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Pilot-Wave Hydrodynamics: Slit Experiments
This post is part of a collaborative series with FYP on pilot-wave hydrodynamics. Previous entries: 1) Introduction; 2) Chladni patterns; 3) Faraday instability; 4) Walking droplets; 5) Droplet lattices; 6) Quantum double-slit experiments
In quantum mechanics, the single and double-slit experiments are foundational. They demonstrate that light and elementary particles like electrons have wave-like and particle-like properties, both of which are necessary to explain the behaviors observed. Similarly, a hydrodynamic walker consists of both a particle and a wave, so, perhaps unsurprisingly, researchers tested them in both single-slit and double-slit experiments.
When a walker passes through a single-slit (top row), it’s deflected in a seemingly random direction due to its waves interacting with the slit. But if you watch enough walkers traverse the slit, you can put together a statistical representation of where the walker will get deflected. Compare that with the results for a series of photons passing through a slit one-at-a-time, and you’ll see a remarkable match-up.
If you test the walker instead with two slits, the droplet can only pass through one slit, but its accompanying wave passes through both (bottom row). Let enough walkers through the system one-by-one, and they, like their photonic cousins, build up interference fringes that match the quantum experiment. Diffraction and interference are only a couple of the walkers’ tricks, however. In the next posts, we’ll take a look at another analog to quantum behavior: tunneling.
(Image and research credits: Couder et al., source, selected papers 1, 2; images courtesy of E. Fort)
January 10, 2018
Pilot-Wave Hydrodynamics: Walking Drops
This post is a collaborative series with FYP on pilot-wave hydrodynamics. Previous entries: 1) Introduction; 2) Chladni patterns; 3) Faraday instability
If you place a small droplet atop a vibrating pool, it will happily bounce like a kid on a trampoline. On the surface, this seems quite counterintuitive: why doesn’t the droplet coalesce with the pool? The answer: there’s a thin layer of air trapped between the droplet and the pool. If that air were squeezed out, the droplet would coalesce. But it takes a finite amount of time to drain that air layer away, even with the weight of the droplet bearing down on it. Before that drainage can happen, the vibration of the pool sends the droplet aloft again, refreshing the air layer beneath it. The droplet falls, gets caught on its air cushion, and then sent bouncing again before the air can squeeze out. If nothing disturbs the droplet, it can bounce almost indefinitely.
Droplets don’t always bounce in place, though. When forced with the right frequency and acceleration, a bouncing droplet can transition to walking. In this state, the droplet falls and strikes the pool such that it interacts with the ripple from its previous bounce. That sends the droplet aloft again but with a horizontal velocity component in addition to its vertical one. In this state, the droplet can wander about its container in a way that depends on its history or “memory” in the form of waves from its previous bounces. And this is where things start to get a bit weird – as in quantum weirdness – because now our walker consists of both a particle (droplet) and wave (ripples). The similarities between quantum behaviors and the walking droplets, the collective behavior of which is commonly referred to as “pilot-wave hydrodynamics,” are rather remarkable. In the next couple posts, we’ll take a look at some important quantum mechanical experiments and their hydrodynamic counterparts.
(Image credit: D. Harris et al., source)
January 9, 2018
Pilot-Wave Hydrodynamics: Faraday Instability
This post is part of a collaborative series with FYP on pilot-wave hydrodynamics. Previous entries: 1) Introduction; 2) Chladni patterns
In 1831, in an appendix to a paper on Chladni plate patterns, physicist Michael Faraday wrote:
“When the upper surface of a plate vibrating so as to produce sound is covered with a layer of water, the water usually presents a beautifully crispated appearance in the neighborhood of the centres of vibration.” #
Faraday was not the first to notice this, as he himself acknowledged, but it was his many clever observations and tests of the phenomenon that led to its naming as the Faraday instability. Like Chladni patterns, Faraday waves can take many forms, depending on the geometry of the vibrator and the frequency and amplitude of its vibration.
Beneath the “crispations” at the air interface, the liquid inside the pool is also moving, driven by the vibrations into streaming patterns. Sprinkling particles into this flow reveals discrete recirculation zones that depend on the vibrations’ characteristics, as seen above. This behavior can even be used to assemble particles into distinct formations.
When the vibrations are large enough at resonant frequencies, the rippling waves at the surface become violent enough to start ejecting droplets. You can experience this for yourself using a Chinese spouting bowl or a Tibetan singing bowl with some water. It’s also, bizarrely enough, a factor in alligator mating behaviors!
Next time, we’ll explore what happens to a droplet atop a Faraday wave.
(Image credits: N. Stanford, source; L. Gledhill, source; The Slow Mo Guys, source)
January 8, 2018
Pilot-Wave Hydrodynamics: Introduction
For the next week on FYFD, I’ll be doing something a little different. I’ve teamed up with FYP to produce a joint series of posts on pilot-wave hydrodynamics, a recent area of investigation on fluid systems that display quantum mechanical behaviors. We’ve touched on some aspects of this previously, but this series will get into more details, building from nineteenth century explorations of vibration all the way to current research. Each weekday FYP and FYFD will each feature a new post in the series, so you can look forward to ten entries total next week. I’ll start each FYFD entry with a recap of links to previous posts so you can be sure you haven’t missed any.
To give you a taste of what’s to come, check out Nigel Stanford’s awesome “Cymatics” music video below. On Monday, we’ll start our exploration of pilot-wave hydrodynamics by examining some of the phenomena featured in the video. (Image credit: D. Harris, original; video credit: N. Stanford)
January 5, 2018
Hair-Washing in Microgravity
I imagine that the most common questions astronauts get come in the form, “How do you do X in space?” In this video, astronaut Karen Nyberg demonstrates how she washes her hair in space. Using no-rinse shampoo, the process is not terribly different from on Earth: wet the hair, work in the shampoo, add a little more water, and use a towel and comb to work it through all the hair. The big difference is that Nyberg’s hair sticks almost straight up the whole time. That’s an effect of microgravity, obviously, but there are fluid forces at play, too, namely elastocapillarity.
Hair typically feels quite different when it’s wet. Strands bunch together and feel stiffer. This is because of the water trapped in the narrow space between individual hairs. The water’s fluid characteristics (capillarity) affect the solid hairs and change their elastic properties – hence elastocapillarity. We see this on Earth, of course, but the effect is especially noticeable without gravity pulling the wet hair down. (Video credit: K. Nyberg/NASA; via APOD; submitted by Guillaume D.)
January 4, 2018
The Best of FYFD 2017
2017 was a busy, busy year here at FYFD, but a lot of that happened behind the scenes with multiple collaborations that were months in the planning. You’ll start to see the results of those collaborations here in January, starting this Friday. I’m really excited for you all to see what I’ve been up to!
In the meantime, we’ll take our traditional look back at the top 10 FYFD posts of 2017, according to you:
1. Cinemagraph of a breaking wave
2. Visualizing radiation in a cloud chamber
3. Fire ants as a fluid
4. The water music of Vanuatu
5. How hummingbirds drink nectar
6. When vortex rings collide
7. How water balloons can bounce off a bed of nails
8. Spinning ice disks form on freezing rivers
9. A hot-tub-sized fluidized bed
10. The physics of fluidized beds
Lots of crazy, cool stuff in there! Special congrats to The Splash Lab for making the top 10 two years in a row. Stay tuned in 2018 for more exciting fluid dynamical developments, and if you’d like to help support FYFD, remember that you can always become a patron, make a one-time donation, or purchase some merch!
(Image credits: R. Collins / J. Maria; Cloudylabs; Vox/Georgia Tech; R. Hurd et al.; A. Varma; A. Lawrence; T. Hecksher et al.; K. Messer; M. Rober; R. Cheng)
January 1, 2018
Breaking Up Turbulence
Under most circumstances, we think about flows changing from ordered and laminar to random and turbulent. But it’s actually possible for disordered flows to become laminar again. This is what we see happening in the clip above. Upstream, the flow in this pipe is turbulent (left). Then four rotors are used to perturb the flow (center). This disrupts the turbulence and causes the flow to become laminar again downstream (right). To understand how this works, we have to talk about one of the fundamental concepts in turbulence: the energy cascade.
Turbulent flows are known for their large range of length scales. Think about a volcanic plume, for example. Some of the turbulent motions in the plume may be a hundred meters across, but there are a continuous range of smaller scales as well, all the way down to a centimeter or less in size. In a turbulent flow, energy starts at the largest scales and flows further and further down until it reaches scales small enough that viscosity can extinguish them.
That should offer a hint as to what’s happening here. The rotors are perturbing the flow, yes, but they’re also breaking the larger turbulent scales down into smaller ones. The smaller the largest lengthscales of the flow are, the more quickly their energy will decay to the smallest lengthscales where viscosity can damp them out. This is what we see here. Once the turbulent energy is concentrated at the smallest scales, viscosity damps them out and the flow returns to laminar. Check out the full video below for a cool sequence where the camera moves alongside the pipe so you can watch the turbulence fading as it moves downstream. (Image and video credit: J. Kühnen et al.)
ETA: As it turns out, there’s more going on here than I’d originally thought. Simulations show that breaking up length scales is not the primary cause of relaminarization in this case. Instead, the rotors are modifying the velocity profile across the pipe in such a way that it tends to cause the turbulence to die out. The full paper is now out in Nature Physics and on arXiv.
December 29, 2017
The Fishbone
The simple collision of two liquid jets can form striking and beautiful patterns. Here the two jets strike one another diagonally near the top of the animation. One is slanted into the screen; the other slants outward. At their point of contact, the liquid spreads into a sheet and forms what’s known as a fishbone pattern. The water forms a thicker rim at the edge of the sheet, and this rim destabilizes when surface tension can no longer balance the momentum of the fluid. Fingers of liquid form along the edge, stretching outward until they break apart into droplets. Ultimately, this instability tears the liquid sheet apart. Under the right conditions, all kinds of beautiful shapes form in a system like this. (Image credit: V. Sanjay et al., source)
December 28, 2017
Swimming Microdroplets
Simple systems can sometimes have surprisingly complex behaviors. In this video, the Lutetium Project outlines a scheme for swimming microdroplets. Most of the droplets shown are just water, but they’re released into a chamber filled with a mixture of oil and surfactants. All flow through the chamber is shut off, but the droplets swim around in complicated, disordered patterns anyway. To see why, we have to zoom way in. The surfactant molecules in the oil cluster around the droplets, orienting so that their hydrophobic parts are in the oil and their hydrophilic parts point toward the water. They actually draw some of the water out of the droplets. This creates a variation in surface tension that causes Marangoni flow, making the droplets swim. Over time, the droplets shrink and slow down as the surfactants pull away more and more of their water and the variations in surface tension get smaller. (Image and video credit: The Lutetium Project; research credit: Z. Izri et al.)
December 27, 2017
Singularities
Black holes, like the collapse of a cavity in a fluid, are a singularity – a point where the mathematical rules we use to describe physical systems break down. No one knows what exists in a black hole, but the short film “Intra” explores one theory – that the exit to a black hole is a white hole, a singularity from which time and space themselves are born. The journey from one to the other is illustrated in the film with CGI visualizations of a black hole (a la Interstellar) and with fluid dynamical sequences depicting diffusion and chemical reactions driving flows. Although no true white holes have ever been observed, there are fluid dynamical analogs for them, namely circular hydraulic jumps, like the one you can make in your kitchen sink! (Video credit: T. Vanz et al.)
December 25, 2017

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