Statistical Mechanics of Two-dimensional Foams

TL;DR

This paper applies statistical mechanics to two-dimensional foams, introducing a new variable for cell curvature, deriving distributions of cell sides, and correlating topological and geometrical disorder, with predictions matching experimental data.

Contribution

It introduces the total cell curvature as an energy analogue and derives a distribution linking topological and geometrical disorder in 2D foams.

Findings

Model predictions align with experimental data.

Derived distribution links cell topology to size.

Introduced total cell curvature as a key variable.

Abstract

The methods of statistical mechanics are applied to two-dimensional foams under macroscopic agitation. A new variable -- the total cell curvature -- is introduced, which plays the role of energy in conventional statistical thermodynamics. The probability distribution of the number of sides for a cell of given area is derived. This expression allows to correlate the distribution of sides ("topological disorder") to the distribution of sizes ("geometrical disorder") in a foam. The model predictions agree well with available experimental data.