title: Statistical mechanics of two-dimensional shuffled foams: geometry-topology correlation in small or large disorder limits.
abstract: Bubble monolayers are model systems for experiments and simulations of two-dimensional packing problems of deformable objects. We explore the relation between the distributions of the number of bubble sides (topology) and the bubble areas (geometry) in the low liquid fraction limit. We use a statistical model [M. Durand, Europhys. Lett. 90, 60002 (2010)] which takes into account Plateau laws. We predict the correlation between geometrical disorder (bubble size dispersity) and topological disorder (width of bubble side number distribution) over an extended range of bubble size dispersities. Extensive data sets arising from shuffled foam experiments, surface evolver simulations, and cellular Potts model simulations all collapse surprisingly well and coincide with the model predictions, even at extremely high size dispersity. At moderate size dispersity, we recover our earlier approximate predictions [M. Durand, J. Kafer, C. Quilliet, S. Cox, S. A. Talebi, and F. Graner, Phys. Rev. Lett. 107, 168304 (2011)]. At extremely low dispersity, when approaching the perfectly regular honeycomb pattern, we study how both geometrical and topological disorders vanish. We identify a crystallization mechanism and explore it quantitatively in the case of bidisperse foams. Due to the deformability of the bubbles, foams can crystallize over a larger range of size dispersities than hard disks. The model predicts that the crystallization transition occurs when the ratio of largest to smallest bubble radii is 1.4.
authors.affiliation: Matière et Systèmes Complexes (MSC), 10 rue Alice Domon et Léonie Duquet, 75205 Paris Cedex 13, France.
authors.forename: Marc
authors.initials: M
authors.lastname: Durand
authors.affiliation: Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA.
authors.forename: Andrew M
authors.initials: AM
authors.lastname: Kraynik
authors.affiliation: Sandia National Laboratories, P.O. Box 5800, Albuquerque, New Mexico 87185, USA and Chemical and Nuclear Engineering Department, The University of New Mexico, Albuquerque, New Mexico 87106, USA.
authors.forename: Frank
authors.initials: F
authors.lastname: van Swol
authors.affiliation: Laboratoire de Biométrie et Biologie Evolutive, 43 Boulevard du 11 Novembre 1918, 69622 Villeurbanne Cedex, France.
authors.forename: Jos
authors.initials: J
authors.lastname: Käfer
authors.affiliation: Laboratoire Interdisciplinaire de Physique, Boîte Postale 87, 38402 Martin d'Hères Cedex, France.
authors.forename: Catherine
authors.initials: C
authors.lastname: Quilliet
authors.affiliation: Departments of Mathematics and Physics, Aberystwyth University, Aberystwyth SY23 3BZ, United Kingdom.
authors.forename: Simon
authors.initials: S
authors.lastname: Cox
authors.affiliation: Laboratoire Interdisciplinaire de Physique, Boîte Postale 87, 38402 Martin d'Hères Cedex, France.
authors.forename: Shirin
authors.initials: S
authors.lastname: Ataei Talebi
authors.affiliation: Matière et Systèmes Complexes (MSC), 10 rue Alice Domon et Léonie Duquet, 75205 Paris Cedex 13, France.
authors.forename: François
authors.initials: F
authors.lastname: Graner
mesh_terms: D003198:Computer Simulation; D003460:Crystallization; D008956:Models, Chemical; D015233:Models, Statistical