Eur. Phys. J. E (2007) 22: 181-192
https://doi.org/10.1140/epje/e2007-00024-y

Regular Articles

Decorated vertices with 3-edged cells in 2D foams: exact solutions and properties

¹ 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

^* e-mail: marco.mancini@univ-rennes1.fr

Received: 20 October 2006
Published online: 22 March 2007

Abstract

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.