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

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  • Zheng, Lin
  • Zheng, Song
  • Zhai, Qinglan

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.

Suggested Citation

  • Zheng, Lin & Zheng, Song & Zhai, Qinglan, 2021. "Reduction-consistent Cahn–Hilliard theory based lattice Boltzmann equation method for N immiscible incompressible fluids," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 574(C).
    • Handle: RePEc:eee:phsmap:v:574:y:2021:i:c:s0378437121002879
    DOI: 10.1016/j.physa.2021.126015
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