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

Junxiang Yang, Yibao Li and Junseok Kim ()
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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

Mathematics, 2022, vol. 10, issue 21, 1-10

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.

Keywords: droplet breakup; simple shear flow; two-phase flow; Navier–Stokes equation; Cahn–Hilliard equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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