Amidst your holiday celebrations, you may have encountered a chocolate fountain. In a recent paper, applied mathematicians have laid out the physics behind these delicious decorations, and it turns out they are an excellent introduction to many fluids concepts. Molten chocolate is a mildly shear-thinning, non-Newtonian fluid, meaning that it becomes less viscous when deformed. This adds a wrinkle to the mathematics describing the flow, but only a little one. The researchers divide the flow into three regimes: pipe flow driving the chocolate up the inside of the fountain, thin-film flow over the fountain’s domes, and, finally, the curtain of falling chocolate where foodstuffs are dipped. The final regime is the most mathematically challenging and may be the most fascinating. The authors found that the free-falling curtain of liquid pulls inward as it falls due to surface tension. Their paper is quite approachable, and I recommend those of you with mathematical inclinations check it out. (Image credit: P. Gorbould; research credit: A. Townsend and H. Wilson)
Month: December 2015
Freezing From Below
Watch closely as a droplet freezes on a cold surface, and you’ll observe something surprising. First, a freeze front will appear, traveling upward from the substrate. It curves slightly near the edges, leaving a liquid cap atop the frozen drop. But, as we’ve all discovered, water expands as it freezes. We can watch the drop freezing and see that the water isn’t expanding radially. Instead, the water expands vertically, forming a sharp tip or cusp just as the drop freezes completely. Remarkably, the geometry of the final tip doesn’t depend on the temperature of the substrate or on the wetting contact angle. (Video credit: L. Posada)
Swimming in Microgravity
For years, I have wondered what a fish swimming in microgravity would look like. Finally, my curiosity has been rewarded. Here is a sphere of water in microgravity, complete with a fish. Personally, I am impressed that, despite the fish’s best efforts, the surface tension of the water is strong enough to keep it confined. This may not bode well for microgravity swimming pools at space hotels. (Video credit: IRPI LLC, source)
Falling Ink
Photographer Linden Gledhill created these nebula-like composites from photos of ink diffusing in water. The work was inspired by Mark Stock’s “Spherical Rayleigh-Taylor Instabilities” series featured here last week. Like Stock’s computational art, the twisted fingers and vortex rings above form due to the denser ink falling through less dense water. The interface between the two fluids distorts under the effects of gravity and the fluids’ relative motion. Such shapes are ephemeral at best; the falling ink will quickly become turbulent and diffuse throughout the water. (Photo credit and submission: L. Gledhill)
Helicopter Tip Vortices
Airplanes and other fixed-wing aircraft produce wingtip vortices as a result of their finite length. Rotor blades, like those on helicopters, produce the effect as well. Both wings and rotors generate lift by trapping low-pressure air on their top surface and high-pressure air below. At their tips, though, the high-pressure air can sneak around the wing or rotor, creating vortices like the ones visualized above. Here smoke from a wire is entrained by the rotors’ inflow and twisted into a tip vortex. The line of vortices drifts downward due to the rotor’s downwash. (Image credit: M. Giuni et al., source)
Inside a Popping Bubble
Popping a soap bubble is more complicated than what the eye can see. In high-speed video, we find that the action is very directional, with the soap bubble film pulling away from the point of rupture. As it does so, waves, like those in a flapping flag, appear along the surface and strings of fluid form along the edge of the film before breaking into droplets. This video takes matters a step further, looking at what happens to air inside a bubble when it pops. Those subtle waves and strings of fluid we see in the high-speed rupture have a distinctive effect on air inside the bubble. As the film pulls away, it leaves behind a rippled, wavy surface rather than a smooth sphere of foggy air. (Video credit: Z. Pan et al.)
Numerical Rayleigh-Taylor
If you’ve ever dripped food coloring or ink into a glass of water, you’ve probably created a cascade of tiny vortex rings similar to the images above. This is the Rayleigh-Taylor instability, in which the heavier ink/food coloring falls under gravity into the less dense water. What’s shown above is a special case–one that no experiment can recreate. It’s a numerical simulation of a spherical Rayleigh-Taylor instability. Imagine a sphere of a dense fluid “falling” outward under the influence of a radial gravitational field. This is one of the interesting aspects of computational fluid dynamics–it can simulate situations that are impossible to create experimentally. That can be both a strength and a weakness, allowing researchers to probe otherwise unavailable physics or fooling the unwary into thinking they have captured something real. (Image credit: M. Stock)
“Monsoon II”
Every child learns about the water cycle in school, but an academic description of the process often lacks nature’s grandeur. In “Monsoon II” photographer Mike Olbinski captures the majesty of cloud formation and rainfall in a way that rekindles awe for the scale of the process. It begins with bright clouds popping up, the result of warm moist air rising from the ground and cooling at altitude. As more water vapor evaporates, rises, and condenses, water droplets collide in these clouds, coalescing and growing until they grow too large and heavy to stay aloft. These are the droplets that fall in sheets of rain, blurring the air beneath them. There’s an incredible beauty to watching rain fall from a distance; it looks calm and localized in a way that’s utterly at odds with the experience from inside the storm. (Video credit: M. Olbinski; submitted by jshoer)
Collecting Water in the Desert
Desert-dwelling plants like cactuses have to be efficient collectors of water. Many types of cactus are particularly good at gathering water from fog that condenses on their spines. Droplets that form near a spine’s tip move slowly but inexorably toward the base of the spine so that the cactus can absorb them. The secret to this clever transport lies in the microstructure of the spine’s surface. The
Gymnocalycium baldianum cactus, for example, has splayed scales along its spines. Capillary interactions with the scales result in differences in curvature on either side of the droplet. Curved fluid surfaces generate what’s known as Laplace pressure, with a tighter radius of curvature causing a larger Laplace pressure. Because the curvature of the droplet varies from the base side to the tip side of the spine, the difference in Laplace pressures across the droplet creates a force that drives the droplet toward the spine’s base. (Image credit: C. Liu et al., source)
The Tightrope Dancers
Boiling is a process most of us don’t pay much attention to. But it can be remarkably entertaining and beautiful. This award-winning video shows boiling on and around a heated wire immersed in oil. Depending on the diameter of the wire and the power used to heat it, the researchers observe several different regimes of behavior. In one, vapor bubbles form on the wire and interact with one another: bouncing, merging, and dancing back and forth. When the bubbles become large enough, their buoyancy lifts them upward. In another regime, the wire is hot enough for film boiling. Like the Leidenfrost effect, film boiling occurs when a surface is so hot that it instantly vaporizes any liquid near it. The vapor layer then acts like coating, insulating the remaining liquid from the hot surface. The bubbles formed on the wire in this regime are mesmerizing, rising in periodic patterns or shifting back and forth gobbling up lesser bubbles. (Video credit: A. Duchesne et al.)
