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Appfel et al., Nature 2020

Watch levitating upside-down boats flip the law of buoyancy

If you’re a water sports fan looking for a new thrill, what about upside-down sailing? The idea might not be so outlandish. In a new study, physicists have managed to float tiny boats on the underside of a layer of liquid levitating in midair (see animation, above). Besides opening up some unusual nautical possibilities, the discovery quite literally flips our understanding of buoyancy on its head.

The science behind why boats float has remained largely unchanged since the ancient Greek mathematician Archimedes explained how the downward force of gravity is balanced by upward pressure from the displaced water. But vibrations can induce strange, gravity-defying behavior. In 1951, Russian Nobel prizewinning physicist Pyotr Kapitsa described how rapidly shaking a pendulum up and down makes it balance upright rather than swing down to its natural stable position. Since then, scientists have used vibrations to make liquids levitate in midair and to get air bubbles to sink rather than rise. The new study suggests they can also reverse the rules of buoyancy.

“It’s very counterintuitive,” says Vladislav Sorokin, an engineer at the University of Auckland. “I have been working in this area for some time, but I wasn't expecting that anything like this could be discovered.”

There was serendipity in the discovery, says Emmanuel Fort, a physicist at ESPCI Paris who led the research. Previous experiments had shown that viscous fluids in a vibrating container can be made to hover. That’s because each time part of the fluid tries to drip down, the shaking provides an opposing force that pushes it back up. That stops the lower surface of the fluid from breaking up and traps a cushion of air underneath.

But Fort, whose lab focuses on optics and imaging, was unaware of this prior research. He and his colleagues were inspired by Kapitsa’s pendulum to see whether they could reproduce similar behavior in a liquid. They built a plexiglass container on top of a shaking machine and filled it with viscous liquids such as silicon oil or glycerol. Then they used a needle to inject a layer of air at the bottom and saw that the vibrating liquid levitated above it.

After realizing the phenomena had been documented decades ago, Fort says they tweaked the experiment further by putting small beads into the levitating liquid layer—and saw that they floated stably on the underside of the liquid. “It was completely unexpected,” Fort says. For visual impact, they swapped the beads for small model boats and found they could be made to float on both the upper and lower surfaces at the same time.

The researchers created a model to explain how the effects of buoyancy are mirrored on the underside of the fluid. Normally, slight disturbances should either nudge the object down into free air, causing it to fall, or up into the liquid, where buoyancy would take over and push it up. But strong vibrations can cancel out these disturbances. They keep the object stable on the lower surface where the downward pull of gravity and upward pull of buoyancy are perfectly balanced, the team reports today in Nature.

It’s not yet clear whether the stunt has any practical uses. Vibrations have been used to control the motion of bubbles in fluids for mineral processing and chemical reactions, but Sorokin says it will take further research to determine whether this new discovery is similarly useful. The bigger contribution, he adds, is showing that vibrating systems still hold undiscovered exotic behaviors.

The team’s setup never used more than half a liter of liquid, but their equations suggest the only thing limiting volume is the strength of the shaking machine. And whereas the approach works well with viscous liquids, it does not perform as well with water, Fort says. So, unless you’re happy casting off into a sea of sticky mineral oil, your dreams of upside-down sailing might be in vain.