lattice Boltzmann model based on the Cahn-Hilliard phase-field theory is proposed for simulating two-phase flows. By introducing a novel and simple force distribution function, the improved model solves the problem that the scale of an additional interfacial force is not consistent with the theoretical one. The Chapman-Enskog analysis shows that the present model can accurately recover the Cahn-Hilliard equation for interface capturing and the incompressible Navier-Stokes equations, and the calculation of macroscopic velocity is also more efficient. A series of classic two-phase flow examples, including static drop test, droplets emerge, spinodal decomposition and Rayleigh-Taylor instability is simulated numerically. It is found that the numerical solutions agree well with the analytical solutions or the existing results, which verifies the accuracy and feasibility of the proposed model. In addition, the Rayleigh-Taylor instability with the imposed random perturbation is also simulated, where the influence of the Reynolds number on the evolution of the phase interface is analyzed. It is found that for the case of the high Reynolds number, a row of “mushroom” shape appears at the fluid interface in the early stages of evolution. At the later stages of evolution, the fluid interface presents a very complex chaotic topology. Unlike the case of the high Reynolds number, the fluid interface becomes relatively smooth at low Reynolds numbers, and no chaotic topology is observed at any of the later stages of evolution.