With the right balance of viscosity and surface tension, many fluid combinations can form fractal or dendritic patterns. Here, researchers use a drop of food coloring atop a mixture of water and xanthan gum. Depending on the concentration of gum (and the age of the viscous fluid) different fractal patterns spread quickly across the surface. (Image and video credit: R. Camassa et al.)
In layers of viscous fluids, lighter and less viscous fluids can displace heavier, more viscous liquids. Here, researchers demonstrate this using four fluids sandwiched between layers of glass and mounted in a rotating frame. (Think of those liquid-air-sand art frames found in museums but bigger!)
In their first example, each layer of fluid is denser than the one beneath it, so buoyancy forces the lowest layer — air — to rise. The air pushes its way through the more viscous layer of olive oil, then slowly makes its way through the even more viscous glycerin before bursting through the last layer in an eruption. As the team varies the viscosity and miscibility of the layers, the movement of the buoyant fluids through the viscous layers changes dramatically. (Image and video credit: A. Albrahim et. al.)
Here’s a simple fluids experiment you can try at home using acrylic paints, ink, isopropyl alcohol and a few other ingredients. When dropped onto diluted acrylic paint, a mixture of black ink and alcohol spreads in a fractal fingering pattern. The radial (outward) flow is driven by the alcohol’s evaporation, which increases the local surface tension and draws fluid outward. The shape and density of the fingers depends, at least in part, on the viscosity of the underlying paint layer; more viscous paint layers grow smaller and denser fractal patterns. (Image and video credit: S. Chan et al.)
Materials like oobleck — a suspension of cornstarch particles in water — are tough to classify. In some circumstances, they behave like a fluid, but in others, they act like a solid. Here researchers sandwiched a thin layer of oobleck between glass plates and injected air into the mixture. For a fluid, this setup creates a classic Saffman-Taylor instability where rounded fingers of air push their way into the more viscous fluid. And, indeed, for low air pressures and low concentrations of cornstarch, the oobleck forms these viscous fingers. You can see examples in the top row’s first and third image, the second row’s middle image, and the bottom row’s third image.
Injecting air at high pressures and high cornstarch concentrations fractures the oobleck like a solid (middle row, first and third images). At intermediate pressures and concentrations, the oobleck forms a pattern called dendritic fracturing, where new branches can grow perpendicularly to their parent branch. Examples of this pattern are in the top row’s second image and the bottom row’s first and second images. (Image and research credit: D. Ozturk et al.; via Physics Today)
Finger-like shapes often form on fluids injected between glass plates, but what happens when that injected fluid contains particles? That’s the situation in this recent study, where researchers sandwiched a fluid between two glass plates and then injected a second, similar fluid laced with particles.
Despite the differences from the traditional Saffman-Taylor set-up, the granular-filled fluid still forms fingers as long as there’s even a slight density difference between the original and injected fluids. It doesn’t even matter which of the two fluids has the greater density! (Image and research credit: A. Kudrolli et al.)
“What happens when two scientists, a composer, a cellist, and a planetarium animator make art?” The answer is “Dendritic,” a musical composition built directly on the tree-like branching patterns found when a less viscous fluid is injected into a more viscous one sandwiched between two plates.
Normally this viscous fingering instability results in dense, branching fingers, but when there’s directional dependence in the fluid, the pattern transitions instead to one that’s dendritic. In this case, that directionality comes from liquid crystals, whose are rod-like shape makes it easier for liquid to flow in the direction aligned with the rods.
For more on the science, math, and music behind the piece, check out this description from the scientists and composer. (Video, image, and submission credit: I. Bischofberger et al.)
If you sandwich a viscous fluid between two plates, then pull the plates apart, you’ll often get a complex branching pattern that forms as air pushes its way into the fluid. But the exact results depend strongly on what kind of viscous fluid you used. A new study looks specifically at what happens when that fluid is a yield-stress gel.
Yield-stress fluids behave like a solid until a critical amount of force causes them to flow. Think about your toothpaste. When you take the cap off, the toothpaste stays put until you squeeze the tube enough to make it flow. The gels used in this experiment behave similarly.
The researchers found that their gels required a critical energy input in order to branch and flow. If the energy applied in pulling the plates apart was too low, no branching occurred (Image 1). But beyond that critical energy, separating the plates created intricate branching patterns consistent with those seen in simpler, Newtonian fluids. (Image, research, and submission credit: T. Divoux et al.; via APS)
Take a mixture of a viscous liquid – like clay mud – and squeeze it between two glass plates and you’ll create a mostly-round layer of liquid. As you pry the two glass plates apart, air will push its way into that layer, forcing through the mud in a dendritic pattern. This is called the Saffman-Taylor instability or viscous fingering. It occurs because the interface between the air and mud is unstable. (Image and video credit: amàco et al.)
Branching, tree-like structures are found throughout nature. Take a thin layer of a viscous fluid pressed between two glass plates and inject a less viscous fluid like air and you’ll get branch-like structures. These are the result of the Saffman-Taylor instability and usually result in a fairly random outcome because of the instability’s sensitivity to small variations. In a new study, researchers use multiple air injection ports to finely control the formation and growth of air fingers, allowing them to build well-ordered branching structures like the one above. By placing the air ports in an array, the same technique can be used to create fluid meshes. The authors suggest this new technique could have wide-ranging applications including the design of heat exchangers and the growth of artificial tissues. (Image and research credit: T. ul Islam and P. Gandhi, source)
These strange flower-like formations appear in a former limestone quarry in France. The black that you see is bitumen, or asphalt. These dendritic structures appear in spots where the rock has fractured. Originally, two rock faces met here, with a thin layer of bitumen glued between them. As one face pulled away, air began to seep into the space between, slowly injecting itself into the more viscous bitumen. Just as we observe in the laboratory, the air and bitumen formed viscous fingers, creating a classic pattern known as the Saffman-Taylor instability. It’s so cool to see an example of this in nature! You can see more photos of the formations here. (Image credit: P. Thomas)