This super high resolution video (check the original on YouTube) by filmmaker Jacob Schwarz features slow motion diffusion of ink into water. The subtle differences in density between the ink and the water promote instabilities such as the Rayleigh-Taylor instability and its distinctive cascade of mushroom- or umbrella-like shapes. The mixing of two fluids seems like a simple concept, but the reality is beautiful, complex, and always fascinating. (Video credit: J. Schwarz; submitted by Rebecca S.)
Tag: Rayleigh-Taylor instability
Dropping Through Strata
When a droplet falls through an air/water interface, a vortex ring can form and fall through the liquid. In this video, the researchers investigate the effects of a stratified fluid interface on this falling vortex ring. In this case, a less dense fluid sits atop a denser one. Depending on the density of the initial falling droplet and the distance it travels through the first fluid, the behavior and break-up of the vortex ring when it hits the denser fluid differs. Here four different behaviors are demonstrated, including bouncing and trapping of the vortex ring. (Video credit: R. Camassa et al.)
Mixing Physics
When a dense fluid sits above a lighter fluid in a gravitational field, the interface between the two fluids is unstable. It breaks down via a Rayleigh-Taylor instability, with mushroom-like protrusions of the lighter fluid into the heavier one. The image above comes from a numerical simulation of this effect well after the initial instability; the darker colors represent denser fluids and lighter colors are less dense fluids. The flow here has progressed to turbulence, and the authors of the simulation are exploring the statistical nature of this flow breakdown relative to the classical case of isotropic, homogeneous turbulence. (Photo credit: W. Cabot and Y. Zhou)
Mixing Physics
One of the most commonly observed fluid instabilities is the Rayleigh-Taylor instability, which occurs between fluids of differing densities. It’s most often seen when a denser fluid sits over a lower density fluid. In the video above, this is demonstrated experimentally: a lower density green fluid mixes in with the clear, higher density fluid. This is the classical case in which each initial region of fluid is uniform in density prior to the removal of the barrier. But what happens when each zone has its own variation in density? This is the second case. Before the barrier is removed, each region of the tank has a varying–or stratified–fluid density. In this case, the unmixed fluids are stably stratified, meaning that the fluid density increases with depth. At the barrier interface, the two separate fluids are still unstably stratified–with the denser fluid on top–so when the barrier is removed, the Rayleigh-Taylor instability still drives their mixing. Because of the stable stratification within the original unmixed fluids, the mixing region after the barrier’s removal is more limited. (Video credit: M. D. Wykes and S. B. Dalziel; via PhysicsCentral by APS)
Accidental Painting
Artist D. A. Siqueiros sometimes used a technique he referred to as “accidental painting” in his work, in which he would pour a layer of one color of paint and then pour a second color over it. The two colors would mix in striking patterns. Here researchers recreate the technique and analyze the fluid dynamics of it. Each paint has a slightly different density thanks to the pigments used to color them. When a denser paint is poured over a less dense one (as in the white on black in the video), this activates the Rayleigh-Taylor instability. The white paint will tend to sink down below the black paint due to gravity. At the same time, the spreading of the two paints also affects the shapes and patterns through mixing and diffusion. (Video credit: S. Zetina and R. Zenit)
Supercomputed Fluids
Computational fluid dynamics and supercomputers can produce some stunning flow visualizations. Above are examples of turbulence, the Rayleigh-Taylor instability, and the Kelvin-Helmholtz instability. Be sure to check out LCSE’s website for more; they’ve included wallpapers of some of the most spectacular ones. (Photo credits: Laboratory for Computational Science and Engineering, University of Minnesota, #)
Fractal Fluids
Part of the beauty of numerical simulation is its ability to explore the physics of a situation that would difficult or impossible to create experimentally. Here the Rayleigh-Taylor instability–which occurs when a heavier fluid sits atop a lighter fluid–is simulated in two-dimensions. Viscosity and diffusion are set extremely low in the simulation; this is why we see intricate fractal-like structures at many scales rather than the simulation quickly fading into gray. (The low diffusion is also what causes the numerical instabilities in the last couple seconds of video.) The final result is both physics and art. (Video credit: Mark Stock)
Ink Sculptures
Dripping ink into water can create fantastic structures as the two fluids mix. In this artwork there are numerous complex mixing phenomena: the eddies and multiple scales of turbulence; the long, thin streams of laminar flow; and the wispy mushrooms and umbrellas of the Rayleigh-Taylor instability. (Photo credit: Mark Mawson; via @thinkgeek)
Water Balloon Physics
[original media no longer available]
This video explores some of the physics behind the much-loved bursting water balloon. The first sections show some “canonical” cases–dropping water balloons onto a flat rigid surface. In some cases the balloon will bounce and in others it breaks. The bursting water balloons develop strong capillary waves (like ripples) across the upper surface and have some shear-induced deformation of the water surface as the rubber peals away. Then the authors placed a water balloon underwater and vibrated it before bursting it with a pin. They note that the breakdown of the interface between the balloon water and surrounding water shows evidence of Rayleigh-Taylor and Richtmyer-Meshkov instabilities. The Rayleigh-Taylor instability is the mushroom-like formation observed when stratified fluids of differing densities mix, while the Richtmyer-Meshkov instability is associated with the impulsive acceleration of fluids of differing density.
High-Res Rayleigh-Taylor Instability
When a heavy fluid sits atop a lighter fluid, the interface between the two breaks down through the Rayleigh-Taylor instability. This computation of a 2D interface shows the near fractal behavior of this instability as whorls and eddies of all different scales form and mix the fluids. (submitted by @markjstock)
