Resonance of “subhemispherical” water balloons: Shape analysis and frequency prediction

Water balloons and water drops are different objects, yet the work by Chang [“On the similarities between the resonance behaviors of water balloons and water drops,” Phys. Fluids 32, 124113 (2020)] reveals the similarities between their resonance behaviors. Chang's work focuses on the balloons with pinning angles beyond 90° (superhemispherical balloons), and the results are based on a limited number of modes. In this study, the resonance of balloons with pinning angles below 90° (subhemispherical balloons) is examined. The setup is similar to that for Chang's work, except each balloon is enlarged to possess a larger inertia, and a correlation-based method is adopted to visualize the balloon's oscillation. With these improvements, this study successfully discovers more than 37 modes, many of them have not been reported in the literature. For these modes, a catalogue is constructed to demonstrate their one-to-one correspondence to the modes of drops. Additionally, a scaling scheme is proposed to assimilate the resonance frequencies of subhemispherical balloons and drops. With these, this study provides a simple framework for predicting a subhemispherical water balloon's resonance with a theory for the resonance of sessile drops on a flat plate.