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structure and evolution of soap-like foams

Abstract : The main subject is the equilibrium and the evolution of 2D and 3D dry soap-like
foams. A star-triangle equivalence is proved using geometrical methods and
invariance by inversion transformations. This equivalence states that triangular bubbles can be freely exchanged with threefold stars without perturbing the overall equilibrium; a star is a set of three edges ending at a central vertex. Considering an equilibrated foam in contact with a solid, curved and smooth, surface and considering the trace of the films on the surface as a non-conventional 2D foam, the equilibrium equations are established for this 2D foam, generalising the standard case of flat Hele-Shaw cells. The invariance of the vertex equilibrium conditions by conformal transformations is proved. As an application, the configurations of foams in thin interstices between two non parallel plates is analysed in details. Normal incidence and Laplace's law lead to an approximate equation relating the plate profile to a conformal map. The predictions are compared to available experimental data and to the constant volumes case.
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Contributor : Marco Mancini <>
Submitted on : Tuesday, September 27, 2005 - 1:18:25 PM
Last modification on : Monday, January 25, 2021 - 2:38:02 PM
Long-term archiving on: : Friday, September 14, 2012 - 2:40:32 PM


  • HAL Id : tel-00010304, version 1


Marco Mancini. structure and evolution of soap-like foams. Mathematical Physics [math-ph]. Université de Cergy Pontoise, 2005. English. ⟨tel-00010304⟩



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