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WATCH: Waves in Liquid Metal Form Entrancing Patterns, Offer Hints on Quantum Theory

Cymatics. If you know the word, it conjures images of hypnotic geometries, shapes of sand that shift and rearrange into ever-more-elaborate configurations, while a humming sound in the background rises in pitch to become a whine, and then a high, warbling tone.

If you don’t know the word…put your headphones on and strap in. You’ll thank us.

Any time you see someone putting on chain mail for a physics demo, it’s a pretty good clue that things are about to get really exciting.

The famous vibrating plate in that video is called a Chladni plate, and it sculpts those elaborate shapes with nothing but sound waves and sand. As the plate gets shaken at a given frequency, standing waves in the metal (like the waves that you can see distorting the cymbal when it’s hit) lead some parts of the plate to oscillate wildly up and down, bouncing the grains of sand around until they settle in one of the relatively motionless spots. This visualization of wave behavior is what we call cymatics.

But as that video demonstrates, there’s more than one way to visualize waves; vibrating liquid surfaces and even flowing water can be used (although the impossible-looking zigzag waterfall trick is semi-synthetic, a variation of what’s called the “wagon-wheel effect”). Now, researchers at Tsinghua University and the Chinese Academy of Sciences have invented a new twist on one of those techniques—and it’s got potential way beyond looking cool.

In the video above, we get a brief glimpse of the interesting patterns that you can get by vibrating a dish full of liquid, but this is a serious under-sell of the medium’s cymatic possibilities. If you vary the parameters of the experiment, like how hard and fast the dish is shaken, or the properties of the liquid (like surface tension and viscosity) you can get a range of behaviors as diverse and entrancing as anything a Chladni plate can do.

In a new paper published in the American Physical Society’s journal Physical Review Fluids, researchers Xi Zhao, Jianbo Tang, and Jing Liu use a new technique to explore that parameter space, with spectacular results.

(Click to enlarge)
Some of the fascinating patterns that emerge on the surface of a liquid metal bath, vibrated at various amplitudes and frequencies.
Image Credit: Zhao, et al, Physical Review Fluids
In the past, we've talked about how droplets bouncing on a vibrating liquid surface can provide an incredible analogy for the behavior of quantum particles, and might yield insights that make quantum mechanics intuitively understandable. But those experiments used silicone oil, and waves on the surface of silicone oil travel too fast and chaotically to produce the kind of standing wave patterns the researchers were hoping to study. So instead, the team really cranked up the density of their medium with a mixture called eutectic gallium-indium, or eGaIn. Eutectic means that, while neither gallium nor indium is liquid at room temperature, they can be combined in such a way that the mixture will melt at around 60°F.

To control the amplitude and frequency of vibrations, the researchers built a special software-controlled motorized arm for wiggling the plate of eGaIn up and down. After adding the liquid metal and illuminating the apparatus from the right angle, all that was left to do was experiment!

As the plate gets shaken faster and harder, the liquid's surface gives rise to ever-more complex patterns. Using liquid metal also allowed the researchers to change the material's properties with the press of a button by turning on an electric current.
Credit: Zhao, et al. Physical Review Fluids.

One of the really stunning things about this experiment is that the standing waves in the liquid's surface can also host a similar kind of bouncing droplet to the ones have been shown to mimic the quantum behavior of electrons in oil droplet experiments.

Credit: Zhao, et al. Physical Review Fluids.
Others have managed to extend the oil droplet analogy by creating "lattices" of wells that confine bouncing droplets while still allowing them to interact—and in these experiments, we've seen behaviors that tantalizingly parallel the behaviors of electrons in lattices of atoms. As exciting as those experiments are for fans of pilot wave theory, the system of wells seem contrived, or artificial; in Zhao, Tang, and Liu's new work, the lattice of localized droplets naturally self-assembles, thanks to the standing waves in the liquid.

The black points, visible most clearly when the surface nears flat, are tiny drops of the liquid metal.
Credit: Zhao, et al. Physical Review Fluids
For an experiment that seems, at first glance, like it's simply about fluid dynamics and eye-catching patterns, this study turns out to be a remarkably powerful reminder of the translational potential—and the possibility for beauty—in basic research.

—Stephen Skolnick

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