A lattice Boltzmann method for binary fluids based on mass-conserved quasi-incompressible phase-field theory

TL;DR

This paper introduces a lattice Boltzmann method for binary fluids based on a quasi-incompressible phase-field theory that conserves mass locally, improving interface tracking accuracy and providing better physical consistency.

Contribution

The paper develops a new lattice Boltzmann model based on quasi-incompressible phase-field theory, enhancing mass conservation and interface accuracy over existing models.

Findings

The proposed model accurately tracks fluid interfaces.

It shows good qualitative agreement with incompressible models.

The model conserves mass locally, unlike previous approaches.

Abstract

In this paper, a lattice Boltzmann equation (LBE) model is proposed for binary fluids based on a quasi-incompressible phase-field model [J. Shen et al, Comm. Comp. Phys. 13, 1045 (2013)]. Compared with the other incompressible LBE models based on the incompressible phase-field theory, the quasi-incompressible model conserves mass locally. A series of numerical simulations are performed to validate the proposed model, and comparisons with an incompressible LBE model [H. Liang et al, Phys. Rev. E 89, 053320 (2014)] are also carried out. It is shown that the proposed model can track the interface accurately, and the predictions by the quasi-incompressible and incompressible models agree qualitatively well as the distribution of chemical potential is uniform, otherwise differ significantly.