Instability is a common feature of fluid flows and can generate a near infinite set of patterns. The video above shows the Saffman-Taylor instability, an interface instability that occurs when a fluid of lower viscosity is injected into a higher viscosity fluid. In this case, the fluids inhabit a thin space between two glass plates. The less viscous fluid displaces the more viscous one in a series of branching finger-like shapes. If the situation were reversed, with a more viscous fluid injected into a less viscous one, the interface would be stable and expand radially without any pattern formation. (Video credit: William Jewell College)
Tag: instability
Meeting the Wall
Even something as simple as a falling sphere meeting a wall is composed of beautiful fluid motion. In Figure 1 above, we see side-view images of a sphere at low Reynolds number falling toward a wall over several time. Initially an axisymmetric vortex ring is visible in the sphere’s wake; when the sphere touches the wall, secondary vortices form and the wake vortex moves down and out along the wall in an axisymmetric fashion (Figure 2, top view). At higher Reynolds numbers, like those in Figure 3, this axisymmetric spreading of the vortex ring develops an instability and ultimately breaks down. (Photo credit: T. Leweke et al.)
Supercell Thunderstorm
Photographer Mike Olbinski has captured a spectacular timelapse of a supercell thunderstorm over the plains of Texas. Supercells are characterized by a strong, rotating updraft known as a mesocyclone, seen clearly in the video. These storms are commonly isolated occurrences, forming when horizontal vorticity in the form of wind shear is redirected upwards by an updraft. Such a strong updraft is typically created by a capping inversion, a situation where a layer of warmer air traps the colder air beneath it. (This is why one sees a distinctive cut-off at the top of some clouds.) As warm air rises from the surface, either the air above the cap will cool or the air below the cap will warm. Either situation results in an instability with cooler air on top of warmer air, providing a catalyst for the kind of dramatic weather seen here. (Video credit: M. Olbinski; via io9)
Fluids Round-up – 9 June 2013
It’s time for some more fluidsy fun around the Internet! Here are some fun links I’ve come across since our last round-up.
- NPR reviews how dolphins and others play with vortex rings.
- Lawrence Berkeley National Laboratory/UC Berkeley offer some insight into simulating bubbles popping. (Hint: it requires supercomputers.)
- FlowViz shares some awesome accidental Rayleigh-Taylor instabilities you can replicate at home.
- PhysicsBuzz brings us a podcast on tornado physics.
- Reader Cedric Vella sent in his fluids-featuring trailer.
- io9 pointed out some great cymatics footage that shows off how granular materials and vibration creates beautiful patterns.
- And finally: what happens when you drop hot charcoal into liquid oxygen? The Periodic Table of Videos shows us, in high speed! (via Flow Visualization)
(Photo credit: L. L. A. Adams et al., multi-fluid double emulsions)
The Kelvin-Helmholtz Instability in the Lab
Though often spotted in water waves or clouds, the Kelvin-Helmholtz instability is easily demonstrated in the lab as well. Here a tank with two layers of liquid – fresh water on top and denser blue-dyed saltwater on the bottom – is used to generate the instability. When level, the two layers are stationary and stable due to their stratification. Upon tilting, the denser blue liquid sinks to the lower end of the tank while the freshwater shifts upward. When the relative velocity of these two fluids reaches a critical point, their interface becomes unstable, forming the distinctive wave crests that tumble over to mix the two layers. (Video credit: M. Stuart)
Breaking into Droplets
A falling column of liquid, like the water from your faucet, will tend to break up into a series of droplets due to the Plateau-Rayleigh instability. This instability is driven by surface tension. Small variations in the radius of the column occur naturally. Where the radius shrinks, the pressure due to surface tension increases, causing liquid to flow away, which shrinks the column’s radius even further. Eventually the column pinches off and breaks into droplets. What’s especially neat is that the size of the final droplets can be predicted based on the column’s initial radius and the wavelength of its disturbances. (Video credit: BYU Splash Lab)
Droplet Impact Visualized
When a drop falls from a moderate height into a shallow pool, its impact creates a complicated pattern. The photo above is a composite image showing a top-down view 100 ms after such an impact. On the left side, the flow is visualized using dye whereas the right shows a schlieren photograph, in which contrast indicates variations in density. Both methods show the same general structure – an inner vortex ring generated at the edge of the impact crater and formed mostly of drop fluid and an outer vortex ring, consisting primarily of pool fluid, formed by the spreading wave. Both regions show signs of instability and breakdown. (Photo credit: A. Wilkens et al.)
Breaking Up a Ferrofluid
Ferrofluids are known for their fascinating behaviors when subjected to magnetic fields, especially for the distinctive peaks they can form. In this video, we see a very thin ferrofluid drop on a pre-wetted surface just as a uniform perpendicular magnetic field is applied. Immediately the droplet breaks up into tiny isolated peaks that migrate out to the circumference. The interface breaks down from center, where the drop height is largest, and moves outward. Simultaneously, the diffusion of ferrofluid from the circumferential droplets into the surrounding fluid lowers the magnetization of those droplets, making it more difficult for them to repel their neighbors. As a result, they drift outward more slowly and get caught by the faster-moving droplets from within. (Video credit: C. Chen)
Stopping Jet Break-Up
When a stream of liquid falls, a surface tension effect called the Plateau-Rayleigh instability causes small variations in the jet’s radius to grow until the liquid breaks into droplets. For a kitchen faucet, this instability acts quickly, breaking the stream into drops within a few centimeters. But for more viscous fluids, like honey, jets can reach as many as ten meters in length before breaking up. New research shows that, while viscosity does not play a role in stretching and shaping the jet as it falls–that’s primarily gravity’s doing–it plays a key role in the way perturbations to the jet grow. Viscosity can delay or inhibit those small variations in the jet’s diameter, preventing their growth due to the Plateau-Rayleigh instability. In this respect, viscosity is a stabilizing influence on the flow. (Photo credit: Harsha K R; via Flow Visualization)
Egg-Spinning Fun
If you have any leftover hard-boiled eggs, you can recreate this bit of fluid dynamical fun. Spin the egg through a puddle of milk, and you’ll find that the egg draws liquid up from the puddle and flights it out in a series of jets. As the egg spins, it drags the milk it touches with it. Points closer to the egg’s equator have a higher velocity because they travel a larger distance with each rotation. This variation in velocities creates a favorable pressure gradient that draws milk up the sides of the egg as it spins, creating a simple pump. To see the effect in action check out this Science Friday video or the BYU Splash Lab’s Easter-themed video. (Photo credit: BYU Splash Lab)
