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

Yongsam Kim, Ming Chih Lai, Charles Peskin, Yunchang Seol

Research output: Contribution to journalArticle

Abstract

In this paper, we extend (Kim et al., 2010 [13]) to the three-dimensional dry foam case, 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 partitions 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 immersed boundary 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 three-dimensional framework, and test it by verifying the 3D generalization of the von Neumann relation, which governs the coarsening of a three-dimensional dry foam.

Original languageEnglish (US)
Pages (from-to)1-21
Number of pages21
JournalJournal of Computational Physics
Volume269
DOIs
StatePublished - Jul 15 2014

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
slip
Thin films

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 three-dimensional foam by the immersed boundary method. / Kim, Yongsam; Lai, Ming Chih; Peskin, Charles; Seol, Yunchang.

In: Journal of Computational Physics, Vol. 269, 15.07.2014, p. 1-21.

Research output: Contribution to journalArticle

Kim, Yongsam ; Lai, Ming Chih ; Peskin, Charles ; Seol, Yunchang. / Numerical simulations of three-dimensional foam by the immersed boundary method. In: Journal of Computational Physics. 2014 ; Vol. 269. pp. 1-21.
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