Phase-field lattice Boltzmann model for interface tracking of a binary fluid system based on the Allen-Cahn equation

Abstract

A lattice Boltzmann (LB) model is proposed to track the interface of binary fluid system based on the conservative-form Allen-Cahn (A-C) equation for phase field. Utilizing an equilibrium distribution function and a modified LB equation, this model is able to correctly recover the conservative A-C equation through the Chapman-Enskog analysis. A series of two-dimensional (2D) and three-dimensional (3D) phase-capturing benchmark tests have been conducted for validation, which include the diagonal translation of a circular interface, the rigid-body rotation of a Zalesak disk, and the deformation of 2D circular interface and 3D spherical interface in shear flows, all illustrating better accuracy and stability of the proposed model than the previous models tested. By coupling the incompressible hydrodynamic equation, a stationary droplet, a spinodal decomposition, and the Rayleigh-Taylor instability are simulated as well, showing the satisfying performance of the model in dealing with complex interfaces of binary fluid systems.