Fractal Fingers

As bizarre as the branching fractal fingers of the Saffman-Taylor instability look, they’re quite a common phenomenon. In his video, Steve Mould demonstrates how to make them by sandwiching a viscous liquid like school glue between two acrylic sheets and then pulling them apart. The more formal lab-version of this is the Hele-Shaw cell, which he also demonstrates. But you may have come across the effect when pealing up a screen protector or in dealing with a cracked phone screen. In all of these cases, a less viscous fluid — specifically air — is forcing its way into a more viscous fluid, something that it cannot manage without the fluid interface fracturing. (Video and image credit: S. Mould)

#flowVisualization #fluidDynamics #fractals #HeleShawCell #instability #physics #SaffmanTaylorInstability #science #viscousFingering

Why Nature Loves Fractals

Trees, blood vessels, and rivers all follow branching patterns that make their pieces look very similar to their whole. We call this repeating, self-similar shape a fractal, and this Be Smart video explores why these branching patterns are so common, both in living and non-living systems. For trees, packing a large, leafy surface area onto the smallest amount of wood makes sense; the tree needs plenty of solar energy (and water and carbon dioxide) to photosynthesize, and it has to be efficient about how much it grows to get that energy. Similarly, our lungs and blood vessels need to pack a lot of surface area into a small space to support the diffusion that lets us move oxygen and waste through our bodies. Non-living systems, like the branches of viscous fingers or river deltas or the branching of cracks and lightning, rely on different physics but wind up with the same patterns because they, too, have to balance forces that scale with surface area and ones that scale with volume. (Video and image credit: Be Smart)

#biology #branchingFlow #diffusion #fluidDynamics #fractals #mathematics #physics #riverDeltas #science #trees #viscousFingering

When surface tension varies along an interface, fluids move from regions of low surface tension to higher surface tension, a behavior known as the Marangoni effect. Here, a drop of (dyed) water is placed on glycerol. The two fluids are miscible, but water has much a lower viscosity and density yet a higher surface tension. The drop’s interface quickly becomes unstable; viscous fingers form along the edge as the less viscous water pushes into the more viscous glycerol. Eventually, the surface-tension-driven Marangoni flow breaks those fingers off into lip-like daughter drops. The researchers also show how the interplay between viscosity and surface tension affects the size of fingers that form by varying the water/glycerol concentration. (Image and video credit: A. Hooshanginejad et al.)

https://fyfluiddynamics.com/2024/10/marangoni-blossoms/

#2021gofm #fluidDynamics #instability #marangoniEffect #physics #science #surfaceTension #viscosity #viscousFingering

Viscous fingers form when a low-viscosity fluid is pumped into a narrow, viscous-fluid-filled gap. The branching pattern that forms depends on the ratio of the two viscosities, among other factors. To better understand what goes on inside these fingers, researchers carefully alternated injecting dyed and undyed fluid. This creates a pattern of concentric rings that deform as the fingers spread.

In this particular study, the initial fluid and injected fluids are miscible, meaning that they can mix into one another. In modeling their experiments, the team found that this mixing created stratification — i.e., layers of fluids with different densities — in the narrow gap between their plates. The stratification’s effects were large enough that the model required a correction term for them; that’s a bit surprising because we’d usually expect that the tiny third-dimension of the gap would be too small to matter! (Image and research credit: S. Gowan et al.)

https://fyfluiddynamics.com/2024/10/peering-inside-viscous-fingering/

#flowVisualization #fluidDynamics #instability #miscibility #physics #SaffmanTaylorInstability #science #viscousFingering

Inject a less viscous fluid into a gap filled with a more viscous fluid, and you’ll get finger-like patterns spreading radially. Here, researchers put a twist on this viscous fingering by taking turns injecting different liquids. Each injection cycle disrupts what came before, layering fingering patterns on fingering patterns. The results resemble fireworks. Happy 4th of July! (Image credit: C. Chou et al.)

https://fyfluiddynamics.com/2024/07/viscous-fireworks/

#2023gofm #flowVisualization #fluidDynamics #fluidsAsArt #instability #physics #SaffmanTaylorInstability #science #viscousFingering

If you sandwich a viscous fluid between two plates and inject a less viscous fluid, you’ll get viscous fingers that spread and split as they grow. This research poster depicts that situation with a slight twist: the viscous fluid (transparent in the image) is shear-thinning. That means its viscosity drops when it’s deformed. In this situation, the fingers formed by the injected (blue) fluid start out the way we’d expect: splitting as they grow (inner portion of the composite image). But then, the tip-splitting stops and the fingers instead elongate into spikes (middle ring). Eventually, as the outer fluid’s viscosity drops further, the fingers round out and spread without splitting (outer arc of the image). (Image credit: E. Dakov et al.; via GoSM)

https://fyfluiddynamics.com/2024/04/evolving-fingers/

#2024gosmp #flowVisualization #fluidDynamics #HeleShawCell #instability #nonNewtonianFluids #physics #SaffmanTaylorInstability #science #shearThinning #surfaceTension #viscosity #viscousFingering

Aus dem #PrincipiaArchiv: Finger im Glas

Es ist eine Glasscheibe gegen die Sonne fotografiert. Aber was sind das für fingrige Blattstrukturen? Man denkt gleich an Eisblumen, aber dafür war es viel zu warm. Aufgenommen habe ich die Bilder am 20. April in Wien am U-Bahnhof Kaisermühlen.

Das Fingerblumenmuster befand sich nicht auf der Oberfläche der Fensterscheiben, sondern in ihrem Inneren. Wie kann das sein?

#Dendriten
#SaffmanTaylorInstabilität
#ViscousFingering

https://www.principia-magazin.de/muster/273-finger-im-glas-das-muster-des-monats-05-2016/