Mathematical modeling and simulation of antibubble dynamics

Junxiang Yang, Yibao Li, Darae Jeong, Junseok Kim

Research output: Contribution to journalArticlepeer-review

Abstract

In this study, we propose a mathematical model and perform numerical simulations for the antibubble dynamics. An antibubble is a droplet of liquid surrounded by a thin film of a lighter liquid, which is also in a heavier surrounding fluid. The model is based on a phase-field method using a conservative Allen-Cahn equation with a space-time dependent Lagrange multiplier and a modified Navier-Stokes equation. In this model, the inner fluid, middle fluid and outer fluid locate in specific diffusive layer regions according to specific phase filed (order parameter) values. If we represent the antibubble with conventional binary or ternary phase-field models, then it is difficult to have stable thin film. However, the proposed approach can prevent nonphysical breakup of fluid film during the simulation. Various numerical tests are performed to verify the efficiency of the proposed model.

Original languageEnglish
Pages (from-to)81-98
Number of pages18
JournalNumerical Mathematics
Volume13
Issue number1
DOIs
Publication statusPublished - 2020 Feb

Keywords

  • Antibubble
  • Conservative Allen-Cahn equation
  • Navier-Stokes equation

ASJC Scopus subject areas

  • Modelling and Simulation
  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics

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