Multiple dynamic regimes in a coarsening foam

Intermittent dynamics driven by internal stress imbalances in disordered systems is a fascinating yet poorly understood phenomenon. Here, we study it for a coarsening foam. By exploiting differential dynamic microscopy and particle tracking we determine the dynamical characteristics of the foam at different ages in reciprocal and direct space, respectively. At all wavevectors $q$ investigated, the intermediate scattering function exhibits a compressed exponential decay. However, the access to unprecedentedly small values of $q$ highlights the existence of two distinct regimes for the $q$-dependence of the foam relaxation rate $Gamma (q)$. At high $q$, $Gamma (q)sim q$ consistent with directionally-persistent and intermittent bubble displacements. At low $q$, we find the surprising scaling $Gamma (q) sim q^{delta}$, with $delta=1.6 pm 0.2$. The analysis of the bubble displacement distribution in real space reveals the existence of a displacement cut-off of the order of the bubble diameter. Introducing such cut-off length in an existing model, describing stress-driven dynamics in disordered systems, fully accounts for the observed behaviour in direct and reciprocal space.