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.)
Search results for: “viscous”
Peering Inside Viscous Fingering
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.)
Viscous Fireworks
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.)
Inside Viscous Fingers
Sandwich a viscous fluid between two transparent plates and then inject a second, less viscous fluid. This is the classic set-up for the Saffman-Taylor instability, a well-studied flow in which the interface between the two fluids forms a wavy edge that develops into fingers. Despite its long history, though, there is still more to learn, as shown in this video. Here, researchers alternately injected a dyed and undyed version of the less viscous fluid. The result (Image 3) is a set of concentric dye rings that show how the fluid moves far from the fingers along the edge. Notice that the waviness of the fingers appears in the flowing fluid well before it approaches the interface. (Image and video credit: S. Gowan et al.)
Fighting a Viscous World
Vaucheria is a genus of yellow-green algae (think pond scum), and some species within this genus reproduce asexually by releasing zoospores. Once mature, the zoospore has to squeeze out of a narrow, hollow filament in order to escape into the surrounding fluid (top). To do so, it uses tiny hair-like flagella on its surface. Despite the minuscule size of these micron-length flagella, they generate some major flows around the zoospore (middle and bottom). Even several body lengths away, the flow field shows significant vorticity. All this active entrainment of fluid from the surroundings helps the zoospore escape its confinement and swim away to start a new plant. (Image and research credit: J. Urzay et al., source)
A Viscous Splash
The splash of a drop may be commonplace, but it is still a mesmerizing and fertile phenomenon. When it comes to splashing, scientists are still learning how to predict the outcome. Here a drop of silicon oil impacts a film of silicon oil with an even higher viscosity. The momentum of that impact creates a crater and a splash curtain that rises and expands from the initial point of impact. Because the film viscosity is higher than the drop’s, the evolution of the corona slows down. Eventually, surface tension and gravity start pulling the splash curtain back down as the crater collapses. Meanwhile at the top of the splash, capillary forces pull fluid into the rim, which becomes unstable and grows cusps that eventually eject a cloud of smaller droplets. (Image and research credit: H. Kittel et al., source)
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)
