Topological and geometrical disorder correlate robustly in two-dimensional foams

TL;DR

This paper investigates the relationship between topological and geometrical disorder in two-dimensional foams, demonstrating a strong correlation that simplifies their characterization and suggesting broader applications to biological tissues.

Contribution

It provides a comparative analysis of topological and geometrical disorder measures in 2D foams and shows their robust correlation under shear-induced shuffling.

Findings

Topological and geometrical disorder are strongly correlated in sheared 2D foams.

Either measure can reliably characterize foam disorder due to their correlation.

The results have potential applications in analyzing biological tissues.

Abstract

A 2D foam can be characterised by its distribution of bubble areas, and of number of sides. Both distributions have an average and a width (standard deviation). There are therefore at least two very different ways to characterise the disorder. The former is a geometrical measurement, while the latter is purely topological. We discuss the common points and differences between both quantities. We measure them in a foam which is sheared, so that bubbles move past each other and the foam is "shuffled" (a notion we discuss). Both quantities are strongly correlated; in this case (only) it thus becomes sufficient to use either one or the other to characterize the foam disorder. We suggest applications to the analysis of other systems, including biological tissues.