Abstract
Bubble monolayers are model systems for experiments and simulations of twodimensional 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)EULEEJ0295507510.1209/0295 5075/90/60002] 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)PRLTAO0031900710.1103/ PhysRevLett.107.168304]. 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.
Original language  English 

Article number  062309 
Journal  Physical Review E 
Volume  89 
Issue number  6 
DOIs  
Publication status  Published  19 Jun 2014 
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Simon Cox
 Faculty of Business and Physical Sciences, Department of Mathematics  Professor, Head of Department (Maths)
Person: Teaching And Research