On the similarities between the resonance behaviors of water balloons and water drops

Abstract

In this study, the resonance of water balloons is examined, and an understanding of their dynamics in terms of our knowledge about resonating sessile drops is reported. The focus is the regime in which the competition between surface and inertial forces dominates the dynamics of the balloon. In experiments, water balloons are mechanically oscillated along their axes of symmetry, and their responses are observed through optical imaging. The observations are compared to the resonance of sessile drops. Balloons differ from drops for having elasticity in place of surface tension. Different as balloons and drops may seem, this study reveals great similarities between them: a resemblance of their normalized pressure–volume curves, a one-to-one shape correspondence between their eigenmodes, and a close approximation of their normalized resonance frequencies. Based on these, turning a drop into a balloon preserves the drop’s mechanical response to a large extent. In fact, as a first approximation, the water balloons respond mechanically as water drops with a much higher surface tension.