This photo shows the Saffman-Taylor instability in a Hele-Shaw cell. Here a viscous fluid has been placed between two glass plates and a second less viscous fluid inserted, resulting in a finger-like instability as the less viscous fluid displaces the more viscous one. This is an effect that can be easily explored at home using common liquids like glycerin, water, dish soap, or laundry detergent. #
Tag: instability
Vibrating Oobleck
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This video explores some of the non-Newtonian behaviors of oobleck when shaken. The pattern across the surface once the vibrations start is called Faraday waves, a type of nonlinear standing wave that forms once a critical vibrational frequency is passed and the flat surface of the fluid becomes unstable. Toward the end of the video, the frequency of the vibrations is increased until “finger-like protrusions” form. This is a behavior exhibited by shear-thickening non-Newtonian fluids.
Wavy Vortices
Shown above is the flow between two concentric cylinders (Taylor-Couette flow). In the laminar regime, the velocity profile between the two cylinders is linear. As the rate of rotation of the inner cylinder increases, the flow develops toroidal vortices known as Taylor vortices, seen in the video above after 9 seconds or so. This is a fluid instability exhibited by transitional flow. Increasing the rotational rate further can result in wavy Taylor vortex flow. At high enough speeds, the flow will become completely turbulent.
Superfluid Dripping
This high-speed video shows superfluid helium dripping and breaking up. Although superfluid has no viscosity, this does not prevent the Plateau-Rayleigh instability from breaking the helium into droplets once the mass of the liquid is too great for surface tension to contain.
Kelvin-Helmholtz Instability
The Kelvin-Helmholtz instability occurs when velocity shear is present in a single fluid or when two different fluids have a velocity difference across their interface. As shown in this numerical simulation, the instability produces a fractal-like pattern of eddies turning over on themselves. The Kelvin-Helmholtz instability is commonly found in nature between cloud layers. #
ETA: It looks like animated GIFs may not work with Tumblr. Be sure to click on the picture to see the animation on Wikipedia.
Effects of Viscosity
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Today’s video demonstrates the effect of viscosity, which measures a fluid’s resistance to deformation. On the left is a column of highly viscous fluid; the fluids become less viscous as one moves right. When a jet of dye is released into the highly viscous fluid, the jet is very slow to penetrate, whereas, in the rightmost column, the dye expands quickly into a turbulent jet. Between these extremes, we see a laminar dye jet entering the liquid. The mushroom-like shape the laminar jet takes is the result of the Rayleigh-Taylor instability, which occurs when a denser fluid is on top of a lighter fluid in a gravitational field.
Convection in Cream and Liqueur
We are used to associating convection with differences in temperature, but what’s actually necessary for a Rayleigh-Taylor-type instability is a density variation (and a gravitational field). The solutal convection seen above when mixing liqueur with cream is caused by the interaction of density and surface tension. When the alcohol of the liqueur mixes with the cream, it forms a less dense alcohol-cream that tries to rise to the surface. The alcohol also breaks the surface tension of the cream, causing it to contract and open cells where the alcohol surfaces. As the alcohol evaporates, the alcohol-cream mixture gets denser and sinks back down where it can pick up more alcohol and start the process again. (via jshoer and io9)
Jupiter and the Kelvin-Helmholtz Instability
Jupiter, known for its colorful bands of stormy clouds, is a beautiful subject for fluid dynamics in action. As the planet turns, the cloud bands move at different relative speeds. This velocity difference at the interface of the bands can trigger the Kelvin-Helmholtz instability, resulting in a line of whorls where the cloud bands meet. The instability has been observed on Saturn and is thought to be fairly common among gas giants.
Benard Cells
When a fluid in a gravitational field is heated from below, it can develop a Rayleigh-Benard instability which causes the formation of convection cells as in the video above. The hexagonal shape of the cells is due to the boundary conditions of the fluid. It’s possible to form other shapes like spirals. The same mechanism drives the formation of granules on the photospheres of stars like our sun.
Breaking up in Crossflow
This video shows some instabilities that occur when a liquid jet impinges on a flowing cross stream. Note how the jet breaks down into droplets in a fashion similar to the Plateau-Rayleigh instability but the broken tip remains stable for some time thereafter. #
