Fuck Yeah Fluid Dynamics

Celebrating the physics of all that flows. Ask a question, submit a post idea or send an email. You can also follow FYFD on Twitter and Google+. FYFD is written by Nicole Sharp, PhD.

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Posts tagged "viscous fingering"

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.)

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 (c), there is still some instability in the interface, but it is dramatically reduced. (Photo credit: D. Pihler-Puzovic et al.)

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)

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.)

In this video, a thin film of viscous glycerin sits between two glass plates. As the plates are forced apart, air gets entrained from either side, causing finger-like instabilities to form between the two fluids. This is a result of the Saffman-Taylor mechanism. The final dendritic pattern depends on the fluid viscosities, surface tension, and any non-uniformities in the apparatus. (Video credit and submission by M. Goodman)

In this video, mixtures of inks (likely printer toners) and fluids move and swirl. Magnetic fields contort the ferrofluidic ink and make it dance, while less viscous fluids spread into their surroundings via finger-like protuberances. (Video credit and submission: Antoine Delach)

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)

Place a viscous fluid in the gap between two plates of glass and you have created a Hele Shaw cell. If a less viscous fluid is then injected between the plates, a fascinating pattern of finger-like protrusions results. This is known as the Saffman-Taylor instability. Because of the relative simplicity of the set-up, it’s possible to create such experiments at home using common household fluids like glycerin, dish soap, dyed water, or laundry detergent. (Photo credits: Jessica Rosencranz, Jessica Todd, Laurel Swift et al, Andrea Fabri et al, Tanner Ladtkow et al, Mike Demmons et al, Trisha Harrison, Justin Cohee, and Erik Hansen)

The Saffman-Taylor instability occurs when a less viscous fluid is injected into a more viscous one, usually in a Hele-Shaw cell. Here oil paint and mineral spirits were painted onto flat surfaces that were pressed together before being pulled apart. The result is viscous fingering of the fluids. #