Scaling state of dry two-dimensional froths: universal angle deviations and structure

TL;DR

This paper investigates the late-time behavior of dry, two-dimensional froths, revealing universal deviations in vertex angles and the dynamics of bubble rearrangements during coarsening.

Contribution

It introduces a force-based vertex model to analyze the scaling state, highlighting systematic angle deviations and side-switching processes in froth evolution.

Findings

Angle deviations are proportional to vertex speed and independent of time.

T1 side-switching processes are common for macroscopic bubbles.

Most bubble annihilations involve microscopic four-sided bubbles.

Abstract

We characterize the late-time scaling state of dry, coarsening, two-dimensional froths using a detailed, force-based vertex model. We find that the slow evolution of bubbles leads to systematic deviations from 120degree angles at three-fold vertices in the froth, with an amplitude proportional to the vertex speed, v ~ sqrt(t), but with a side-number dependence that is independent of time. We also find that a significant number of T1 side-switching processes occur for macroscopic bubbles in the scaling state, though most bubble annihilations involve four-sided bubbles at microscopic scales.