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Self-similar coalescence of clean foams

Authors
Journal
Journal of Fluid Mechanics
0022-1120
Publisher
Cambridge University Press
Publication Date
Volume
722
Identifiers
DOI: 10.1017/jfm.2013.145
Keywords
  • Complex Fluids
  • Foams
  • Interfacial Flows (Free Surface)

Abstract

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 and 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. © 2013 Cambridge University Press.

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