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Self-similar coalescence of clean foams

Published online by Cambridge University Press:  15 April 2013

Peter S. Stewart  and
Stephen H. Davis
Peter S. Stewart*
Affiliation:
Oxford Centre for Collaborative Applied Mathematics, Mathematical Institute, The University of Oxford, Oxford OX1 3LB, UK
Stephen H. Davis
Affiliation:
Department of Engineering Sciences and Applied Mathematics, McCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL 60208, USA
*
†Email address for correspondence: peter.stewart@maths.ox.ac.uk
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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 & 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.

JFM classification

Complex Fluids: Complex Fluids Complex Fluids: Foams Interfacial Flows (free surface): Interfacial Flows (free surface)
Type
Papers
Information
Journal of Fluid Mechanics , Volume 722 , 10 May 2013 , pp. 645 - 664
Copyright
©2013 Cambridge University Press

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References

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Stewart and Davis supplementary movie

Animation of bubble coalescence in a foam initially composed of 72 uniformly pressurized bubbles, corresponding to the snapshots shown in figure 4 and the time-traces shown in figures 5 and 6 in the paper. The movie illustrates how the breakage of the first film triggers a large-scale topological rearrangement of the foam, evolving toward a new quasi-equilibrium composed of only a few bubbles.

Download Stewart and Davis supplementary movie(Video)
Video 7.5 MB