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

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.