Taylor and Culick predicted a constant velocity for the rim of an opening hole in a soap film of uniform thickness. Unfortunately, it is difficult to experimentally produce a soap film of uniform thickness. It is much easier to create films of uniform thickness with liquid crystals in their smectic-A phase, in which the molecules are ordered in layers along a single direction. When smectic-A bubbles burst, however, it bears little resemblance to a soap bubble. Smectic-A bubbles burst spontaneously during oscillations, the holes in the film growing until a network of filaments is left behind. The filaments themselves will rapidly break up into droplets due to the Plateau-Rayleigh instability. (Photo credit: R. Stannarius et al.)
Tag: instability
Marangoni Flows
Differences in surface tension cause fluid motion through the Marangoni effect. Because an area with higher surface tension pulls more strongly on nearby liquid than an area of low surface tension, fluid will flow toward areas of higher surface tension. Here surfactants, shown in white, are constantly injected onto a layer of water dyed blue. You can also see the flow in motion in this video. Outside of the central source flow, the pattern features lots of 2D mushroom-like shapes reminiscent of Rayleigh-Taylor instabilities. But these shapes are driven by variations in surface tension rather than unstable density variations. For more, check out the original paper or learn about other examples of Marangoni effect. (Photo credit: M. Roché et al.)
Fluid Sculptures From Bursting Bubbles
A bubble initiated near a free surface–like the air-water interface here–can generate some spectacular dynamics. Beginning at the far left, the expanding subsurface bubble causes a dome at the surface that sharpens into a spike. By Frame 3, the bubble is collapsing but overshoots and rebounds, which introduces the tiny instability in Frame 4 that grows in subsequent time steps to form the water skirt that surrounds the spike. Although generated entirely differently, the end result is reminiscent of the water sculptures made by artists like Marcus Reugels, Corrie White, Jack Long, and others. (Image credit: A. M. Zhang et al.)
Shaping and Levitating Droplets
Opposing ultrasonic speakers can be used to trap and levitate droplets against gravity using acoustic pressure. Changes to field strength can do things like bring separate objects together or flatten droplets. The squished shape of the droplet is the result of a balance between acoustic pressure trying to flatten the drop and surface tension, which tries to pull the drop into a sphere. If the acoustic field strength changes with a frequency that is a harmonic of the drop’s resonant frequency, the drop will oscillate in a star-like shape dependent on the harmonic. The video above demonstrates this for many harmonic frequencies. It also shows how alterations to the drop’s surface tension (by adding water at 2:19) can trigger the instability. Finally, if the field strength is increased even further, the drop’s behavior becomes chaotic as the acoustic pressure overwhelms surface tension’s ability to hold the drop together. Like all of this week’s videos, this video is a submission to the 2103 Gallery of Fluid Motion. (Video credit: W. Ran and S. Fredericks)
Spiraling Break-up
Instabilities in fluids are sometimes remarkable in their uniformity. Here we see a hollow spinning cup with a thin film of fluid flowing down the interior. The rim of fluid at the cup’s lip stretches into long, evenly spaced, spiraling threads. These filaments stretch until centrifugal forces overcome surface tension and viscous forces and break the liquid into a multitude of tiny droplets. This process is called atomization and is vital to everyday applications like internal combustion and inkjet printing. (Photo credit: R. P. Fraser et al.)
Ink Diffusion
Alberto Seveso’s gorgeous high-speed photos of ink diffusing in water have a dramatic sense of texture to them. Though still delicate, the whorls of fluid seem almost solid enough to touch. Watch the edges, though, and you can see thin wisps of color and hints of instabilities. Like cream poured into coffee, these ink sculptures are short-lived. Some of his works are available as prints or wallpapers (zip file). (Photo credit: Alberto Seveso)
The Real Raindrop
What is the shape of a falling raindrop? Surface tension keeps only the smallest drops spherical as they fall; larger drops will tend to flatten. The very largest drops stretch and inflate with air as they fall, as shown in the image above. This shape is known as a bag and consists of a thin shell of water with a thicker rim at the bottom. As the bag grows, its shell thins until it ruptures, just like a soap bubble. The rim left behind destabilizes due to the surface-tension-driven Plateau-Rayleigh instability and eventually breaks up into smaller droplets. This bag instability limits the size of raindrops and breaks large drops into a multitude of smaller ones. The initial size of the drop in the image was 12 mm, falling with a velocity of 7.5 m/s. The interval between each image is 1 ms. (Photo credit: E. Reyssat et al.)
Shocking Instabilities
The Richtmyer-Meshkov (RM) instability occurs when the interface between two fluids of different density is impulsively accelerated – usually by the passage of a shock wave. The image above shows a thin layer of gaseous sulfur hexafluoride embedded in air. Each vertical line, from left to right, shows the distortion of the two fluids at subsequent time steps after a Mach 1.2 shock wave passes through the gases. The interface’s initial waviness grows into mushroom-like shapes that mix the two gases together, ultimately leading to turbulence. Scenarios involving the RM instability include supersonic combustion ramjet engines, supernovas, and inertial confinement fusion. The RM instability is closely related to Rayleigh-Taylor instability and shares a similar morphology. (Photo credit: D. Ranjan et al.)
Flame Feedback
When a flame is enclosed in a combustion chamber, it can create violent oscillations in the pressure field. Flames have a natural unsteadiness in their heat release. These temperature fluctuations create pressure waves in the chamber. In the right enclosure, those pressure waves resonate and feed energy back into the initial perturbation. This creates a self-exciting oscillation, not dissimilar from aeroelastic flutter. This combustion instability is known as a thermoacoustic instability because of the coupling between temperature and pressure (acoustic) waves. The quick demo above lets you see and hear such an instability; here’s the same setup in high-speed, which makes the oscillating flame even clearer. The violence of this instability can be great enough to destroy engines. Famously, the F1 engine used in the Saturn V rocket had a history of instability issues before the fuel-injector was redesigned. For another great demo of this effect, check out this video from T. Poinsot. (Video credit: V. Anandan)
Elastic Walls and Viscous Fingers
The Saffman-Taylor instability, characterized by the branchlike fingers formed when a less viscous fluid is injected into a more viscous one, is typically demonstrated between two rigid walls, as in part (a) of the figure above. But what happens if one of the rigid walls forming the Hele-Shaw cell is replaced with an elastic wall? This is the case for (b) and (c) in the figure. The flexibility of the wall causes the expansion of the air-fluid interface to slow down relative to the rigid wall case and causes the interface to move toward a narrowing fluid-filled gap (as opposed to a constant thickness one). Both of these effects reduce the viscous instability mechanism that drives the fingering instability. With a high enough mass flow rate as in ©, there is still some instability in the interface, but it is dramatically reduced. (Photo credit: D. Pihler-Puzovic et al.)
