Decorated vertices with 3-edged cells in 2D foams: exact solutions and properties.
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.
Mancini
M
M
GMCM, CNRS UMR 6626, Université de Rennes I, 35042, Rennes Cedex, France. marco.mancini@univ-rennes1.fr
Oguey
C
C
D000465:Algorithms; D055592:Biophysical Phenomena; D001703:Biophysics; D002468:Cell Physiological Phenomena; D005740:Gases; D008566:Membranes / Q000502:physiology*; D008954:Models, Biological; D013500:Surface Tension; D013816:Thermodynamics
D005740:Gases