Planar network statistics for two-dimensional rupturing foams

TL;DR

This study investigates the topological and geometric properties of two-dimensional rupturing foams, analyzing how certain network laws hold during foam aging and rupture, with implications for understanding foam coarsening and disorder.

Contribution

The paper introduces metrics for foam disorder and models their evolution, revealing the conditions under which classical network laws break down during foam rupture.

Findings

Aboav law and quadratic Lewis Law hold for preheated foams.

Quadratic Lewis Law remains valid throughout rupture.

Aboav law breaks down when Gini coefficient reaches about 0.8.

Abstract

We conduct experiments on a class of two-dimensional semiwet foams generated through compressing a three-dimensional soap foam between two glass plates. To induce a spatially uniform rupturing process on foam boundaries, an additional plate is heated and placed on top of the unheated plates. For 30 separate foam samples, we record network statistics related to cell side numbers and areas as the foam coarsens over a half-minute. We find that the Aboav law and a quadratic Lewis Law, two commonly used relations between network topology and geometry, hold well for preheated foams. To track how well these laws are maintained as the foam ages, we introduce metrics for measuring a foam's disorder over time and build simple autonomous models for these metrics. While the quadratic Lewis Law is found to hold well throughout the rupture process, the Aboav law breaks down rapidly when the Gini coefficient, used for measuring disparity of cell areas, is approximately 0.8.