Simple acts like the coalescence of two droplets sitting on a surface can be beautiful and complex. As the droplets come together, they form a thin neck between them, and the curvature of that surface causes capillary forces that drive fluid into the neck. For two dissimilar droplets, like the ones above, there can be additional forces. Here, the upper drop is pure water, but the lower one has added surfactants, which reduce its surface tension. That difference in surface tension creates a Marangoni flow that tends to pull fluid away from the neck. The result is that full coalescence takes longer. Depending on other factors in this tug-of-war between capillary action and Marangoni flow, the process of coalescence can look very different. In this example, there’s a fingering instability that occurs as the neck spreads. Change the circumstances slightly and the drops may chase each other instead of merging or will merge with a perfectly smooth contact front. (Image and research credit: M. Bruning et al.)
Tag: instability
“Le Temps”
Thomas Blanchard is back with another beautiful music video. This one features ink cascading over various shapes underwater. Lots of tiny mushroom-shaped Rayleigh-Taylor instabilities here caused by the ink’s greater density compared to the surrounding water. There are also some lovely examples of transitional flow, especially around the spheres. Initially, flow over the spheres looks completely smooth and laminar. But, on the latter half of the sphere, where the flow is under increasing pressure, you see disturbances growing until little fingers of ink break away entirely. Be sure to watch the whole video; you don’t want to miss this! (Video and image credit: T. Blanchard)
Breaking With a Wave
For rocket combustion and other applications, like watering your lawn with a hose, a stream of fluid may need to be broken up into droplets. While simply spraying a liquid jet will make it break up, waving that jet back and forth will break it up faster. A recent study simulated this problem numerically to determine the exact mechanisms driving that break-up. The researchers found two major culprits.
The first is a Kelvin-Helmholtz, or shear-based, instability. When a jet leaves the nozzle, there’s friction between it and the comparatively still air surrounding it. This creates tiny ripples in the surface that eventually grow into the distortions we can see, and it’s found in all jets, regardless of their side-to-side motion.
The second culprit, which is only found in the oscillating jet, is a Rayleigh-Taylor instability. By moving the jet side-to-side, you’re driving the dense liquid into less dense air, which creates a different set of disturbances that also help break up the jet. The final result: swinging the jet side-to-side breaks it into smaller droplets faster. (Image and research credit: S. Schmidt et al.)
Folding Fluids
Highly viscous liquids – like cake batter, lava, or the spider silk above – fold as they fall. Several factors impact this instability including the fluid’s density, viscosity, surface tension, and how thin the falling sheet is. As with the coiling of falling honey, this behavior is actually a form of buckling. It’s also fascinating to watch how persistent the layers are. Even out near the edge of the puddle, you can still see individual folds. This is a sign of just how incredibly viscous the spider silk is. Imagine if this were cake batter instead: we’d see folding just like we do with the spider silk proteins, but the individual folds would quickly fade as the batter flowed to fill its container. The spider silk is more viscous, so it’s more resistant to flowing. (Image credit and submission: D. Breslauer, source)
The Fluid Dynamical Sewing Machine
If you’ve drizzled viscous liquids like honey or syrup, you’ve no doubt witnessed their ability to coil. Combine that coiling with a moving platform and you form a system known as the fluid dynamical sewing machine, which creates different consistent patterns of loops and curves depending on the speed at which the liquid falls and the velocity of the moving platform. The predictability of these patterns makes them especially useful for 3D printing. Previously a group at MIT developed a glass printer that could use the instability, and here a group from Montreal demonstrates how they can build solid coils at various scales. Their video also explores what the structural properties of such coils are after they solidify. (Image, video, and research credit: R. Passieux et al.)
The Coexistence of Order and Chaos
One of the great challenges in fluid dynamics is understanding how order gives way to chaos. Initially smooth and laminar flows often become disordered and turbulent. This video explores that transition in a new way using sound. Here’s what’s going on.
The first segment of the video shows a flat surface covered in small particles that can be moved by the flow. Initially, that flow is moving in right to left, then it reverses directions. The main flow continues switching back and forth in direction. This reversal tends to provoke unstable behaviors, like the Tollmien-Schlichting waves called out at 0:53. Typically, these perturbations in the flow start out extremely small and are difficult or even impossible to see by eye. So researchers take photos of the particles you see here and analyze them digitally. In particular, they are looking for subtle patterns in the flow, like a tendency for particles to clump together with a consistent spacing, or wavelength, between them. Normally, researchers would study these patterns using graphs known as spectra, but that’s where this video does something different.
Instead of representing these subtle patterns graphically, the researchers transformed those spectra into sound. They mapped the visual data to four octaves of C-major, which means that you can now hear the turbulence. When the audio track shifts from a pure note to an unsteady warble, you’re hearing the subtle disturbances in the flow, even when they’re too small for your eye to pick out.
The last part of the video takes this technique and applies it to another flow. We again see a flat plate, but now it has a roughness element, like a tiny hockey puck, stuck to it. As the flow starts, we see and hear vortices form behind the roughness. Then a horseshoe-shaped vortex forms upstream of it. Aside from the area right around the roughness, this flow is still laminar. But then turbulence spreads from upstream, its fingers stretching left until it envelops the roughness element and its wake, making the music waver. (Video and image credit: P. Branson et al.)
Using Air to Break Up Jets
One method of breaking a liquid into droplets, or atomizing it, uses a slow liquid jet surrounded by an annulus of fast-moving gas. The gas along the outside of the liquid shears it, creating waves that the wind blowing past can amplify. This draws the liquid into thin ligaments that then break into droplets. This is a popular technique in rocket engines, where cryogenic liquid fuels often need to be atomized for efficient combustion. When things aren’t working exactly right, however, the liquid jet may start flapping instead of breaking up. In this case, the jet will swing back and forth, but only part of it will atomize. For a rocket engine, this would mean slower and less efficient combustion – never desirable outcomes! (Image credit: A. Delon et al.)
“Water Ballet”
Artist Kamiel Rongen uses common substances like paint, oil, eggs, and even air freshener to create what he calls “water ballet.” His videos are full of ethereal and surreal landscapes full of color and motion. Buoyancy (or the lack thereof) plays a major role in his work – fluids often spurt upward like alien creatures emerging from a chrysalis. I’ve been debating with myself whether the fluids are actually rising or if they’re falling in front of an upside-down camera, and I’m not completely certain either way! I think that’s a testament both to Rongen’s artistry and to the awesome physics involved. Check out the full video below and you can see many more examples of Rongen’s work on his website. (Image and video credit: K. Rongen; h/t to James H.)
Soap Film Catenoid
Even very simple fluid systems can have surprising complexity. What you see here is a catenoid – the hourglass-like soap film that forms between two rings. In this case, the space in the center of the catenoid has a secondary film separating the top and bottom halves of the catenoid. When the rings are pulled apart, the waist of the catenoid and the secondary film inside it collapse. The secondary film gets thicker as its diameter decreases. (The fluid has to go somewhere, after all.) As the film thickens, the pressure inside it rises, eventually pushing some of the fluid out through the catenoid. This is what causes the fingers flowing down the lower half of the catenoid in the bottom two images. (Image and research credit: R. Goldstein et al.)
Fractal Fingers
Dyed isopropyl alcohol atop a thin layer of acrylic medium spreads in a fractal fingering pattern. Although the shapes are reminiscent of the viscous fingers seen in in the Saffman-Taylor instability, these patterns are most likely a result of surface tension. The lower surface tension of the alcohol causes Marangoni forces to pull it outward. The branching shapes indicate an instability, likely driven by surface tension, but the details of the mechanism behind it are unclear. (Image credits: J. Nahabetian)
