“Walkers” Go Super

Without context, you might think a “superwalker” is an extra-fast power walker, topnotch zombie, or even a high-tech mobility device. But this is a physics blog, so that’s your first clue that we’re headed in a different direction. The superwalkers in this story don’t even have legs—they are small drops of liquid with surprising capabilities that were serendipitously discovered by researchers at Monash University in Australia.

Two superwalking droplets. Credit: R. Valani, T. Simula A. Slim / PRL,

DOI: 10.1103/PhysRevLett.123.024503.

Before we get into the details of superwalkers, let’s start with regular walkers. About 15 years ago, researchers discovered that if you vibrate a small, open container of liquid in the right way and under the right conditions, a droplet of the same liquid will “walk” horizontally across the liquid surface.

Sáenz, et alSpin lattices of walking dropletsAPS Gallery of Fluid Motion

When a droplet hits the liquid for the first time, it bounces upward and creates waves in the liquid. When it falls back down again, the droplet interacts with the waves it created previously and gets a horizontal kick, even as it creates new waves. Interactions with the waves compel the droplet, or a collection of droplets, to walk on the surface in fascinating ways.

These “walkers” are more than the subject of cool videos, they also turn out to be an interesting model for quantum behavior. The most common interpretation of the strange behavior we see in experiments with small particles, like electrons, is that they are both waves and particles. One of the results of this dual existence is that particles don’t have an exact position until they are measured.

However, a lesser-known alternative interpretation, called the Pilot Wave Theory, proposes that particles do have an exact location and that they guided (or pushed) by matter waves—similar to how walkers are pushed around by liquid waves. “Working with this experiment of moving droplets across a pool of liquid can stretch the analogy of Pilot Wave Theory to a larger scale, attempting to relate this interpretation of quantum mechanics to a more intuitive, classical system,” explains Phoebe Sharp in a Physics Buzz post on this topic in 2018.

Needless to say, walkers attracted a lot of attention. Most of the time, researchers create walkers by placing a small container of oil on a speaker and driving the speaker with a pure sine wave. As the speaker cone vibrates, so does the pool. Then the researchers create a droplet of the same liquid and let it fall onto the surface.

Rahil Valani, a graduate student working with Tapio Simula and Anja Slim at Monash University, was interested in exploring this phenomenon from a new angle. Previous research had shown that driving a liquid with two different frequencies can create waves with interesting, ordered patterns on the scale of the waves that propel walkers. Valani, Simula, and Slim wondered how droplets would respond to such waves. “Broadly, the idea at the time was to explore two-frequency driving to try finding new kinds of droplet behaviors by modifying the system in any and every possible way,” says Valani.

He started the exploration by driving the pool at one frequency and then adding in a second frequency that was half the value—and struck gold. “I created droplets of all different sizes and found that when I switch on the second frequency, suddenly the bigger droplets start walking very fast,” says Valani. This was unexpected and curious. Especially because when the team tried to recreate these “superwalkers” on a different experimental setup with the same frequencies, it didn’t work.

Eventually, they realized the problem. The two frequencies were the same in both setups, but the phase difference, or overlap, between the two waves, was different. Once they adjusted the phase difference in the second set up to match that of the first, things fell into place. Superwalkers only exist for a narrow range of frequencies and phase differences. With this finding Valani realized just how lucky he was, “coincidentally, we just happened to have the right phase difference between the two frequencies to discover the superwalkers!”

Using this two-frequency, phase-dependent system, the team created walkers twice as big and up to three times as fast as any walker previously created. This led to cool videos of course, but here’s the most important result: Superwalkers are big enough and fast enough that they interact directly with other droplets—they can easily overcome wave barriers that keep regular walkers from such close interactions. That means there’s a whole new world of behaviors to explore. Some examples are shown below. Unless otherwise noted, the droplets are driven at 80 Hz and 40 Hz.

Promenading droplets. Credit: R. Valani, T. Simula A. Slim, Monash University.

Superwalking droplets displaying stop-and-go behavior. This behavior is the result of driving the droplets at 80 Hz and 39.5 Hz. Credit: R. Valani, T. Simula A. Slim, Monash University.

One droplet chasing another. Credit: R. Valani, T. Simula A. Slim, Monash University.

“At this stage, we are particularly interested in exploring the dynamics of many superwalkers,” says Valani. “The most intriguing thing about these walking droplets is that they have been shown to mimic several features that are intrinsic to the quantum world. It will be interesting to see how superwalkers behave in such experiments,” he says.

This research was published in a recent issue of the American Physical Society’s journal Physical Review Letters.

–Kendra Redmond.

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