1997/01/02 by Cristian F. Moukarzel · 1 citation
Engineering · Materials Science · Physics and Astronomy · #Advanced Materials and Mechanics #Characterization and Applications of Magnetic Nanoparticles #Pickering emulsions and particle stabilization #cond-mat.mtrl-sci #cond-mat.soft
paper · pdf · doi:10.1103/physreve.55.6866
RevTeX + epsfig, 19 pages + 19 eps figures
arxiv created 1997/01/02 · openalex publication_date 1997/06/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Pi on the plane, one per bubble, such that the segments (Pi Pj) 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.