Multiple dynamic regimes in a coarsening foam

TL;DR

This study reveals two distinct dynamic regimes in coarsening foam, characterized by different q-dependencies of the relaxation rate, linked to bubble displacements and strain rates, using advanced microscopy techniques.

Contribution

It uncovers the existence of two regimes in foam relaxation dynamics and relates them to bubble displacement distributions and strain rates, providing a unified understanding of foam aging.

Findings

At high q, relaxation rate scales as q, indicating persistent bubble displacements.

At low q, relaxation rate scales as q^{1.6}, related to bubble displacement cut-off length.

Normalized data collapses onto a master curve, linking dynamics to bubble size and strain rate.

Abstract

We use differential dynamic microscopy and particle tracking to determine the dynamical characteristics of a coarsening foam in reciprocal and direct space. At all wavevectors $q$ investigated, the intermediate scattering function exhibits a compressed exponential decay. However, the access to unprecedentedly small $q$s highlights the existence of two distinct regimes for the $q$-dependence of the foam relaxation rate $\Gamma (q)$. At any given foam age, $\Gamma (q)\sim q$ at high $q$, consistent with directionally-persistent and intermittent bubble displacements. At low $q$, we find $\Gamma (q) \sim q^{1.6}$. We show that such change in $q$-dependence of $\Gamma (q)$ relates to a bubble displacement distribution exhibiting a cut-off length of the order of the bubble diameter. Investigations of the $q$-dependence of $\Gamma (q)$ at different foam ages reveal that foam dynamics is not only governed by the bubble length scale, but also by the strain rate imposed by the bubble growth; normalizing $\Gamma (q)$ by this strain rate and multiplying $q$ with the age-dependent bubble radius leads to a collapse of all data sets onto a unique master-curve.