Fuck Yeah Fluid Dynamics

Celebrating the physics of all that flows. Ask a question, submit a post idea or send an email. You can also follow FYFD on Twitter and Google+. FYFD is written by Nicole Sharp, PhD.

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The coalescence of two liquid droplets takes less than the blink of an eye, but it is the result of an intricate interplay between surface tension, viscosity, and inertia. The high-speed video above was filmed at 16000 frames per second, yet the initial coalescence of the silicone oil drops is still nearly instantaneous. At the very instant the drops meet, an infinitesimally small neck is formed between the droplets. Mathematically speaking, the pressure and curvature of the droplets diverge as a result of this tiny contact area. This is an example of a singularity. Surface tension rapidly expands the neck, sending capillary waves rippling along the drops as they become one. (Video credit: S. Nagel et al.; research credit: J. Paulsen)

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Reader isotropicposts writes:

Hi, I’m taking a fluids class and I’m not sure I understand the whole lagrangian-eulerian measurements of velocity and acceleration. Could you explain this?

This is a really great question because the Eulerian versus Lagrangian distinction is not obvious when you first learn about it. If you think about a fluid flowing, there are two sensible reference frames from which we might observe. The first is the reference frame in which we are still and the fluid rushes by. This is the Eulerian frame. It’s what you get if you stand next to a wind tunnel and watch flow pass. It’s also how many practical measurements are made. The photo above shows a Pitot tube on a stationary mount in a wind tunnel. With the air flow on, the probe measures conditions at a single stationary point while lots of different fluid particles go past.

The other way to observe fluid motion is to follow a particular bit of fluid around and see how it evolves. This is the Lagrangian method. While this is reasonably easy to achieve in calculations and simulations, it can be harder to accomplish experimentally. To make these kinds of measurements, researchers will do things like mount a camera system to a track that runs alongside a wind tunnel at the mean speed of the flow. The resulting video will show the evolution of a specific region of flow as it moves through time and space. The video below has a nice example of this type of measurement in a wave tank. The camera runs alongside the the wave as it travels, making it possible to observe how the wave breaks.

In the end, both reference frames contain the same physics (Einstein would not have it any other way), but sometimes one is more useful than the other in a given situation. For me, it’s easiest to think of the Eulerian frame as a laboratory-fixed frame, whereas the Lagrangian frame is one that rides alongside the fluid. I hope that helps! (Photo credit: N. Sharp; video credit: R. Liu et al.)

Human eyesight is not always the best for observing how nature behaves around us. Fortunately, we’ve developed cameras and sensors that allow us to effectively see in wavelengths beyond those of visible light. What’s shown here is a frying pan with a thin layer of cooking oil. To the human eye, this would be nothing special, but in the infrared, we can see Rayeigh-Benard convection cells as they form. This instability is a function of the temperature gradient across the oil layer, gravity, and surface tension. As the oil near the bottom of the pan heats up, its density decreases and buoyancy causes it to rise to the surface while cooler oil sinks to replace it. Here the center of the cells is the hot rising oil and the edges are the cooler sinking fluid. The convection cells are reasonably stable when the pan is moved, but, even if they are obscured, they will reform very quickly.  (Video credit: C. Xie)

Loris Cecchini’s "Wallwave Vibration" series is strongly reminiscent of Faraday wave patterns. The Faraday instability occurs when a fluid interface (usually air-liquid though it can also be two immiscible liquids) is vibrated. Above a critical frequency, the flat interface becomes unstable and nonlinear standing waves form. If the excitation is strong enough, the instability can produce very chaotic behaviors, like tiny sprays of droplets or jets that shoot out like fountains. In a series of fluid-filled cells, the chaotic behaviors can even form synchronous effects above a certain vibration amplitude. (Image credit: L. Cecchini; submitted by buckitdrop)

Aerogel is an extremely light porous material formed when the liquid inside a gel is replaced with gas. When combined with water, aerogel powders can have some wild superhydrophobic effects. Here water condensed on a liquid nitrogen cooler has dripped onto a floor scattered with aerogel powder from the nitrogen’s shipping container. The result is that the water gets partially coated in aerogel powder and takes on some neat properties. Its contact angle with the surface increases - in other words, it beads up - which is typical of superhydrophobicity. When disturbed, the water breaks easily into droplets which do not immediately recombine upon contact. With sufficient distortion, they can rejoin. You can see some other neat examples of aerogel-coated water behaviors in this second video as well. (Video credit: ophilcial; submitted by Jason I.)

The Kaye effect is particular to shear-thinning non-Newtonian fluids - that is, fluids with a viscosity that decreases under deformation. The video above includes high-speed footage of the phenomenon using shampoo. When drizzled, the viscous liquid forms a heap. The incoming jet causes a dimple in the heap, and the local viscosity in this dimple drops due to the shear caused by the incoming jet. Instead of merging with the heap, the jet slips off, creating a streamer that redirects the fluid. This streamer can rise as the dimple deepens, but, in this configuration, it is unstable. Eventually, it will strike the incoming jet and collapse. It’s possible to create a stable version of the Kaye effect by directing the streamer down an incline. (Video credit: S. Lee)

Sneezing and coughing are major contributors to the spread of many pathogens. Both are multiphase flows, consisting of both liquid droplets and gaseous vapors that interact. The image on the left shows a sneeze cloud as a turbulent plume. The kink in the cloud shows that plume is buoyant, which helps it remain aloft. The right image shows trajectories for some of the larger droplets ejected in a sneeze. Like the sneeze cloud, these droplets persist for significant distances. The buoyancy of the cloud also helps keep aloft some of the smaller pathogen-bearing droplets. Researchers are building models for these multiphase flows and their interactions to better predict and counter the spread of such airborne pathogens. For similar examples of fluid dynamics in public health, see what coughing looks like, how hospital toilets may spread pathogens, and how adjusting viscoelastic properties may counter these effects. (Image credit: L. Bourouiba et al.)

Ocean waves contain substantial amounts of energy, and many projects are underway to harness them as renewable energy sources. Most of these projects use the motion caused by waves to generate electrical energy. In this example, a flexible carpet is attached to hydraulic pumps. As the waves move over the carpet, it oscillates, raising and lowering the piston of the pumps. This adds hydraulic pressure to the discharge lines that run from the wave carpet to the shore. Once on dry land, that hydraulic pressure can be converted to electrical energy. This design addresses one of the major challenges in ocean-wave-energy technologies—namely how to safely transmit power from the wave farm to the shore. (Video credit: University of California Television)

A core-collapse, or Type II, supernova occurs in massive stars when they can no longer sustain fusion. For most of their lives, stars produce energy by fusing hydrogen into helium. Eventually, the hydrogen runs out and the core contracts until it reaches temperatures hot enough to cause the helium to fuse into carbon. This process repeats through to heavier elements, producing a pre-collapse star with onion-like layers of elements with the heaviest elements near the center. When the core consists mostly of nickel and iron, fusion will come to an end, and the core’s next collapse will trigger the supernova. When astronomers observed Supernova 1987A, the closest supernova in more than 300 years, models predicted that the onion-like layers of the supernova would persist after the explosion. But observations showed core materials reaching the surface much faster than predicted, suggesting that turbulent mixing might be carrying heavier elements outward. The images above show several time steps of a 2D simulation of this type of supernova. In the wake of the expanding shock wave, the core materials form fingers that race outward, mixing the fusion remnants. Hydrodynamically speaking, this is an example of the Richtmyer-Meshkov instability, in which a shock wave generates mixing between fluid layers of differing densities. (Image credit: K. Kifonidis et al.; see also B. Remington)

These satellite images show the effects of a sudden influx of warm freshwater on sea ice in the Arctic Ocean. On the left are natural color satellite images of Canada’s Mackenzie River delta where it enters the Beaufort Sea. On the right are temperature maps of the ice and water surface temperatures for the same regions. In June 2012, the coastal sea ice that had been blocking the river's delta broke, releasing a massive discharge of river water. The natural color images show brown and tan sediment reaching far out from the river delta, but the temperature maps on the right are even more dramatic. Warmer river water has spread many hundreds of kilometers from the delta, melting sea ice and raising the open water surface temperatures by an average of 6.5 degrees Celsius. The effects of river discharge on sea ice melt are increasing as inland Arctic areas warm more in the summers and the sea ice becomes thinner and more vulnerable each year. (Image credits: NASA Earth Observatory)