Turning buoyancy on its head

At risk of stating the obvious: boats float on top of water. Yet French researchers have seemingly inverted gravity and made a boat float on the underside of a levitating layer of liquid.

Make your own jokes about the antipodes.

The research into unusual buoyancy found that tiny plastic boats are able to float upside down on the interface between air and liquid. Not only that, gas bubbles in the lower half of the liquid layer don’t rise, they sink. The mind-bending results have been published in the journal Nature.

When placed above a less-dense medium, such as air, liquids fall with gravity due to a destabilising effect called the Rayleigh–Taylor instability.

As the liquid forms into drops, it displaces the air underneath, and falls to the bottom. However, this can be overcome by vibrating a container vertically – the movement keeps the bottom of the liquid layer flat, preventing drops from forming and thus unable to displace the air underneath. The result is a levitating liquid layer unable to fall, and an air layer beneath which is compressed, but unable to rise.

This is not a new phenomenon; it’s been known about and used for a while. But until now, no one has studied how that affects buoyancy on the bottom interface.

Benjamin Apffel from ESPCI Paris and colleagues reveal that this vertical shaking also causes buoyancy to flip at the lower surface of the levitated liquid — as if the gravity there has been inverted.

Using small model boats and plastic balls, they showed that at this lower interface, the objects would “float” upside-down as if they were at the upper surface. The effect worked for objects up to 7 g in mass and 2.5 cm long.

The effect is in part due to the balance of pressures from the air trapped underneath, and the liquid from above. The air layer is compressed due to the mass of the liquid pushing down from above; similarly, the density of the liquid at the bottom is slightly higher than at the top due to the mass of the liquid above.

As a result, the object at the bottom interface is pushed upwards by the pressure of the air layer. Then, in the liquid layer, the object exerts an upwards buoyancy force towards the upper surface. These upwards forces are counteracted by gravity and the mass of the object. These forces reach an equilibrium in the liquid layer, and it floats in place.

“Archimedes’ principle states that the upward buoyant force exerted on an immersed body, whether fully or partially submerged, is equal to the weight of the displaced fluid. Although it may seem counterintuitive, the transpose symmetric position at the lower interface also exhibits an upward buoyant force equal to the weight of displaced liquid,” the researchers write.

In other words, the buoyancy force is always operating opposite to gravity and is equivalent to its displacement, and not towards the liquid/air interface.

The effect only occurs as a dynamic phenomenon – the liquid and air both need to be vibrating vertically, says the University of Auckland’s Vladislav Sorokin, who wasn’t involved in the research.

“Due to vibration, a ‘special’ time-averaged force occurs that acts on the immersed object (boat) at the lower interface of the fluid. Without vibration (or if vibration frequency is too low) this phenomenon will not occur.”

In the experiments the team were able to levitate up to half a litre of viscous liquids – silicon oil or glycerol – in a containers up to 20 cm wide.

“Many remarkable phenomena arising in vibrating mechanical systems are yet to be revealed and explained, particularly at interfaces between gases and fluids,” Sorokin writes in an accompanying commentary.

“It will be exciting to discover what counter-intuitive phenomena can be induced by high-frequency excitations in non-mechanical systems – is there a chemical or biological counterpart of inverse gravity?”

Boats floating at the interfaces of the levitating liquid layer. Credit: Benjamin Apffel et al., Nature.

The Royal Institution of Australia has an Education resource based on this article. You can access it here.