IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i21p4092-d961513.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/21/4092/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/21/4092/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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. 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).
    3. 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).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Poochinapan, Kanyuta & Wongsaijai, Ben, 2022. "Numerical analysis for solving Allen-Cahn equation in 1D and 2D based on higher-order compact structure-preserving difference scheme," Applied Mathematics and Computation, Elsevier, vol. 434(C).
    2. Chaeyoung Lee & Darae Jeong & Junxiang Yang & Junseok Kim, 2020. "Nonlinear Multigrid Implementation for the Two-Dimensional Cahn–Hilliard Equation," Mathematics, MDPI, vol. 8(1), pages 1-23, January.
    3. Choi, Yongho & Jeong, Darae & Kim, Junseok, 2017. "A multigrid solution for the Cahn–Hilliard equation on nonuniform grids," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 320-333.
    4. 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).
    5. Uzunca, Murat & Karasözen, Bülent, 2023. "Linearly implicit methods for Allen-Cahn equation," Applied Mathematics and Computation, Elsevier, vol. 450(C).
    6. Tan, Zhijun & Yang, Junxiang & Chen, Jianjun & Kim, Junseok, 2023. "An efficient time-dependent auxiliary variable approach for the three-phase conservative Allen–Cahn fluids," Applied Mathematics and Computation, Elsevier, vol. 438(C).
    7. Xiao, Xufeng & Feng, Xinlong, 2022. "A second-order maximum bound principle preserving operator splitting method for the Allen–Cahn equation with applications in multi-phase systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 202(C), pages 36-58.
    8. Ham, Seokjun & Kim, Junseok, 2023. "Stability analysis for a maximum principle preserving explicit scheme of the Allen–Cahn equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 453-465.
    9. Lee, Hyun Geun & Lee, June-Yub, 2015. "A second order operator splitting method for Allen–Cahn type equations with nonlinear source terms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 432(C), pages 24-34.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:21:p:4092-:d:961513. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.