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A Correct Benchmark Problem of a Two-Dimensional Droplet Deformation in Simple Shear Flow

Author

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  • Junxiang Yang

    (School of Computer Science and Engineering, Sun Yat-sen University, Guangzhou 510006, China)

  • Yibao Li

    (School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China)

  • Junseok Kim

    (Department of Mathematics, Korea University, Seoul 02841, Korea)

Abstract

In this article, we numerically investigate a two-dimensional (2D) droplet deformation and breakup in simple shear flow using a phase-field model for two-phase fluid flows. The dominant driving force for a droplet breakup in simple shear flow is the three-dimensional (3D) phenomenon via surface tension force and Rayleigh instability, where a liquid cylinder of certain wavelengths is unstable against surface perturbation and breaks up into individual droplets to reduce the total surface energy. A 2D droplet breakup does not occur except in special cases because there is only one curvature direction of the droplet interface, which resists breakup. However, there have been many numerical simulation research works on the 2D droplet breakups in simple shear flow. This study demonstrates that the 2D droplet breakup phenomenon in simple shear flow is due to the lack of space resolution of the numerical grid.

Suggested Citation

  • Junxiang Yang & Yibao Li & Junseok Kim, 2022. "A Correct Benchmark Problem of a Two-Dimensional Droplet Deformation in Simple Shear Flow," Mathematics, MDPI, vol. 10(21), pages 1-10, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:21:p:4092-:d:961513
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    References listed on IDEAS

    as
    1. Dehghan, Mehdi & Gharibi, Zeinab, 2021. "Numerical analysis of fully discrete energy stable weak Galerkin finite element Scheme for a coupled Cahn-Hilliard-Navier-Stokes phase-field model," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    2. 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.
    3. Li, Yaxiang & Wang, Jiangxing, 2022. "Unconditional convergence analysis of stabilized FEM-SAV method for Cahn-Hilliard equation," Applied Mathematics and Computation, Elsevier, vol. 419(C).
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