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PPT : The Physics of Foams by Simon Cox

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Kelvin’s Bedspring (tetrakaidecahedron)
Polyhedral cells with curved faces packed together to fill space. What’s the best arrangement? (Kelvin problem) Euler & Plateau: need structure with average of 13.39 faces and 5.1 edges per face
14 “delicately curved” faces (6 squares, 8 hexagons) =5.14
See Weaire (ed), The Kelvin Problem (1994)
Weaire-Phelan structure
Kelvin’s candidate structure reigned for 100 years WP is based on A15 TCP structure/ ß-tungsten clathrate =13.5, =5.111 0.3% lower in surface area
2 pentagonal dodecahedra 6 Goldberg 14-hedra
Swimming pool for 2008 Beijing Olympics (ARUP)
Surface Evolver
3D Monodisperse Foams

Finite 3D clusters
J.M.Sullivan (Berlin)
Find minimal energy cluster for N bubbles. Must eliminate strange possibilities:
Proof that “obvious” answer is the right one for N=2 bubbles in 3D, but for no greater N.
Finite 3D clusters

Central bubble from 123 bubble cluster
27 bubbles surround one other
Dynamics
Coarsening Drainage Rheology
Graner, Cloetens (Grenoble)
Von Neumann’s Law – rate of change of area due to gas diffusion depends only upon number of sides:
Gas diffuses across soap films due to pressure differences between bubbles.
Only in 2D. Also applies to grain growth.

Stationary bubble has 13.39 faces
Foam Rheology
* Elastic solids at low strain * Behave as plastic solids as strain increases * Liquid-like at very high strain
Exploit bubble-scale structure (Plateau’s laws) to predict and model the rheological response of foams. Energy dissipated through topological changes (even in limit of zero shear-rate). Properties scale with average bubble area.
2D contraction flow
J.A. Glazier (Indiana)
Shear banding? Localization? cf Lauridsen et al. PRL 2002
Couette Shear (Experiment)
Experiment by G. Debregeas (Paris), PRL ‘01
Much faster than real-time.

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