The pop-up effect: Why buoyant spheres don't always leap out of the water

November 2, 2016, Utah State University
A metallic sphere rising through water. Credit: The Splash Lab

It's a common swimming pool game: Force a buoyant ball underwater and let it go. The ball springs to the surface and jumps into the air. But, submerge the ball deeper underwater and the effect is often disappointing. Contrary to our intuition, increasing the release depth often leads to a decreased pop-up height.

This simple fluid dynamics question has puzzled physicists for decades, but a new study published Nov. 1 in Physical Review Fluids, offers new perspective into the phenomenon and may clarify topics related to water exit dynamics and ocean engineering.

A team of researchers from Utah State University, Dartmouth College and Brigham Young University used high-speed imaging and particle image velocimetry to describe why buoyant spheres ascending through a fluid don't always behave the way we expect them to.

"The pop-up height depends on the speed of the sphere at the point it breaches the free surface," said lead investigator and assistant professor of mechanical engineering at USU, Tadd Truscott. "It doesn't matter how deep the ball is when it's released. There are a number of factors that affect its speed and trajectory until it reaches the surface."

During ascent, wake and vortex structures often form around the sphere. Asymmetric vortex shedding and wake formations can alter a sphere's upward movement and result in a non-linear trajectory. The authors demonstrate that rising spheres usually fall under one of two acceleration categories: 1) a vertical regime, or 2) an oscillatory regime.

"The vertical regime exhibits a nearly vertical underwater trajectory and results in the largest pop-up heights," explains Brenden Epps, assistant professor of engineering at Dartmouth and co-author on the study. "The oscillatory regime exhibits a trajectory with periodic lateral motions and results in lower pop-up heights. Sometimes the ball may even breach the surface and skim across it rather than rising into the air."

To test rising sphere behavior, researchers submerged stainless steel balls into a test tank at various depths and held them in place using a suction cup connected to a vacuum release mechanism. After sufficient wait time to allow the water to become quiescent, the suction cup released the sphere while four synchronized high-speed cameras recorded its ascent.

In total, 664 tests were performed using four balls of varying diameters and release depths. As expected, the maximum pop-up heights occurred when spheres were released from shallow depths. The lowest pop-up heights occurred when spheres were released from greater depths.

But the conversation doesn't end there. Part of the pop-up height problem also depends on what happens to the sphere at the point of surface breach.

As expected, spheres released from greater depths, exhibit lower pop-up heights. Credit: Splash Lab.

"Once the sphere clears the surface, the only force acting on it is gravity," Truscott added. "So the pop-up height is determined by a transfer of kinetic energy to potential energy of the sphere after clearing the surface. However, the speed (and thus kinetic energy) ofthe after it has cleared the surface is dictated both by the speed at which it approaches the surface (set by the underwater dynamics) and the change in speed during breach."

The authors say their study has a broad range of applications. A better understanding of water exit dynamics, they explain, can be useful in maritime engineering and marine biology.

"Penguins exit the water after a hunt or to avoid predators," they write. "It has been hypothesized that emperor penguins use bubbles released from their feathers during ascent in order to reduce drag and increase exit velocity and pop-up height. ... Other important applications of the pop-up effect include underwater vehicle exit, floating sea structures and wave-energy converters."

Explore further: Walking on water: Researchers unravel science of skipping spheres

More information: Tadd T. Truscott et al, Water exit dynamics of buoyant spheres, Physical Review Fluids (2016). DOI: 10.1103/PhysRevFluids.1.074501

Related Stories

How water flows near the superhydrophobic surface

October 14, 2016

Water has an unusual property when it flows closely to some specially designed surfaces—its speed isn't equal to zero, even in the layer that directly touches the wall. This means that liquid doesn't adhere to the surface, ...

Image: French fluidics experiment bound for ISS

October 12, 2016

Have you ever tried walking while carrying a full cup of water? Your steps invariably cause the water to slosh about, making spills hard to avoid. Now imagine a satellite turning – the fuel inside will slosh, affecting ...

Liquid jets and bouncing balls combine for surprising results

January 3, 2013

A new study published in the American Institute of Physics' (AIP) journal Physics of Fluids reveals that the normal rebounding of a ball changes when it is partially filled with a liquid. Unlike an empty sphere or a solid ...

Recommended for you

How community structure affects the resilience of a network

June 22, 2018

Network theory is a method for analyzing the connections between nodes in a system. One of the most compelling aspects of network theory is that discoveries related to one field, such as cellular biology, can be abstracted ...

The pho­to­elec­tric ef­fect in stereo

June 22, 2018

In the photoelectric effect, a photon ejects an electron from a material. Researchers at ETH have now used attosecond laser pulses to measure the time evolution of this effect in molecules. From their results they can deduce ...

Water can be very dead, electrically speaking

June 21, 2018

In a study published in Science this week, the researchers describe the dielectric properties of water that is only a few molecules thick. Such water was previously predicted to exhibit a reduced electric response but it ...

0 comments

Please sign in to add a comment. Registration is free, and takes less than a minute. Read more

Click here to reset your password.
Sign in to get notified via email when new comments are made.