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 in a direction perpendicular to the driving, exhibiting motion reminiscent of galloping. Depending on the combination of parameters, a single bubble may exhibit straight-line, orbital, or chaotic motion through the interaction of axisymmetric and non-axisymmetric shape modes excited by the external driving. Here, we investigate the collective dynamics of galloping bubbles through experiments and simulations, focusing on characterizing pair dynamics as a step towards understanding their many-bubble behaviors. Our experiments reveal rich collective dynamics, including the formation of orbiting pairs, leapfrogging along vertical walls, and self-assemblies. Using simulations, we characterize the fluid-mediated interactions between two bubbles and between a bubble and a vertical wall as a function of external driving, bubble volume, separation, and orientation. We perform a spectral decomposition of the bubble shape oscillations and the induced far-field flow, paving the way for the development of a reduced model for interactions and collective dynamics.