Self-similar coalescence of clean foams

Peter S. Stewart*, Stephen H. Davis

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


We consider the stability of a planar gas-liquid foam with low liquid fraction, in the absence of surfactants and stabilizing particles. We adopt a network modelling approach introduced by Stewart & Davis (J. Rheol., vol. 56, 2012, p. 543), treating the gas bubbles as polygons, the accumulation of liquid at the bubble vertices (Plateau borders) as dynamic nodes and the liquid bridges separating the bubbles as uniformly thinning free films; these films can rupture due to van der Waals intermolecular attractions. The system is initialized as a periodic array of equally pressurized bubbles, with the initial film thicknesses sampled from a normal distribution. After an initial transient, the first film rupture initiates a phase of dynamic rearrangement where the bubbles rapidly coalesce, evolving toward a new quasi-equilibrium. We present Monte Carlo simulations of this coalescence process, examining the time intervals over which large-scale rearrangement occurs as a function of the model parameters. In addition, we show that when this time interval is rescaled appropriately, the evolution of the normalized number of bubbles is approximately self-similar.

Original languageEnglish (US)
Pages (from-to)645-664
Number of pages20
JournalJournal of fluid Mechanics
StatePublished - May 2013


  • Complex fluids
  • Foams
  • Interfacial flows (free surface)

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

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