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Nonlinear bubble dynamics in a slowly driven foam

Aqueous foams consist of a dense random pack­ ing of gas bubbles stabilized by surface active macromolecules [1,2]. The bubble shapes can vary from nearly spherical to nearly polyhedral, forming a complex ge­ ometrical structure insensitive to details of the liquid composition or the average bubble size. As a form of matter, foams exhibit remarkable mechanical properties that arise from this structure in ways that are not well un­ derstood. Namely, foams can support static shear stress, like a solid, but can also flow and deform arbitrarily, like a liquid, if the applied stress is sufficiently large [3,4]. The solidlike properties are due to surface tension and the shape distortion of bubbles in linear response to a small applied strain. The liquidlike properties, however, cannot be similarly understood by linear response since large de­ formations, though macroscopically homogeneous, are ac­ complished by microscopically inhomogeneous neighbor­ switching rearrangements of bubbles from one tightly packed configuration to another. Intermittent structural rearrangements also occur in quiescent foams due to the alteration of packing conditions from the diffusion of gas from smaller to larger bubbles [5-8]. No matter what the driving force, all such dynamics are highly nonlinear and complex, involving abrupt topology changes and large lo­ cal motions that depend on structure at the bubble scale. For example, in the Princen-Prud’homme model of foam as a two-dimensional periodic array of hexagonal bub­ bles, topological rearrangements happen instantaneously and simultaneously throughout the entire sample [9,10]. In a more realistic dense random packing of bubbles, how­ ever, the rearrangement events can be localized, occurring with variable size and duration in different regions at dif­ ferent times. The influence of randomness on the link between microscopic structure and macroscopic deforma­ tion has been studied by computer simulation [5,11-14]. Recently, Okuzono and Kawasaki [15] predicted that rear­ rangements in a slowly driven foam have a broad, powerlaw, distribution of event rate vs energy release, and thus exhibit self-organized criticality.