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  • Statistical Mechanics of Two-Dimensional Shuffled Foams: Prediction of the Correlation between Geometry and Topology

Statistical Mechanics of Two-Dimensional Shuffled Foams: Prediction of the Correlation between Geometry and Topology

Authors: Marc Durand1,*, Jos Käfer2, Catherine Quilliet3, Simon Cox4, Shirin Ataei Talebi3, and François Graner5

DOI: 10.1103/PhysRevLett.107.168304

Abstract:

We propose an analytical model for the statistical mechanics of shuffled two-dimensional foams with moderate bubble size polydispersity. It predicts without any adjustable parameters the correlations between the number of sides n of the bubbles (topology) and their areas A (geometry) observed in experiments and numerical simulations of shuffled foams. Detailed statistics show that in shuffled cellular patterns n correlates better with √A (as claimed by Desch and Feltham) than with A (as claimed by Lewis and widely assumed in the literature). At the level of the whole foam, standard deviations Δn and ΔA are in proportion. Possible applications include correlations of the detailed distributions of n and A, three-dimensional foams, and biological tissues.

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Authors

Professor Simon Cox

Professor Simon Cox

Study of foam, an example of soft condensed matter. Interested in modelling structural and dynamic properties of collections of bubbles to be able to predict their response in various applications.