Cluster persistence: A discriminating probe of soap froth dynamics

– The persistent decay of bubble clusters in coarsening two-dimensional soap froths is measured experimentally as a function of cluster volume fraction. A dramatically stronger decay is observed in comparison to soap froth models and to measurements and calculations of persistence in other systems. The fraction of individual bubbles that contain any persistent area also decays, implying significant bubble motion and suggesting that T1 processes play an important role in froth persistence. Cellular structures are common in nature [1–3], and are studied in soap froths, polycrystallites, Potts models, biological cell clusters, and magnetic bubble arrays. They are composed of cells with varying sizes but identical composition, packed tightly against neighbors so that cell boundaries meet at vertices. In most cases, this structure is dynamic, i.e., part of an ongoing non-equilibrium process, and the challenge is to understand the role of dynamics in determining the structure. Individual cells continually evolve so as to reduce the total interfacial area in the system, which results in coarsening, or growth of the characteristic bubble size. “Topological” changes of cell adjacencies occur when neighbors swap (T1 process) and when cells are destroyed (T2 process) [4]. Topological transitions are effectively instantaneous in soap froths, while bubble areas grow smoothly. This is in contrast to polycrystallites or dynamical Potts models where topological processes occur at the same slow time scales as the evolution of bubble areas. Rapid topological transitions in soap froths allow us, in principle, to isolate the effects of these processes. Soap froths are ideal systems to study cellular pattern evolution, since they coarsen at laboratory time scales and their time-dependent structure can be directly imaged in twodimensions (2d) with video microscopy [5]. In this paper, we study isotropic froths in 2d. We limit ourselves to the scaling regime [6] at late times, when the absence of non-universal transients facilitates both the analysis and the comparison with model systems. A relatively new and general probe of non-equilibrium dynamics is the local power law decay of persistence towards zero [7], P (t) ∼ t−θ, which in froths measures the fraction of the