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A conservative Allen–Cahn model for a hydrodynamics coupled phase-field surfactant system

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  • Wu, Jingwen
  • Tan, Zhijun

Abstract

In this study, we develop a model for a binary fluid–surfactant system utilizing a coupling of two kinds conservative Allen–Cahn type equations and the Navier–Stokes equations. To ensure mass conservation, we incorporate hybrid Lagrange multipliers into the two Allen–Cahn type equations. Specifically, for the concentration variable, a global correction using a time-dependent Lagrange multiplier is utilized, while for the binary fluid variable, a space–time dependent Lagrange multiplier is applied to minimize the impact of dynamics of motion by mean curvature. We propose a linear second order scheme for practical solution of the model. Computational tests demonstrate that the proposed model is effective for the binary fluid–surfactant system and is capable of preserving the small features of interfaces.

Suggested Citation

  • Wu, Jingwen & Tan, Zhijun, 2024. "A conservative Allen–Cahn model for a hydrodynamics coupled phase-field surfactant system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 226(C), pages 42-65.
    • Handle: RePEc:eee:matcom:v:226:y:2024:i:c:p:42-65
    DOI: 10.1016/j.matcom.2024.06.016
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    References listed on IDEAS

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    1. Choi, Jeong-Whan & Lee, Hyun Geun & Jeong, Darae & Kim, Junseok, 2009. "An unconditionally gradient stable numerical method for solving the Allen–Cahn equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(9), pages 1791-1803.
    2. Lee, Hyun Geun & Yang, Junxiang & Kim, Sangkwon & Kim, Junseok, 2021. "Modeling and simulation of droplet evaporation using a modified Cahn–Hilliard equation," Applied Mathematics and Computation, Elsevier, vol. 390(C).
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