Simple, Inexpensive Magnetic Levitation: The Flight of the Humble “Flea”

From flying broomsticks to floating cities and container-less storage, levitation has a tendency to capture the imagination. Among the impractical and impossible ideas, there are some good ones that have already taken hold. Maglev trains now carry passengers in Japan, South Korea, and China, and have been proposed in countries across the world. Fun (but less useful) hoverboards operate on similar technology, as do magnetic bearings used in industrial machinery.

In an upcoming issue of the American Physical Society’s journal Physical Review Letters, a team of researchers demonstrates a new route to magnetic levitation, one that you can try if you have access to a basic science lab—no sub-zero temperature or specialized equipment required.

One method the researchers used to demonstrate the spinning and waggling of a levitating “flea” magnet was to image it from above with a high-speed camera, and then combine all the images into a 3D spiral. This image shows a snapshot of the levitating flea with one of these spirals.
Image Credit: Kyle Baldwin.

The story starts back in 2014, when researchers at Nottingham Trent University (NTU) in the UK were mixing solutions with a magnetic stirrer. This common piece of lab equipment consists of two pieces, a small magnetic stir bar and a plate. The plate has a magnet inside that is attached to a motor, and when you turn the motor on, the magnet—called the drive magnet—spins, producing a rotating magnetic field. When you put the stir bar inside of a fluid-filled container and set the container on the plate, the rotating magnetic fields causes the stir bar to spin and mix the solution.

Magnetic stirrers are efficient, don’t have a lot of moving parts that can break down, and are easy to use in sealed container (as long as you plan ahead!). You can also adjust the spinning speed. As new users learn quickly, if you drive the stir bar too fast the magnet will go from spinning to hopping around chaotically, a performance that has earned it the nickname “flea.”

Now back to the story. The researchers were mixing solutions with high viscosity, and drove the flea too quickly. To their surprise, the bar didn’t just hop: it jumped up from the bottom of the container and then stayed there—levitating in the solution as it spun.

“I was very surprised when we observed a bar magnet levitating another bar magnet at room temperature!” says Kyle Baldwin, a physicist at NTU and the Max Planck Institute for Dynamics and Self-Organization in Germany. “We were even more surprised to discover that this phenomenon had not been reported on previously. So we set out to discover what stabilizes this levitation.”

To find out, the researchers explored what happens to the flea when you adjust three things in the system: the spin speed, the viscosity of the fluid, and the height of the flea relative to the drive magnet.

Here’s what they found. Initially, the flea spins synchronously with the drive magnet, but unlike champion synchronized swimmers, the timing is a little offset. This is because the flea spins in a fluid and the drive magnet doesn’t. The more viscous the fluid, the more offset the timing.

If you continue increasing the spin speed, you eventually hit a point when the drive magnet suddenly repels the flea vertically, because of their relative alignment. What happens next depends primarily on the viscosity of the fluid. In low viscosity fluids, like water, the repulsive force causes the well-known hopping motion. In fluids with just the right viscosity (0.4 Pascal-seconds), the repulsive vertical force overcomes gravity, causing the flea to jump up and levitate in a stable vertical position while spinning and waggling back-and-forth. If you slow down the spin speed, the flea falls back down.

The researchers suspected that the surprising stability had something to do with hydrodynamics—the motion of the fluid around the flea—so they worked with colleagues at the University of Nottingham to simulate the fluid flow caused by a waggling flea at different viscosities. Right around the viscosity where levitation becomes stable, they saw the fluid flow change directions.

“This was our smoking gun,” says Baldwin. “We then devised a way to visualize these real flows in the experiment using a laser sheet and a custom-built device that replicates the waggle but without all the other complex motion that the flea undergoes as it levitates. The experimental flows matched the simulations beautifully, and so finally we had our answers.”

He goes on to explain, “When the flea is stable, we see in experiment and simulation that the waggle pumps fluid outwards to the sides. But, if viscosity is reduced, the flow direction switches from outwards to inwards, and it’s during that switch that levitation becomes unstable. This is probably why this hasn’t been observed before – in water and most solvents, the viscosity is so low that flows are more chaotic, and if driven to stir too quickly, [the bar] won’t levitate, but it will just jump around instead.”

This insight, combined with the levitating behavior, could have practical implications for the designs of bidirectional pumps, micro-scale submersibles, scientific instruments, and other applications yet to be discovered. It’s also a fun, simple, inexpensive way to levitate something! If you give it a try, be sure to comment here with your results.

The most exciting phrase to hear in science, the one that heralds new discoveries, is not ‘Eureka!’, but ‘That’s funny …’
-Isaac Asimov

—Kendra Redmond

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