Generalized conservative phase field model and its lattice Boltzmann scheme for multicomponent multiphase flows

Abstract

In this paper a generalized conservative phase field-lattice Boltzmann model is proposed for immiscible incompressible flows with any number of components. In this phase field model, the each phase field variable satisfies a generalized eikonal equation and the volume fraction constraint. By introducing a quadratic functional, the dynamics of phase field variables can be treated as a gradient flow method. The phase field equations are reformulated based on the mass conservative law and the reduction-consistency conditions. Moreover, based on the generalized free energy functional, a family of generalized continuous surface tension force formulations is deduced by using the virtual work method. A lattice Boltzmann model (LBM) is developed to solve the generalized conservative phase field equations and the hydrodynamics equations. In the numerical simulation section, the motion of circular interfaces and Poiseuille flow with four phases are simulated first. The convergence rate and reduction-consistent of present model for the phase field equations are validated. The computational accuracy of present model for the hydrodynamics equations is also validated. Then serval two-dimensional (2D) examples with pairwise surface tension effect, including the droplets immersed in another fluid with four fluid phases, spreading of liquid lenses and spinodal decomposition with four fluid phases, are simulated. The obtained numerical results are in good agreement with the analytical solutions. Four continuous surface tension force formulations are also comparative studied. Finally, as a practical application, a three-dimensional (3D) bubble rising in a three-layer liquid is investigated.