Take a viscous fluid, like laundry detergent, and sandwich it between two plates of glass. Fluid dynamicists call this set-up a Hele-Shaw cell. If you then inject a less viscous fluid, like air, between the plates–or if you try to pry them apart–you’ll see a distinctive pattern of dendritic fingers form. This viscous fingering, also known as the Saffman-Taylor instability, occurs because the interface between the two fluids is unstable. Invert the problem, though–inject a more viscous fluid into a less viscous one–and no special shapes will form because the interface will remain stable. (Image credit: Random Walk Studios, source)
Tag: instability
Cream in Coffee
Pouring cream in coffee produces some of the most mesmerizing displays of fluid dynamics. The density difference between the two fluids sets up Rayleigh-Taylor instabilities that mushroom out and help create the turbulence that eventually mixes the drink. You can learn more about Rayleigh-Taylor instabilities in this FYFD video, and, if you need more awesome caffeine-filled examples of fluids, check out the coffee dynamics blog. (Video credit: S. Geraldine and L. Kang)
Waves Over the Rockies
These spectacular wave-like clouds are the result of the Kelvin-Helmholtz instability. When two layers of air move past one another at different velocities, an unstable shear layer forms at their interface. Disturbances in this shear layer grow exponentially, creating these short-lived overturning waves that quickly turn turbulent. The strong resemblance of these clouds to breaking ocean waves is no coincidence–the Kelvin-Helmholtz instability occurring between the wind and water is what generates many ocean waves. Kelvin-Helmholtz patterns are also common on other planets, like Jupiter, Saturn, and Mars. (Image credit: Breckenridge Resort; submitted by jshoer)
Pollock-Style Physics
Here on FYFD, we like to show off the artistic side of fluid dynamics. But some researchers are actively studying how artists use fluid dynamics in their art. In this video, they examine one of Jackson Pollock’s painting techniques, in which filaments of paint were applied by flinging paint off a paintbrush. Getting the technique to work requires a fine balance of forces and effects. Firstly, the paint must be viscous enough to hold together in a filament when flung. Secondly, the centripetal acceleration of the rotation must be high to both form the catenary filament and throw it off the brush. And, finally, the Reynolds number needs to be high enough to add some waviness and instability to the filament so that it looks interesting once it hits the canvas. Also be sure to check out the group’s previous work exploring Siqueiros’s painting techniques. (Video credit: B. Palacios et al.)
Printing in Glass
A group at MIT have created a new 3D printer that builds with molten glass. This allows them to manufacture items that would difficult, if not impossible, to create with traditional glassblowing or other modern techniques. One of the coolest aspects of this technique is that it can use viscous fluid instabilities like the fluid dynamical sewing machine to create different effects with the glass. You can see this around 1:56 in the video. Varying the height of the head and the speed at which it moves will cause the molten glass to fall and form into different but consistent coiling patterns. All in all, it’s a very cool application for using some nonlinear dynamics! (Video credit: MIT; via James H. and Gizmodo)
Boiling Water in Oil
Most people know that throwing water into hot oil is a bad idea. But, as dramatic as the results can be, the boiling of a water droplet submerged in oil is remarkably beautiful, as seen in the animations above. The initial water droplet expands as it shifts from liquid to vapor (top). At a critical volume, the expansion occurs explosively (middle), causing the bubble to overexpand relative to the pressure of the surrounding fluid. The higher pressure of the oil around it collapses the drop, which then re-expands, creating the cycle we see in the final two animations. This oscillation triggers a Rayleigh-Taylor type instability along the bubble’s interface, causing the surface corrugations observed. The vapor bubble will continue to rise through the oil, eventually breaking the surface and scattering hot oil droplets. (Image credits: R. Zenit, source)
Wave Clouds Over the Galapagos
This dramatic example of Kelvin-Helmholtz clouds was taken near the Galapagos Islands last week. The shark-fin-like clouds are the result of two air layers moving past one another. The velocity difference at their interface creates an unstable shear layer that quickly breaks down. The resemblance of the clouds to breaking ocean waves is no coincidence – the wind moving over the ocean’s surface generates waves via the same Kelvin-Helmholtz instability. In the case of the clouds above, the lower layer of air was moist enough to condense, which is why the pattern is visible. Clouds like these don’t tend to last for long because the disturbances that drive the instability grow exponentially quickly, leading to turbulence. (Image credit: C. Miller; via Washington Post; submitted by @jmlinhart)
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Breaking Jets Into Drops
A falling stream of water will break into droplets due to the Plateau-Rayleigh instability. Small disturbances can create a wavy perturbation in the falling jet. Under the right conditions, the pressure caused by surface tension will be larger in the narrower regions and smaller in the wider ones. This imbalance will drive flow toward the wider regions and away from the narrower ones, thereby increasing the waviness in the jet. Eventually, the wavy jet breaks into droplets, which enclose the same volume of water with less surface area than the perturbed jet did. The instability is named for Joseph Plateau and Lord Rayleigh, who studied it in the late 19th century and showed that a falling jet of a non-viscous fluid would break into droplets if the wavelength of its disturbance was larger than the jet’s circumference. (Image credit: N. Morberg)
Sharkskin Instability
Homemade spaghetti noodles exhibit a roughened surface that’s the result of viscoelastic behavior known as the sharkskin instability. It’s usually observed in the industrial extrusion of polymer plastics. In the case of spaghetti, the long, complex polymer molecules necessary for the instability come from the proteins in eggs. The characteristically rough surface of the extruded material is caused by the transition from flow through the die to air. Inside the die, friction from the walls exerts a strong shear force on the outer part of the fluid while the inner portion flows freely. When the material exits the die, the sudden lack of friction on the outer portion of the fluid causes it to accelerate to the same velocity as the middle of the flow. This acceleration stretches the polymers until they snap free of the die; after the strained polymers relax, the material keeps a rough, saw-tooth pattern. In industry, the sharkskin instability can be prevented by regulating temperature or flow speed. In the case of spaghetti, though, Modernist Cuisine suggests the roughness is desirable because it helps trap the pasta sauce. Bon appetit! (Image credit: Modernist Cuisine)
The Dance of the Droplets
Milk and juice vibrating on a speaker can put on a veritable fireworks display of fluid dynamics. Vibrating a fluid can cause small standing waves, called Faraday waves, on the surface of the fluid. Add more energy and the instabilities grow nonlinearly, quickly leading to tiny ligaments and jets of liquid shooting upward. With sufficiently high energy, the jets shoot beyond the point where surface tension can hold the liquid together, resulting in a spray of droplets. (Image credit: vurt runner, source video; h/t to @jchawner)
