Collective Dynamics of Galloping Bubbles

Recent work has shown that a capillary-size bubble, held by buoyancy against the top wall of a vertically vibrated fluid chamber, may spontaneously break symmetry and self-propel along the wall through periodic shape deformations reminiscent of "galloping" motion. Depending on the bubble size and driving parameters, a single bubble may exhibit straight-line, orbital, or chaotic trajectories, arising from the nonlinear interaction of axisymmetric and non-axisymmetric shape modes parametrically excited by the effective gravity. Here, we investigate the collective dynamics of galloping bubbles in the dilute regime, where the bubbles occupy only a small fraction of the available domain, and move without geometric confinement while interacting through flow mediated forces. In this setting, our experiments reveal a rich variety of emergent collective behaviors, including self-assembly, orbiting pairs, promenading motion, and gas-like states, which we characterize as functions of external driving, bubble volume, and bubble number. To elucidate the underlying mechanisms, we supplement experiments with direct numerical simulations that resolve the full bubble shape oscillation and surrounding flow fields. We interpret these dynamics in terms of a minimal spectrum of modes and use them to rationalize the far-field interaction force between bubble pairs, paving the way for a reduced model capable of capturing the emergent many-body dynamics of galloping bubbles.