Statistical properties and shell analysis in random cellular structures

TL;DR

This paper analyzes the topological and statistical properties of two-dimensional random cellular structures, comparing experimental soap froths with Voronoi models, revealing key differences and providing analytical explanations.

Contribution

It introduces exact relations for shell structures in froths and explains differences between real soap froths and geometrical models with parameter-free formulas.

Findings

Differences in topological charge distributions between soap froths and Voronoi models

Asymptotic defect concentrations differ between systems

Derived formulas accurately predict observed behaviors

Abstract

We investigate the statistical properties of two dimensional random cellular systems (froths) in term of their shell structure. The froth is analyzed as a system of concentric layers of cells around a given central cell. We derive exact analytical relations for the topological properties of the sets of cells belonging to these layers. Experimental observations of the shell structure of two-dimensional soap froth are made and compared with the results on two kinds of Voronoi constructions. It is found that there are specific differences between soap froths and purely geometrical constructions. In particular these systems differ in the topological charge of clusters as a function of shell number, in the asymptotic values of defect concentrations, and in the number of cells in a given layer. We derive approximate expressions with no free parameters which correctly explain these different behaviors.