Relaxation of fractal foam

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’.

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“…The fractal foam check has already been mentioned in an earlier paper (Herdtle & Aref 1991a). An example is shown in figure 7.…”

Section: Code Verificationmentioning

confidence: 88%

Numerical experiments on two-dimensional foam

Herdtle

Aref

1992

J. Fluid Mech.

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“…Foams can be considered as complex systems in several ways, for instance focusing in the fractal structure of foams [ 53 , 54 ] and foams flowing through porous media [ 55 ] and in Hele Shaw radial cells [ 56 ] (see §4, Fig. 8 ) or even the fractal-like patterns in chaotic light scattering by foams [ 57 ].…”

Section: Foams As Complex Systemsmentioning

confidence: 99%

Complexity and self-organized criticality in liquid foams. A short review

Ritacco

2020

Advances in Colloid and Interface Science

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“…The bubbles can assemble in various stable arrangements with different topologies and different free energies. The configurations of three-dimensional clusters have been determined only for clusters with 2 to 4 bubbles [1], for which the films are spherical. For larger numbers of cells, the clusters may have non-spherical films [2] and 'solving' them is not a simple problem.…”

Section: Introductionmentioning

confidence: 99%

Two-dimensional clusters of identical bubbles

Vaz¹,

Fortes²

2001

J. Phys.: Condens. Matter

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We discuss in detail the assembly of two-dimensional identical bubbles in stable clusters. The clusters are classified into perfect and defective clusters, depending on the number of sides of their inner cells (defective clusters have inner cells with a number of neighbours different from 6). We evaluate the surface energy of clusters by a broken-bond method and compare with exact energy calculations for simple clusters. Special attention is given to perfect clusters which are classified by their symmetry. For particular values of the number of cells, N, called magic numbers, perfect clusters have special properties. We identify the clusters of smallest energy, for fixed number of cells N (minimal clusters). For large N the minimal clusters are perfect, but for small N a minimal cluster may be a defective cluster. We produced two-dimensional clusters with N up to 15 by the `monolayer foam' method and studied their relative incidence for N = 6.

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Relaxation of fractal foam

Cited by 11 publications

References 3 publications

Numerical experiments on two-dimensional foam

Numerical experiments on two-dimensional foam

Complexity and self-organized criticality in liquid foams. A short review

Two-dimensional clusters of identical bubbles

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