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

Junxiang Yang, Yibao Li, Junseok Kim

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

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.

Original languageEnglish
Article number4092
JournalMathematics
Volume10
Issue number21
DOIs
Publication statusPublished - 2022 Nov

Bibliographical note

Publisher Copyright:
© 2022 by the authors.

Keywords

  • Cahn–Hilliard equation
  • Navier–Stokes equation
  • droplet breakup
  • simple shear flow
  • two-phase flow

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • General Mathematics
  • Engineering (miscellaneous)

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