Reduction-consistent phase-field lattice Boltzmann equation for N immiscible incompressible fluids.

Abstract

In this paper, we develop a reduction-consistent conservative phase-field method for interface-capturing among N (N≥ 2) immiscible fluids, which is governed by conservative Allen-Cahn equation (CACE); here the reduction-consistent property is that if only M (1≤M≤N-1) immiscible fluids are present in a N-phase system, the governing equations for N immiscible fluids must reduce to the corresponding M immiscible fluids system. Then we propose a reduction-consistent lattice Boltzmann equation (LBE) method for solving N immiscible incompressible fluids with high density and viscosity contrasts. Some numerical simulations are carried out to validate the present LBE such as stationary droplets, spreading of a liquid lens, and spinodal decomposition together with the reduction-consistent property, and the numerical results predicted by present LBE are in good agreement with the analytical solutions/other numerical results, which also demonstrate the reduction-consistent property by present LBE.