Decorated vertices with 3-edged cells in 2D foams: exact solutions and properties
GMCM, CNRS UMR 6626, Université de Rennes I, 35042, Rennes Cedex, France
2 LPTM, CNRS UMR 8089, Université de Cergy-Pontoise, 95031, Cergy-Pontoise, France
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Published online: 22 March 2007
The energy, area and excess energy of a decorated vertex in a 2D foam are calculated. The general shape of the vertex and its decoration are described analytically by a reference pattern mapped by a parametric Moebius transformation. A single parameter of control allows to describe, in a common framework, different types of decorations, by liquid triangles or 3-sided bubbles, and other non-conventional cells. A solution is proposed to explain the stability threshold in the flower problem.
PACS: 83.80.Iz Emulsions and foams – / 82.70.Rr Aerosols and foams – / 82.70.Kj Emulsions and suspensions – / 68.03.Hj Structure: measurements and simulations –
© EDP Sciences/Società Italiana di Fisica/Springer-Verlag, 2007