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.)
Tag: fingering instability
A Colorful Rinse
In this image a jet of water (clear/white) is rinsing a solution of polyacrylamide (PAM; blue) off a silicon surface. In the center, a hydraulic jump marks the interface where fast-moving laminar flow changes to a slower turbulent one. At the same time, the water, which is less viscous than the PAM, creates viscous finger-like protrusions into the blue liquid as it rinses the surface clean. (Photo credit: T. Walker, T. Hsu, and G. Fuller)
Green Fingers
Differences in surface tension between two layers of fluid can cause fascinating finger-like instabilities. Here glycerol is spread in a thin film on a silicon wafer. Then a wire coated in oleic acid, which has a lower surface tension than glycerol, was touched to the wafer. As the oleic acid spreads across the film surface, Marangoni and capillary stresses cause variations in the film thickness, which results in the dendritic patterns seen here. (Photo credit: B. Fischer et al.)
Viscous Fingers
High viscosity silicon oil is sandwiched between two circular plates. As the upper plate is lifted at a constant speed, air flows in from the sides. The initially circular interface develops finger-like instabilities, due to the Saffman-Taylor mechanism, as the air penetrates. Eventually the fluid will completely detach from one plate. (Photo credit: D. Derks, M. Shelley, A. Lindner)
Viscoelastic Fingers
This series of photos shows two plates with a thin layer of polymer-laced, viscoelastic liquid. As the two plates are separated, complex instabilities form. The lower section of each photograph shows the fluid on the plate, with finger-like Saffman-Taylor instabilities forming as air rushes in between the gap in the plates. As the separation increases, the polymers in the liquid stretch under the increased strain, inducing elastic stresses in the fluid that cause the formation of secondary structures. (Photo credit: R. Welsh, J. Bico, and G. McKinley)
Labyrinth
A labyrinthine pattern forms in this timelapse video of a multiphase flow in a Hele-Shaw cell. Initially glass beads are suspended in a glycerol-water solution between parallel glass plates with a central hole. Then the fluid is slowly drained over the course of 3 days at a rate so slow that viscous forces in the fluid are negligible. As the fluid drains, fingers of air invade the disk, pushing the beads together. The system is governed by competition between two main forces: surface tension and friction. Narrow fingers gather fewer grains and therefore encounter less friction, but the higher curvature at their tips produces larger capillary forces. The opposite is true of broader fingers. Also interesting to note is the similarity of the final pattern to those seen in confined ferrofluids. (Video credit and submission: B. Sandnes et al. For more, see B. Sandes et al.)
Viscous Fingers
When less viscous fluids are injected into a more viscous medium, the low-viscosity fluid forms finger-like protrusions into the background fluid. This is known as the Saffman-Taylor instability. The video above shows this effect but in a more dynamic setting. Blue-dyed water and a clear solution of water and glycerol fifty times more viscous than the water are injected in alternating fashion to a microfluidic channel. The blue water spreads into the clear glycerol solution via fingers that quickly diffuse, creating a homogeneous–or uniform–mixture. (Video credit: Juanes Research Group)
Squeezing Bubbles
An air bubble trapped inside a viscoelastic fluid is squeezed between two plates in this video, revealing a Saffman-Taylor-like fingering instability stemming from local stress concentrations. (Video credit: Baudouin Saintyves)
Stick-Slip Bubbles
Varying the rate of injection of air into a wet granular mixture contained in a Hele Shaw cell results in very different flow patterns. At low injection rates, stick-slip bubbles form. As the injection rate increases, patterns are affected by “temporal intermittency” where continuous motion is occasionally interrupted by jamming. Increasing the injection rate still further results in Saffman-Taylor-like fingering. #
Viscous Fingers
A Hele Shaw cell is little more than two glass plates separated by a thin layer of viscous fluid. The cell serves as a good test bed for viscous, low Reynolds number flows such as those found in microfluidics. Here a less viscous fluid is injected into the center of the cell, causing the finger-like protrusions of the less viscous fluid into the more viscous one via the Saffman-Taylor instability.
