TY - JOUR

T1 - Statistical mechanics of two-dimensional shuffled foams: Geometry-topology correlation in small or large disorder limits

AU - Durand, Marc

AU - Kraynik, Andrew M.

AU - Van Swol, Frank

AU - Käfer, Jos

AU - Quilliet, Catherine

AU - Cox, Simon

AU - Ataei Talebi, Shirin

AU - Graner, François

N1 - Durand, M., Kraynik, A. M., Van Swol, F., Käfer, J., Quilliet, C., Cox, S., Talebi, S. A., Graner, F. (2014). Statistical mechanics of two-dimensional shuffled foams: Geometry-topology correlation in small or large disorder limits. Physical Review E, 89(6), [062309]

PY - 2014/6/19

Y1 - 2014/6/19

N2 - 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)EULEEJ0295-507510.1209/0295- 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)PRLTAO0031-900710.1103/ 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.

AB - 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)EULEEJ0295-507510.1209/0295- 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)PRLTAO0031-900710.1103/ 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.

UR - http://www.scopus.com/inward/record.url?scp=84903647318&partnerID=8YFLogxK

UR - http://hdl.handle.net/2160/14130

U2 - 10.1103/PhysRevE.89.062309

DO - 10.1103/PhysRevE.89.062309

M3 - Article

AN - SCOPUS:84903647318

SN - 1539-3755

VL - 89

JO - Physical Review E

JF - Physical Review E

IS - 6

M1 - 062309

ER -