fluid dynamics

Mathematicians finally solved Feynman’s “reverse sprinkler” problem

fluid dynamics, mathematical modeling, mathematical physics, Physics, reverse sprinkler, Richard Feynman, Science / Ryan Harris / February 2, 2024

A decades-old conundrum —

We might not need to “unwater” our lawns, but results could help control fluid flows.

Jennifer Ouellette – Feb 2, 2024 6: 27 pm UTC

Light-scattering microparticles reveal the flow pattern for the reverse (sucking) mode of a sprinkler, showing vortices and complex flow patterns forming inside the central chamber. Credit: K. Wang et al., 2024

A typical lawn sprinkler features various nozzles arranged at angles on a rotating wheel; when water is pumped in, they release jets that cause the wheel to rotate. But what would happen if the water were sucked into the sprinkler instead? In which direction would the wheel turn then, or would it even turn at all? That’s the essence of the “reverse sprinkler” problem that physicists like Richard Feynman, among others, have grappled with since the 1940s. Now, applied mathematicians at New York University think they’ve cracked the conundrum, per a recent paper published in the journal Physical Review Letters—and the answer challenges conventional wisdom on the matter.

“Our study solves the problem by combining precision lab experiments with mathematical modeling that explains how a reverse sprinkler operates,” said co-author Leif Ristroph of NYU’s Courant Institute. “We found that the reverse sprinkler spins in the ‘reverse’ or opposite direction when taking in water as it does when ejecting it, and the cause is subtle and surprising.”

Ristroph’s lab frequently addresses these kinds of colorful real-world puzzles. For instance, back in 2018, Ristroph and colleagues fine-tuned the recipe for the perfect bubble based on experiments with soapy thin films. (You want a circular wand with a 1.5-inch perimeter, and you should gently blow at a consistent 6.9 cm/s.) In 2021, the Ristroph lab looked into the formation processes underlying so-called “stone forests” common in certain regions of China and Madagascar. These pointed rock formations, like the famed Stone Forest in China’s Yunnan Province, are the result of solids dissolving into liquids in the presence of gravity, which produces natural convective flows.

In 2021, his lab built a working Tesla valve, in accordance with the inventor’s design, and measured the flow of water through the valve in both directions at various pressures. They found the water flowed about two times slower in the nonpreferred direction. And in 2022, Ristroph studied the surpassingly complex aerodynamics of what makes a good paper airplane—specifically what is needed for smooth gliding. They found that paper airplane aerodynamics differ substantially from conventional aircraft, which rely on airfoils to generate lift.

Enlarge / Illustration of a “reaction wheel” from Ernst Mach’s *Mechanik* (1883).

Public domain

The reverse sprinkler problem is associated with Feynman because he popularized the concept, but it actually dates back to a chapter in Ernst Mach’s 1883 textbook The Science of Mechanics (Die Mechanik in Ihrer Entwicklung Historisch-Kritisch Dargerstellt). Mach’s thought experiment languished in relative obscurity until a group of Princeton University physicists began debating the issue in the 1940s.

Feynman was a graduate student there at the time and threw himself into the debate with gusto, even devising an experiment in the cyclotron laboratory to test his hypothesis. (In true Feynman fashion, that experiment culminated with the explosion of a glass carboy used in the apparatus because of the high internal pressure.)

One might intuit that a reverse sprinkler would work just like a regular sprinkler, merely played backward, so to speak. But the physics turns out to be more complicated. “The answer is perfectly clear at first sight,” Feynman wrote in Surely You’re Joking, Mr. Feynman (1985). “The trouble was, some guy would think it was perfectly clear [that the rotation would be] one way, and another guy would think it was perfectly clear the other way.”

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Should you flush with toilet lid up or down? Study says it doesn’t matter

bacteria, Biology, cross contamination, epidemiology, fluid dynamics, hygiene, sanitation, Science, toilet plumes, toilets, viral aerosols / Ryan Harris / January 31, 2024

Whether the toilet lid is up or down doesn't make much difference in the spread of airborne bacterial and viral particles. — Enlarge / Whether the toilet lid is up or down doesn’t make much difference in the spread of airborne bacterial and viral particles.

File this one under “Studies We Wish Had Let Us Remain Ignorant.” Scientists at the University of Arizona decided to investigate whether closing the toilet lid before flushing reduces cross-contamination of bathroom surfaces by airborne bacterial and viral particles via “toilet plumes.” The bad news is that putting a lid on it doesn’t result in any substantial reduction in contamination, according to their recent paper published in the American Journal of Infection Control. The good news: Adding a disinfectant to the toilet bowl before flushing and using disinfectant dispensers in the tank significantly reduce cross-contamination.

Regarding toilet plumes, we’re not just talking about large water droplets that splatter when a toilet is flushed. Even smaller droplets can form and be spread into the surrounding air, potentially carrying bacteria like E. coli or a virus (e.g., norovirus) if an infected person has previously used said toilet. Pathogens can linger in the bowl even after repeated flushes, just waiting for their chance to launch into the air and spread disease. That’s because larger droplets, in particular, can settle on surfaces before they dry, while smaller ones travel further on natural air currents.

The first experiments examining whether toilet plumes contained contaminated particles were done in the 1950s, and the notion that disease could be spread this way was popularized in a 1975 study. In 2022, physicists and engineers at the University of Colorado, Boulder, managed to visualize toilet plumes of tiny airborne particles ejected from toilets during a flush using a combination of green lasers and cameras. It made for some pretty vivid video footage:

Colorado researchers managed to visualize toilet plumes in 2022 using green lasers and strategically placed cameras.

“If it’s something you can’t see, it’s easy to represent it doesn’t exist,” study co-author John Grimaldi said at the time. They found that the ejected airborne particles could travel up to 6.6 feet per second, reaching heights of 4.9 feet above the toilet within 8 seconds. And if those particles were smaller (less than 5 microns), they could hang around in that air for over a minute.

More relevant to this latest paper, it’s been suggested that closing the lid before flushing could substantially reduce the airborne spread of contaminants. For example, in 2019, researchers at University College Cork deployed bioaerosol sensors in a shared lavatory for a week to monitor the number and size of contaminant particles. They concluded that flushing with the toilet lid down reduced airborne droplets between 30 and 60 percent. But this scenario also increased the diameter of the droplets and bacteria concentration. Leaving the lid down also means the airborne microdroplets are still detectable 16 minutes after flushing, 11 minutes longer than if one flushed with the lid up.

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Watch sand defy gravity and flow uphill thanks to “negative friction”

12 days of Christmas, collective motion, engineering, fluid dynamics, granular flow, granular materials, Physics, Science / Ryan Harris / December 27, 2023

On the second day of Christmas —

Applying magnetic forces to single iron oxide-coated particles spurs strange collective motion.

Jennifer Ouellette – Dec 26, 2023 2: 00 pm UTC

There’s rarely time to write about every cool science-y story that comes our way. So this year, we’re once again running a special Twelve Days of Christmas series of posts, highlighting one science story that fell through the cracks in 2023, each day from December 25 through January 5. Today: how applying magnetic forces to individual “micro-roller” particles spurs collective motion, producing some pretty counter-intuitive results.

Enlarge / Engineering researchers at Lehigh University have discovered that sometimes sand can actually flow uphill.

Lehigh University

We intuitively understand that the sand pouring through an hourglass, for example, forms a neat roughly pyramid-shaped pile at the bottom, in which the grains near the surface flow over an underlying base of stationary particles. Avalanches and sand dunes exhibit similar dynamics. But scientists at Lehigh University in Pennsylvania have discovered that applying a magnetic torque can actually cause sand-like particles to collectively flow uphill in seeming defiance of gravity, according to a September paper published in the journal Nature Communications.

Sand is pretty fascinating stuff from a physics standpoint. It’s an example of a granular material, since it acts both like a liquid and a solid. Dry sand collected in a bucket pours like a fluid, yet it can support the weight of a rock placed on top of it, like a solid, even though the rock is technically denser than the sand. So sand defies all those tidy equations describing various phases of matter, and the transition from flowing “liquid” to a rigid “solid” happens quite rapidly. It’s as if the grains act as individuals in the fluid form, but are capable of suddenly banding together when solidarity is needed, achieving a weird kind of “strength in numbers” effect.

Nor can physicists precisely predict an avalanche. That’s partly because of the sheer number of grains of sand in even a small pile, each of which will interact with several of its immediate neighboring grains simultaneously—and those neighbors shift from one moment to the next. Not even a supercomputer can track the movements of individual grains over time, so the physics of flow in granular media remains a vital area of research.

But grains of sand that collectively flow uphill? That is simply bizarre behavior. Lehigh University engineer James Gilchrist manages the Laboratory for Particle Mixing and Self-Organization and stumbled upon this odd phenomenon while experimenting with “micro-rollers”: polymer particles coated in iron oxide (a process called micro-encapsulation). He was rotating a magnet under a vial of micro-rollers one day and noticed they started to pile uphill. Naturally he and his colleagues had to investigate further.

For their experiments, Gilchrist et al. attached neodymium magnets to a motorized wheel at 90-degree intervals, alternating the outward facing poles. The apparatus also included a sample holder and a USB microscope in a fixed position. The micro-rollers were prepared by suspending them in a glass vial containing ethanol and using a magnet to separate them from dust or any uncoated particles. Once the micro-rollers were clean, they were dried, suspended in fresh ethanol, and loaded onto the sample holder. A vibrating motor agitated the samples to produce flattened granular beds, and the motorized wheel was set in motion to apply magnetic torque. A gaussmeter measured the magnetic field strength relative to orientation.

Uphill granular flow of microrobotic microrollers. Credit: Lehigh University.

The results: each micro-roller began to rotate in response to the magnetic torque, creating pairs that briefly formed and then split, and increasing the magnetic force increased the particle cohesion. This in turn gave the micro-rollers more traction and enabled them to move more quickly, working in concert to counterintuitively flow uphill. In the absence of that magnetic torque, the miro-rollers flowed downhill normally. The torque-induced action was so unexpected that the researchers coined a new term to describe it: a “negative angle of repose” caused by a negative coefficient of friction.

“Up until now, no one would have used these terms,” said Gilchrist. “They didn’t exist. But to understand how these grains are flowing uphill, we calculated what the stresses are that cause them to move in that direction. If you have a negative angle of repose, then you must have cohesion to give a negative coefficient of friction. These granular flow equations were never derived to consider these things, but after calculating it, what came out is an apparent coefficient of friction that is negative.”

It’s an intriguing proof of principle that could one day lead to new ways to control how substances mix or separate, as well as potential swarming microrobotics applications. The scientists have already started building tiny staircases with laser cutters and videotaping the micro-rollers climbing up and down the other. One micro-roller can’t overcome the height of each step, but many working collectively can do so, per Gilchrist.

DOI: Nature Communications, 2023. 10.1038/s41467-023-41327-1 (About DOIs).

Listing image by Lehigh University

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Marbled paper, frosty fireworks among 2023 Gallery of Fluid Motion winners

fluid dynamics, gallery of fluid motion, Physics, Science, science and art / Mike M. / December 10, 2023

Enlarge / Harvard University graduate student Yue Sun won a Milton Van Dyke Award for her video on the hydrodynamics of marbled paper.

Y. Sun/Harvard University et al.

Marbled paper is an art form that dates back at least to the 17th century, when European travelers to the Middle East brought back samples and bound them into albums. Its visually striking patterns arise from the complex hydrodynamics of paint interacting with water, inspiring a winning video entry in this year’s Gallery of Fluid Motion.

The American Physical Society’s Division of Fluid Dynamics sponsors the gallery each year as part of its annual meeting, featuring videos and posters submitted by scientists from all over the world. The objective is to highlight “the captivating science and often breathtaking beauty of fluid motion” and to “celebrate and appreciate the remarkable fluid dynamics phenomena unveiled by researchers and physicists.”

The three videos featured here are the winners of the Milton Van Dyke Awards, which also included three winning posters. There were three additional general video winners—on the atomization of impinging jets, the emergent collective motion of condensate droplets, and the swimming motion of a robotic eel—as well as three poster winners. You can view all the 2023 entries (winning and otherwise) here.

The hydrodynamics of marbling art

Harvard University graduate student Yue Sun was fascinated by the process and the resulting patterns of making marbled paper, particularly the randomness. “You don’t really know what you’re going to end up with until you have it printed,” she told Physics Magazine.

Although there are several different methods for marbling paper, the most common involves filling a shallow tray with water, then painstakingly applying different ink or paint colors to the water’s surface with an ink brush to cover the surface with concentric circles. Adding surfactants makes the colors float so that they can be stirred—perhaps with a very fine human hair—or fanned out by blowing on the circles of ink or paint with a straw. The final step is to lay paper on top to capture the colorful floating patterns. (Body marbling relies on a similar process, except the floating patterns are transferred onto a person’s skin.)

Sun was curious about the hydrodynamics at play and explored two key questions in the simulations for the video. Why does the paint or ink float despite being denser than the liquid bath? And why don’t the colors mix together to create new colors when agitated or stirred? The answer to the former is basically “surface tension,” while the latter does not occur because the bath is too viscous, so the diffusion of the paint or ink colors across color boundaries happens too slowly for mixing. Sun hopes to further improve her simulations of marbling in hopes of reverse-engineering some of her favorite patterns to determine which tools and movements were used to create them.

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