Mathematical modeling and simulation of antibubble dynamics

Junxiang Yang, Yibao Li, Darae Jeong, Junseok Kim

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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
Issue number1
Publication statusPublished - 2020 Feb

Bibliographical note

Funding Information:
Science Foundation (No. 2018M640968). The corresponding author (J. S. Kim) was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2019R1A2C1003053).

Funding Information:
Acknowledgements The author (D. Jeong) was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF-2017R1E1A1A03070953). The author (Y. B. Li) is supported by National Natural Science Foundation of China (Nos. 11601416, 11631012) and by the China Postdoctoral

Publisher Copyright:
© 2020 Global-Science Press.


  • 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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