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

Flow Behind Viscous Fingers

Nature is full of branching patterns: trees, lighting, rivers, and more. In fluid dynamics, our prototypical branching pattern is the Saffman-Taylor instability, created when a less viscous fluid is injected into a more viscous one in an confined space. Most attention in this problem has gone to the branching interface where the two fluids meet, but recently, a team has examined the flow away from the fingers by alternately injecting dyed and undyed fluid to visualize what goes on. That’s what we see here. Notice how the central dye rings, far from the branching fingers, still appear circular. Yet, even a few centimeters away from the fingers, the dye is starting to show ripples that correspond to the fingers. That’s an indication that the pressure gradient generated at the tips of the fingers is pretty far-reaching! (Image and research credit: S. Gowen et al.)

#flowVisualization #fluidDynamics #HeleShawCell #physics #SaffmanTaylorInstability #science #surfaceTension

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