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

Authors Organisations
  • Marc Durand(Author)
  • Jos Kafer(Author)
  • Catherine Quilliet(Author)
  • Simon Cox(Author)
  • Shirin Ataei Talebi(Author)
  • Francois Graner(Author)
Type Article
Original languageEnglish
Pages (from-to)168304-168309
Number of pages5
JournalPhysical Review Letters
Issue number16
Publication statusPublished - 13 Feb 2012
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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 sqrt(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 Delta n and Delta A are in proportion. Possible applications include correlations of the detailed distributions of n and A, three-dimensional foams, and biological tissues.