FYFD

Tag: viscous fingering

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    “Kingdom of Colours”

    Oil, paint, and soap combine to create a polychrome landscape in Thomas Blanchard’s “Kingdom of Colours” short film. Colorful droplets of paint coated in oil form anti-bubbles that skim along the liquid surface until they burst, dispersing new colors. One of my favorite touches in this video, though, are the branching fingers of color that appear repeatedly (most often in blue-violet). This is an example of a phenomenon known as the Saffman-Taylor instability. It’s a hallmark of a low viscosity fluid pushing into a higher viscosity one–like air into honey. (Image/video credit: T. Blanchard; via Flow Vis)

  • Fingering Under Elastic

    Fingering Under Elastic

    Take a couple panes of glass and stick a viscous fluid in between them; you’ve now constructed what fluid dynamicists call a Hele-Shaw cell. If you inject a low-viscosity fluid, like air, into the cell, you’ll get a beautiful finger-like pattern like the one shown on the left. If you change one of the walls to an elastic sheet, though, things get a bit different. The flexibility of the wall allows the upper surface to inflate as air gets pushed in. This can suppress the usual viscous fingers, as seen in the center animation. However, if you push the air in quickly, as in the right animation, the sudden inflation can wrinkle the elastic sheet. In this case, the wrinkles are the dominant influence, causing the the fluid to finger – but in an entirely different way than before! (Image credit: D. Pihler-Puzovic et al., sources 1, 2, 3; see also)

  • Fluid Fingers

    Fluid Fingers

    Fluid phenomena can show up in unexpected places. The collage above shows patterns formed when an aluminum block is lifted during wet sanding, a polishing technique. The dendritic fingers are formed from oil and the slurry of sanded particles being polished away. They are an example of the Saffman-Taylor instability, which forms when less viscous fluids (oil) protrude into a more viscous one (the slurry). Each image contains a different concentration of oil, resulting in very different fingering patterns. (Image credit: D. Lopez)

  • Viscous Fingers

    Viscous Fingers

    Viscous fingers form between air and titanium dioxide sol-gel in this photograph. The two fluids are trapped in a thin gap between glass plates – a set-up known as a Hele-Shaw cell. The dendritic fingers we see form when the less viscous air pushes into the more viscous sol-gel. This is an example of the Saffman-Taylor instability. The psychedelic colors are a result of thin-film interference and the way light interacts with very thin materials. The same effect is responsible for the colors on soap bubbles. (Image credit: C. Trease)

  • Viscous Fingers

    Viscous Fingers

    Take a viscous fluid, like laundry detergent, and sandwich it between two plates of glass. Fluid dynamicists call this set-up a Hele-Shaw cell. If you then inject a less viscous fluid, like air, between the plates–or if you try to pry them apart–you’ll see a distinctive pattern of dendritic fingers form. This viscous fingering, also known as the Saffman-Taylor instability, occurs because the interface between the two fluids is unstable. Invert the problem, though–inject a more viscous fluid into a less viscous one–and no special shapes will form because the interface will remain stable. (Image credit: Random Walk Studios, source)

  • Fluid Fingers

    Fluid Fingers

    Differences in viscosity or surface tension between two fluids can lead to finger-like instabilities. Here food dye placed on corn syrup forms narrow tendrils driven by the differing surface tensions of the two liquids. Similar dendritic shapes can be generated by injecting a low viscosity fluid into a high viscosity one (Saffmann-Taylor instability) or by pulling apart glass plates sandwiched around a high viscosity fluid. (Photo credit: T. Gaskill et al.)

  • Viscous Fingers

    Viscous Fingers

    Viscous liquid placed between two plates forms a finger-like instability when the top plate is lifted. The photos above show the evolution of the instability for four initial cases (top row, each column) in which the initial gap between the plates differs. Each row shows a subsequent time during the lifting process. As the plate is pulled up, the viscous liquid adheres to it and air from the surroundings is entrained inward to replace the fluid. This forms patterns similar to the classic Saffman-Taylor instability caused when less viscous fluid is injected into a more viscous one.   (Photo credit: J. Nase et al.)

  • Elastic Walls and Viscous Fingers

    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.)

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    Protruding Fingers

    Instability is a common feature of fluid flows and can generate a near infinite set of patterns. The video above shows the Saffman-Taylor instability, an interface instability that occurs when a fluid of lower viscosity is injected into a higher viscosity fluid. In this case, the fluids inhabit a thin space between two glass plates. The less viscous fluid displaces the more viscous one in a series of branching finger-like shapes. If the situation were reversed, with a more viscous fluid injected into a less viscous one, the interface would be stable and expand radially without any pattern formation. (Video credit: William Jewell College)

  • Dendritic Designs

    Dendritic Designs

    Imagine a thin layer of viscous liquid sandwiched between two horizontal glass plates. Then pull those plates apart at a constant velocity. What you see in the image above is the shape the viscous fluid takes for different speeds, with velocity increasing from left to right and from top to bottom. For lower velocities, the fluid forms tree-like fingers as air comes in from the edges. At higher velocities, though, there’s a transition from the finger-like pattern to a cell-like one. The cells are actually caused by cavitation within the fluid. When the plates are pulled apart fast enough, the local low pressure in the fluid causes cavitation bubbles to form just before the force required to remove the plate reaches its peak. (Photo credit: S. Poivet et al.)