Numerical simulations of two-dimensional foam by the immersed boundary method

Yongsam Kim, Ming Chih Lai, Charles Peskin

Research output: Contribution to journalArticle

Abstract

In this paper, we present an immersed boundary (IB) method to simulate a dry foam, i.e., a foam in which most of the volume is attributed to its gas phase. Dry foam dynamics involves the interaction between a gas and a collection of thin liquid-film internal boundaries that partition the gas into discrete cells or bubbles. The liquid-film boundaries are flexible, contract under the influence of surface tension, and are permeable to the gas, which moves across them by diffusion at a rate proportional to the local pressure difference across the boundary. Such problems are conventionally studied by assuming that the pressure is uniform within each bubble. Here, we introduce instead an IB method that takes into account the non-equilibrium fluid mechanics of the gas. To model gas diffusion across the internal liquid-film boundaries, we allow normal slip between the boundary and the gas at a velocity proportional to the (normal) force generated by the boundary surface tension. We implement this method in the two-dimensional case, and test it by verifying the von Neumann relation, which governs the coarsening of a two-dimensional dry foam. The method is further validated by a convergence study, which confirms its first-order accuracy.

Original languageEnglish (US)
Pages (from-to)5194-5207
Number of pages14
JournalJournal of Computational Physics
Volume229
Issue number13
DOIs
StatePublished - Jul 2010

Fingerprint

foams
Foams
Computer simulation
Liquid films
Gases
simulation
gases
Surface tension
interfacial tension
bubbles
liquids
Diffusion in gases
Fluid mechanics
Coarsening
Bubbles (in fluids)
gaseous diffusion
fluid mechanics
partitions
Thin films
slip

Keywords

  • Capillary-driven motion
  • Foam
  • Immersed boundary method
  • Permeability
  • Von Neumann relation

ASJC Scopus subject areas

  • Computer Science Applications
  • Physics and Astronomy (miscellaneous)

Cite this

Numerical simulations of two-dimensional foam by the immersed boundary method. / Kim, Yongsam; Lai, Ming Chih; Peskin, Charles.

In: Journal of Computational Physics, Vol. 229, No. 13, 07.2010, p. 5194-5207.

Research output: Contribution to journalArticle

Kim, Yongsam ; Lai, Ming Chih ; Peskin, Charles. / Numerical simulations of two-dimensional foam by the immersed boundary method. In: Journal of Computational Physics. 2010 ; Vol. 229, No. 13. pp. 5194-5207.
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