Tag: instability

Order in Chaos
Although turbulent flow is chaotic, it’s not completely disordered. In fact, order can emerge from turbulence, though exactly how this happens has been a long-enduring mystery. Take the animations above. They show the flow that develops between two plates moving in opposite direction that are separated by a small gap. (The formal name for this is planar Couette flow.) The visualization is taken in a plane at a fixed height between the plates.
Initially (top), the flow shows narrow bands of turbulence, shown in green, separated by calmer, laminar zones in black. As time passes, these areas of laminar and turbulent flow self-organize, eventually forming diagonal stripes that are much longer than the gap between plates (bottom), the natural length-scale we would expect to see in the flow. Researchers have wondered for years why these distinctive stripes form. What sets their spacing, and why are they along diagonals?
To answer those questions, researchers explored the full Navier-Stokes equations, searching for equilibrium solutions that resemble the striped patterns seen in experiments and simulation. And for the first time, they’ve found a mathematical solution that matches. What the work shows is that the pattern emerges naturally from the equations; in fact, given the characteristics of the solution, the researchers found that many disturbances should lead to this result, which explains why the pattern appears so frequently. (Image and research credit: F. Reetz et al., source; via phys.org; submitted by Kam-Yung Soh)
June 11, 2019
Engineering Droplets
A jet of falling liquid doesn’t remain a uniform cylinder; instead, it breaks into droplets. In this video, Bill Hammack explores why this is and what engineers have learned to do to control the size of the droplets formed.
The technical name for this phenomenon is the Plateau-Rayleigh instability. It begins (like many instabilities) with a tiny perturbation, a wobble in the falling jet. This begins a game of tug of war. One of the competitors, surface tension, is trying to minimize the surface area of the liquid, which means breaking it into spherical droplets. But doing so requires forcing some of the the liquid to flow upward, against both gravity and the liquid’s inertia. The battle takes some time, but eventually surface tension wins and the jet breaks up.
That’s not necessary a bad thing. It’s actually key to many engineering processes, like ink-jet printing and rocket combustion, as Bill explains in the full video. (Video and image credit: B. Hammack; submitted by @eclecticca)
June 10, 2019
Inside an Evaporating Drop
The evaporation of a simple droplet holds far more complexity than one would expect. If you look closely at the edge of the drop, there’s a tiny, beautiful display at work. It begins with small variations in surface tension at the contact line where solid, liquid, and gas meet. These could be caused by local temperature or concentration differences; either way, the gradient in surface tension creates a flow. It starts out as a series of microjets spaced evenly around the contact line (left).
As the microjets strengthen, they merge into larger and larger vortical structures (right). This kind of feature – large structures emerging from smaller ones – is known as an inverse cascade. Fluid dynamicists have traditionally studied the classic (turbulent) energy cascade, where kinetic energy moves from large scales into smaller ones, but researchers are beginning to recognize more situations where the inverse cascade occurs, such as in the storms of Jupiter. (Image and research credit: A. Ghasemi et al., source)
May 22, 2019
Granular Instabilities
Granular mixtures show surprising similarities to fluids, even though their underlying physics differ. The latest example of this is a Rayleigh-Taylor-like instability that occurs when heavy particles sit atop lighter ones. By combining vertical vibration and an upward gas flow, researchers found that the lighter particles form fingers and bubbles that seep up between the heavier grains (upper left). Visually, it looks remarkably similar to a lava lamp or other Rayleigh-Taylor-driven instability (upper right).
But the physics behind the two are distinctly different. In the fluid, buoyancy drives the instability while surface tension acts as a stabilizing force. There’s no surface tension in a granular material, though. Instead, the drag force from gas flowing upward provides the vertical impetus while friction between the grains – essentially an effective viscosity – replaces surface tension as a stabilizing influence.
The similarities don’t stop there, though. When the researchers tested a “bubble” of heavy grains suspended in lighter ones (lower left), they found that, instead of sinking, the granular bubble split in two and drifted downward on a diagonal. Eventually, those daughter bubbles also split. Again, visually, this looks a lot like what happens to a drop of ink or food coloring falling through water (lower right), but the physics aren’t the same at all.
In the fluid, the breakup happens when a falling vortex ring splits. In the granular example, gas moving upward tends to channel around the heavy grains because they’re harder to move through. Eventually, this builds up a solidified region under the bubble. When the heavy grains can’t move directly down, they split and sink through the surrounding suspended particles until they build up another jammed area and have to split again. (Image credits: granular RTI – C. McLaren et al.; RTI simulation – M. Stock; bag instability – D. Zillis; research credit: C. McLaren et al.; submitted by Kam-Yung Soh)
May 8, 2019
Patterns of Flame
In nature, the way a system behaves often depends on multiple competing factors. This is particularly apparent for chemical reactions, some of of which can oscillate in wild patterns as different forces compete. Similar patterns can occur in combustion, as shown above.
What you see here are patterns formed on a flame propagating down a tube. They’re a result of what’s known as a thermal-diffusive instability. Flames like these typically propagate by conducting heat into the fuel-air mixture ahead of the flame front, thereby raising its temperature, while, simultaneously, fuel and air diffuse into the flame to sustain the chemical reactions. If the rates of heat transfer and chemical diffusion are balanced, the flame moves steadily. But if there’s an imbalance between those factors, instabilities occur.
In this case, the temperature rises much faster than the time needed for fresh fuel to move into the flame. As the temperature goes up, the reaction rate increases exponentially, and the flame surges forward. But the slow resupply of fuel makes the reaction rate drop, causing the flame’s progress to stall. This interplay results in the complex, pulsating instabilities we see here. (Image and submission credit: H. Pearlman; research credit: H. Pearlman and D. Ronney)
February 22, 2019
Liquid Antispiral
Spiral formations are common in nature, from galaxies to chemical reactions. But most examples in nature rotate such that their arms trail the direction of rotation. Viewed side-on, this makes the arms appear to spiral outward from the the center. The opposite – an antispiral, where the arms appear to be drawn in toward the center – also exists, but there are far fewer examples. Which is why it’s notable that physicists have described a new one, seen above.
You’re watching silicone oil draining through a plate with an array of holes in it. There’s a reservoir of oil on top supplying a constant flow rate. The patterns that form in this system vary widely – they can form between one and six arms – but the results are always antispirals. The driving mechanism seems to be the periodic nature of the discharge from individual holes, which is caused by a Rayleigh-Taylor instability. Hopefully systems like this can shed some light on why spirals are often preferred over antispirals. (Image and research credit: H. Yoshikawa et al.; via APS Physics)
January 23, 2019
Dripping Down the Rivulet
If you’ve ever watched water running down the side of the street, you’ve probably noticed that it doesn’t flow smoothly. Instead, you’ll see waves, rivulets, and disturbances that form. That’s because the simple action of flowing down an incline is unstable. Water and other viscous liquids can’t flow downhill smoothly. Any disturbances – an uneven surface, the rumble of passing cars, a pebble in the way – will create a disruption that grows, often until the entire flow is affected. This video shows some of the complex and beautiful patterns you get then. (Video and image credit: G. Lerisson et al.)
January 18, 2019
“The Empire of C”
Filmmaker Thomas Blanchard has once again released a beautiful, fluid-filled short to captivate us. Built from paint, oil, and liquid soap, “The Empire of C” feels like it gives viewers a birds-eye perspective over a fantastical land. I was particularly drawn to two fluid dynamical aspects of the film. The first were the dendritic sequences in the opening, which feel a bit like watching river deltas form in real time. Despite their resemblance to the Saffman-Taylor instability, I think these fingers are interfacially driven – meaning that they result from differences in surface tension between the different liquids Blanchard is using.
The second thing that caught my eye and made me rewind the video over and over were the glittery droplets. The glitter acts like tracer particles, allowing you to see the flow inside the droplets. Check out that counter-circulation compared to the paint flowing by outside! It’s a reminder that even inside a seemingly still droplet, there’s lots going on. (Video and image credit: T. Blanchard)
January 11, 2019
“If I Say”
The new Mumford & Sons single “If I Say” features a fluid-dynamical music video. It’s full of dendritic fingers and flowing colors – likely from combinations of inks, paints, and other fluids. Although the fingers are reminiscent of the viscosity-dependent Saffman-Taylor instability, these appear to be driven by variations in surface tension between the different fluids. That’s a major feature throughout the video; although some of the flow is caused by the syringes depositing fluids, much of it seems to be a Marangoni effect, where flow moves away from areas of low surface tension to ones with higher surface tension. (Video credit: Mumford & Sons; filmed by P. Hofstede; via Katie M.)
November 30, 2018
Vortex Dome
Are you staring into the eye of a hurricane or watching the spin of a simple desk toy? Part of the beauty of fluid dynamics is recognizing how similar they both are. This is high-speed footage of a toy known as a “Vortex Dome,” which contains a fluid filled with tiny mica particles that react to local forces and allow users to “see” the flow. Before the video begins, the toy has been spinning for long enough that the fluid inside rotates as if it were a solid body. Then an unseen hand sets the disk spinning in the opposite direction and we observe what happens.
Fluid at the outer edge of the toy has to immediately change direction due to friction with the wall. That change in momentum slowly passes from the wall inward as viscosity between one layer of fluid to the next passes that signal. This creates the rolls we see in the first animation. Initially, those rolls are smooth, but they quickly roughen as disturbances in them grow into full-blown turbulence. Meanwhile, viscosity continues to pass the change in rotation inward, ultimately swallowing the entire interior of the toy. Left spinning indefinitely, the disturbances will eventually quiet out and the entire fluid will spin as one. (Image and video credit: D. van Gils)
November 29, 2018