Whenever a hollow cavity forms at the surface of a liquid, the cavity’s collapse generates a jet–a rising, high-speed column of liquid. The composite images above show snapshots of the process, from the moment of the cavity’s greatest depth to the peak of the jet. The top row of images shows water, and the bottom row contains a fluid 800 times more viscous than water. The added viscosity both smooths the geometry of the process and slows the jet down, yet strong similarities clearly remain. Focusing on similarities in fluid flows across a range of variables, like viscosity, is key to building mathematical models of fluid behavior. Once developed, these models can help predict behaviors for a wide range of flows without requiring extensive calculation or experimentation. (Image credit: E. Ghabache et al.)
Tag: physics
Is the Star Trek Voyager Opening Sequence Physically Realistic?
Today’s post is largely brought to you by the fact that I have been sick the past four days and my fiance and I have been bingeing on Star Trek Voyager. At some point, we began wondering about the sequence from 0:30-0:49 in which Voyager flies through a nebula and leaves a wake of von Karman vortices. Would a starship really leave that kind of wake in a nebula?
My first question was whether the nebula could be treated as a continuous fluid instead of a collection of particles. This is part of the continuum assumption that allows physicists to treat fluid properties like density, temperature, and velocity as well-defined quantities at all points. The continuum assumption is acceptable in flows where the Knudsen number is small. The Knudsen number is the ratio of the mean free path length to a characteristic flow length, in this case, Voyager’s size. The mean free path length is the average distance a particle travels before colliding with another particle. Nebulae are much less dense than our atmosphere, so the mean free path length is larger (~ 2 cm by my calculation) but still much smaller than Voyager’s length of 344 m. So it is reasonable to treat the nebula as a fluid.
As long as the nebula is acting like a fluid, it’s not unreasonable to see alternating vortices shed from Voyager. But are the vortices we see realistic relative to Voyager’s size and speed? Physicists use the dimensionless Strouhal number to describe oscillatory flows and vortex shedding. It’s a ratio of the vortex shedding frequency times the characteristic length to the flow’s velocity. We already know Voyager’s size, so we just need an estimate of its velocity and the number of vortices shed per second. I visually estimated these as 500 m/s and 2.5 vortices/second, respectively. That gives a Strouhal number of 0.28, very close to the value of 0.2 typically measured in the wake of a cylinder, the classical case for a von Karman vortex street.
So far Voyager’s wake is looking quite reasonable indeed. But what about its speed relative to the nebula’s speed of sound? If Voyager is moving faster than the local speed of sound, we might still see vortex shedding in the wake, but there would also be a bow shock off the ship’s leading edge. To answer this question, we need to know Voyager’s Mach number, its speed relative to the local speed of sound. After some digging through papers on nebulae, I found an equation to estimate speed of sound in a nebula (Eq 9 of Jin and Sui 2010) using the specific gas constant and temperature. Because nebulae are primarily composed of hydrogen, I approximated the nebula’s gas constant with hydrogen’s value and chose a representative temperature of 500 K (also based on Jin and Sui 2010). This gave a local speed of sound of 940 m/s, and set Voyager’s Mach number at 0.53, inside the subsonic range and well away from any shock wave formation.
Of course, these are all rough estimates and back-of-the-envelope fluid dynamics calculations, but my end conclusion is that Voyager’s vortex shedding wake through the nebula is realistic after all! (Video credit: Paramount; topic also requested by heuste11)
The Inside of an Evaporating Drop
[original media no longer available]
Evaporating droplets may not look like much to the naked eye, but they contain complicated flow patterns. The type of pattern observed depends strongly on the contact line, the place where the liquid, solid, and air meet. When the contact line is pinned–kept unchanged–during evaporation, any particulates in the drop get pulled toward the edges as the drop evaporates. This is what leaves the classic coffee ring stain. It is also what is shown in the first clip in the video above. Contrast this with the second clip, in which the contact line is unpinned and varies irregularly as the drop evaporates. In the unpinned drop, particles are drawn inward during evaporation. The flow patterns are very different as well, complicated by swirling that is the result of force imbalances caused by the irregularly receding contact line. (Video credit: H. Kim)
What Makes Squids Fast
Cephalopods like the octopus or squid are some of the fastest marine creatures, able to accelerate to many body lengths per second by jetting water behind them. Part of what makes its high speed achievable, though, is the way the animal changes its shape. In general, drag forces are proportional to the square of velocity, meaning that doubling the velocity increases the drag by a factor of four. The energy necessary to overcome such large drag increases generally prevents marine animals from going very fast (compared to those of us used to moving through air!) But drag is also proportional to frontal area. Like the bio-inspired rocket in the video above, jetting cephalopods begin their acceleration from a bulbous shape and then shrink their exposed area as they accelerate. Not only does this shape change help mitigate increases in drag due to velocity, it prevents flow from separating around the animal, shielding it from more drag. The result is incredible acceleration using only a simple jet for thrust. For example, the octopus-like rocket in the video above reaches velocities of more than ten body lengths per second in less than a second. (Video credit: G. Weymouth et al.)
Impacts on Sand
Granular materials like sand are sometimes very fluid-like in their behaviors. The high-speed video above shows a ball bearing being dropped into packed sand. Many features of the splash are fluid-like; the initial impact creates a spreading crownlike splash, followed by a strong upward jet that eventually collapses back into the medium. At the same time, many of the impact characteristics are decidedly non-fluidic. Sand has no surface tension, so both the crown and the jet readily break up into small particles. The granular jet is very narrow and energetic, reaching heights greater than the impacter’s drop height. Interestingly, the column begins collapsing on its lower end before the jet even reaches its highest peak. This may be due to the lower energy of the sand particles that were ejected later in the crater formation process. (Video credit: J. Verschuur, B. van Capelleveen, R. Lammerink and T. Nguyen)
The Science of Champagne
Champagne owes much of its allure to its tiny bubbles. Unlike other wines, champagne undergoes a secondary fermentation in the bottle, during which the yeasts in the wine consume sugars and produce carbon dioxide, which dissolves into the wine. When opened, the carbon dioxide can begin to escape. Bubbles form in the glass around imperfections, either due to intentional etching of the glass or impurities left behind by cleaning. Once formed, trails of bubbles rise to the surface, swelling as more dissolved carbon dioxide is absorbed into each bubble. The bubbles then cluster near the surface of the champagne, occasionally popping and creating a flower-like distortion of the surrounding bubbles. The gases within the bubbles contains higher concentrations of aromatic chemicals than the surrounding wine, and the bursting of each bubble propels tiny droplets of these aromatics upwards, carrying the scent of the champagne to the drinker. For more beautiful champagne photos, I recommend this LuxeryCulture article; for more on the science of champagne, see Chemistry World’s coverage. Happy 2014! (Image credits: G. Liger-Belair et al.)
Frozen Bubbles
Snowflakes aren’t the only frozen crystals to play with outside in the winter. Photographer Angela Kelly recently posted a series of frozen soap bubbles made by her and her son. In temperatures well below freezing, the thin film of the soap bubble does not survive long before it begins to freeze. The bubbles do not freeze all at once; instead the frost creeps gradually across it. For bubbles sitting on a surface, the ice front expands upward, much the same as with a freezing water drop. Once frozen, the bubbles crack or rip when touched instead of melting and popping. (Photo credit: A. Kelly; via BoredPanda; submitted by jshoer)
Holiday Fluids: What is Fire?
Snowy holidays and long, dark nights are a great time to sit by the fire or enjoy some candlelight. We’ve talked before about how buoyancy affects a flame’s shape, how atomization mixes liquid fuel and oxidizers, how flames propagate, how internal combustion works and how instabilities can end combustion. But in all that we haven’t addressed what fire actually is! Combustion is a chemical process–a reaction between a hydrocarbon fuel and oxygen, but the flame we’re accustomed to seeing is a combination of blue light produced by the complete reaction and incandescent red/orange/yellow light from glowing soot particles produced when there is insufficient oxygen for the reaction. If you have time after the Minute Physics version, this video from Ben Ames has a wonderful explanation of flames. Of course, if you just prefer your holiday fun with more explosive high-speed videos, you’re going to want to see this Christmas tree made from detonation cord (see 2:40 for the start of the best part). This wraps up our holiday-themed fluid dynamics series. Happy holidays from FYFD! (Video credit: Minute Physics)
Holiday Fluids: Cocoa Convection
If you make a proper cup of hot chocolate this holiday, watch carefully and you just may catch some Rayleigh-Benard convection like the video above. (Note, video playback is 3x.) The canonical Rayleigh-Benard problem is one in which fluid is heated from below and cooled from above. For the cup of hot chocolate, the cooling comes from the colder, ambient air at the cocoa’s surface. Because cooler fluid is denser than warmer fluid, the cocoa near the surface will tend to sink down, allowing warmer cocoa to rise. As that warm cocoa reaches the surface, it too will cool and sink back down, continuing the cycle. The effect relies on buoyancy and, by extension, gravity; on the International Space Station, for example, astronauts would not observe such convection. The distinctive shape of the cells depends on the boundaries of the cup. This post is part of our weeklong holiday-themed fluid dynamics series. (Video credit: Armuotas)
Holiday Fluids: German Pyramids
I broke out some of my family’s Christmas decorations for today’s video. Enjoy and be sure to come back tomorrow when our week of holiday-themed fluid dynamics continues! (Video credit: N. Sharp)
