Physics – Condensed Matter – Soft Condensed Matter
Scientific paper
1997-01-02
Physics
Condensed Matter
Soft Condensed Matter
RevTeX + epsfig, 19 pages + 19 eps figures
Scientific paper
10.1103/PhysRevE.55.6866
The equilibrium conditions impose nontrivial geometrical constraints on the configurations that a two-dimensional foam can attain. In the first place, the three centers of the films that converge to a vertex have to be on a line, i.e. all vertices are aligned. Moreover an equilibrated foam must admit a reciprocal figure. This means that it must be possible to find a set of points P_i on the plane, one per bubble, such that the segments (P_i P_j) are normal to the corresponding foam films. It is furthermore shown that these constraints are equivalent to the requirement that the foam be a Sectional Multiplicative Voronoi Partition (SMVP). A SMVP is a cut with a two-dimensional plane, of a three-dimensional Multiplicative Voronoi Partition. Thus given an arbitrary equilibrated foam, we can always find point-like sources (one per bubble) in three dimensions that reproduce this foam as a generalized Voronoi partition. These sources are the only degrees of freedom that we need in oder to fully describe the foam.
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