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Durand M, Kraynik AM, van Swol F, et al. Statistical mechanics of two-dimensional shuffled foams: geometry-topology correlation in small or large disorder limits. Phys Rev E Stat Nonlin Soft Matter Phys. 2014;89(6):062309doi: 10.1103/PhysRevE.89.062309.
Durand, M., Kraynik, A. M., van Swol, F., Käfer, J., Quilliet, C., Cox, S., Ataei Talebi, S., & Graner, F. (2014). Statistical mechanics of two-dimensional shuffled foams: geometry-topology correlation in small or large disorder limits. Physical review. E, Statistical, nonlinear, and soft matter physics, 89(6), 062309. https://doi.org/10.1103/PhysRevE.89.062309
Durand, Marc, et al. "Statistical mechanics of two-dimensional shuffled foams: geometry-topology correlation in small or large disorder limits." Physical review. E, Statistical, nonlinear, and soft matter physics vol. 89,6 (2014): 062309. doi: https://doi.org/10.1103/PhysRevE.89.062309
Durand M, Kraynik AM, van Swol F, Käfer J, Quilliet C, Cox S, Ataei Talebi S, Graner F. Statistical mechanics of two-dimensional shuffled foams: geometry-topology correlation in small or large disorder limits. Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Jun;89(6):062309. doi: 10.1103/PhysRevE.89.062309. Epub 2014 Jun 19. PMID: 25019778.
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Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Jun;89(6):062309. doi: 10.1103/PhysRevE.89.062309. Epub 2014 Jun 19.

Statistical mechanics of two-dimensional shuffled foams: geometry-topology correlation in small or large disorder limits.

Physical review. E, Statistical, nonlinear, and soft matter physics

Marc Durand, Andrew M Kraynik, Frank van Swol, Jos Käfer, Catherine Quilliet, Simon Cox, Shirin Ataei Talebi, François Graner

Affiliations

  1. Matière et Systèmes Complexes (MSC), 10 rue Alice Domon et Léonie Duquet, 75205 Paris Cedex 13, France.
  2. Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA.
  3. 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.
  4. Laboratoire de Biométrie et Biologie Evolutive, 43 Boulevard du 11 Novembre 1918, 69622 Villeurbanne Cedex, France.
  5. Laboratoire Interdisciplinaire de Physique, Boîte Postale 87, 38402 Martin d'Hères Cedex, France.
  6. Departments of Mathematics and Physics, Aberystwyth University, Aberystwyth SY23 3BZ, United Kingdom.

PMID: 25019778 DOI: 10.1103/PhysRevE.89.062309

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.

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