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Numerical experiments on two-dimensional foam

Published online by Cambridge University Press:  26 April 2006

Thomas Herdtle  and
Hassan Aref
Thomas Herdtle
Affiliation:
Department of Applied Mechanics and Engineering Science, University of California at San Diego, La Jolla, CA 92093-0411, USA
Hassan Aref
Affiliation:
Department of Applied Mechanics and Engineering Science, University of California at San Diego, La Jolla, CA 92093-0411, USA
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Abstract

The statistical evolution of a two-dimensional polygonal, or ‘dry’, foam during diffusion of gas between bubbles lends itself to a very simple mathematical description by combining physical principles discovered by Young. Laplace, Plateau, and von Neumann over a period of a century and a half. Following a brief review of this ‘canonical’ theory, we report results of the largest numerical simulations of this system undertaken to date. In particular, we discuss the existence and properties of a scaling regime, conjectured on the basis of laboratory experiments on larger systems than ours by Glazier and coworkers, and corroborated in computations on smaller systems by Weaire and collaborators. While we find qualitative agreement with these earlier investigations, our results differ on important, quantitative details, and we find that the evolution of the foam, and the emergence of scaling, is very sensitive to correlations in the initial data. The largest computations we have performed follow the relaxation of a system with 1024 bubbles to one with O(10), and took about 30 hours of CPU time on a Cray-YMP supercomputer. The code used has been thoroughly tested, both by comparison with a set of essentially analytic results on the rheology of a monodisperse-hexagonal foam due to Kraynik & Hansen, and by verification of certain analytical solutions to the evolution equations that we found for a family of ‘fractal foams’.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 241 , August 1992 , pp. 233 - 260
Copyright
© 1992 Cambridge University Press

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