Mapping resonance dynamics in water balloons

A water balloon can signal a fun activity on a hot summer day, but it can also present a challenging problem for researchers looking to understand its dynamics. When subjected to mechanical oscillation, a water balloon can resonate in any of an infinite number of modes, and modeling that resonance behavior is extremely difficult.

Chang and Huang developed an experimental approach to study the resonance dynamics of subhemispherical balloons. They identified several resonant modes of these balloons and produced a method to predict resonant frequencies based on a similar theory for water drops.

“A water balloon and a water drop are totally different objects,” said author Chun-Ti Chang. “However, our study reveals the similarities between how their surface forces respond to the same external forcing.”

While no hydroelastic theory exists to determine the resonant frequencies of water balloons, such theories are available for water drops. Because of the physical similarities between the two objects, their resulting resonance dynamics are similar enough that a water drop resonance theory can be applied to balloons.

“Thanks to the similarities, we are able to propose a simple frequency-scaling scheme to assimilate the resonance frequencies of balloons and drops,” said Chang. “The assimilation then allows one to predict a balloon’s resonance behaviors with a theory for a drop’s natural oscillation.”

The researchers plan to expand their work to cover superhemispherical balloons as well as balloons without a fixed volume, for instance during inflation or deflation. They hope their work will have applications in fluid and heat pumps, medicine, and robotics.

Source: “Resonance of ‘subhemispherical’ water balloons: Shape analysis and frequency prediction,” by Chun-Ti Chang and Ming-Siang Huang, Physics of Fluids (2023). The article can be accessed at https://doi.org/10.1063/5.0135137 .