Direct Numerical Simulations of Vibrating Bubbles Self-Propelling Along Solid Boundaries

Recent experiments have revealed that vertically vibrated bubbles may spontaneously self-propel along horizontal walls. We use 3D direct numerical simulations to demonstrate that asymmetric vibration modes drive the propulsion in agreement with experiments, and to extend the study beyond the parameter regime accessible in the laboratory. We characterize the bubble motion in terms of the system parameters, including vibrational frequency and forcing, bubble size, viscosity, and gravity. We explore the influence of nonlinearities in the resonant frequencies predicted by the classic theory of Rayleigh for inviscid bubbles. Notably, we demonstrate that the same propulsion mechanism may be harnessed to propel sessile bubbles attached to solid boundaries. This generalization makes the problem amenable to theoretical analysis.