Reduction-consistent Cahn–Hilliard theory based lattice Boltzmann equation method for N immiscible incompressible fluids

Lin Zheng, Song Zheng and Qinglan Zhai

Physica A: Statistical Mechanics and its Applications, 2021, vol. 574, issue C

Abstract: When some fluid components are absent from N (N≥ 2) immiscible fluids, the reduction-consistent property should be guaranteed. In phase-field theory, the evolution of fluid–fluid interface in N immiscible fluids can be captured by a reduction-consistent Cahn–Hilliard equation (CHE), which has a variable dependent mobility. However, it is difficult for lattice Boltzmann equation (LBE) method to solve this kind of CHE with variable mobility. To eliminate this issue, in this paper, a reduction-consistent LBE is proposed for N immiscible fluids. In the model, the reduction-consistent formulation of fluid–fluid interface force is reformulated into a chemical potential form, which can be implemented by a force term in LBE, while a source term treatment is used to achieve the reduction-consistent property for CHE. Numerical simulations of spreading of a liquid lens, spinodal decomposition, and dynamic interaction of drops are carried out to validate present LBE, and the results show the accuracy and capability of present phase-field based LBE for N (N≥2) immiscible fluids.

Keywords: Lattice Boltzmann equation; Reduction-consistent Cahn–Hilliard equation; N immiscible fluids (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:574:y:2021:i:c:s0378437121002879

DOI: 10.1016/j.physa.2021.126015

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