Water balloon physics: A proxy for simplifying the study of water drops

Despite the presence of a membrane, water balloons exhibit qualitative similarities as “naked” water droplets in their pressure-volume curves. Inspired by the possibility to study droplet dynamics using water balloons, Chun-Ti Chang compared the resonance behavior of water balloons and sessile droplets to determine scenarios where water balloons can be suitable analogous substitutes in studies.

“Visualizing the oscillation of these small drops requires high-speed imaging, intense lighting and substantial magnification. All of these may be challenging and expensive,” Chang said. “If the drops could be made larger, the length scale and the response time would be larger.”

Below a certain volume threshold, the relationship between the pressure and volume of a water balloon is similar to that of a droplet to the first order. This implies a balloon’s resonance behavior, pressure and surface forces can be approximated using the same fluid dynamics equations as droplets. When normalized to appropriate timescales, the resonance frequencies of the two systems are the same, and balloons can simply be treated as droplets with much higher surface tension.

“Balloons are not drops, and a membrane’s elasticity does not equal a drop’s surface tension,” said Chang. “Because of this, I find the agreement between the normalized frequencies of balloons and drops the most surprising.”

He oscillated water balloons and water drops with a mechanical vibrator to observe their resonance behaviors, and identified the standing waves on their surfaces and compare their resonance frequencies and pressure-volume curves.

Using water balloons instead of droplets will enable scientists to use techniques otherwise impossible, such as marking the surface of the balloon to track surface motion and directly accessing waveform geometry.

Source: “On the similarities between the resonance behaviors of water balloons and water drops,” by Chun-Ti Chang, Physics of Fluids (2020). The article can be accessed at https://doi.org/10.1063/5.0031388 .