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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., Commun. Comput. Phys. 13, 1045 (2013)10.4208/cicp.300711.160212a. 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)PLEEE81539-375510.1103/PhysRevE.89.053320 are also carried out. It is shown that the proposed model can track the interface accurately. As the stationary droplet and rising bubble problems, the quasi-incompressible LBE gives nearly the same predictions as the incompressible model, but the compressible effect in the present model plays a significant role in the phase separation problem. Therefore, in general cases the present mass-conserving model should be adopted.
Yang et al. (Tue,) studied this question.