Multiple dynamic regimes in a coarsening foam

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 qs highlights the existence of two distinct regimes for the q-dependence of the foam relaxation rate Γ(q). At any given foam age, Γ(q) ∼ q at high q, consistent with directionally-persistent and intermittent bubble displacements. At low q, we find Γ(q) ∼ q 1.6 . We show that such change in q-dependence of Γ(q) relates to a bubble displacement distribution exhibiting a cut-off length of the order of the bubble diameter. Investigations of the qdependence of Γ(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 Γ(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.