Bubbles rising through a viscous fluid deform and interact. As they collapse into one another, the lower bubble induces a gravity-driven jet that projects upward into the higher bubble. The more elongated the bubble, the faster the jet. The same behavior is seen in the rebound of a cavity at the free surface of a liquid. The authors suggest a universal scaling law for this behavior. (Video credit: T. Seon et al.)
Tag: viscous flow
Fluidic Public Art by Charles Sowers
Artist Charles Sowers creates exhibits and public art focused on illuminating natural phenomenon that might otherwise go unnoticed, and much of his work features fluid dynamics directly or indirectly. “Windswept” and “Wave Wall” are both outdoor exhibits that show undulations and vortices corresponding to local wind flow. Other pieces explore ferrofluids through magnetic mazes or feature foggy turbulence. My own favorite, “Drip Chamber”, oozes with viscous fluids whose dripping forms patterns reminiscent of convection cells. Be sure to check out his website for videos of the exhibits in action. (Photo credits: Charles Sowers; submitted by rreis)
Polygonal Jumps
Hydraulic jumps occur when a fast-moving fluid enters a region of slow-moving fluid and transfers its kinetic energy into potential energy by increasing its elevation. For a steady falling jet, this usually causes the formation of a circular hydraulic jump–that distinctive ring you see in the bottom of your kitchen sink. But circles aren’t the only shape a hydraulic jump can take, particularly in more viscous fluids than water. In these fluids, surface tension instabilities can break the symmetry of the hydraulic jump, leading to an array of polygonal and clover-like shapes. (Photo credits: J. W. M. Bush 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)
Shark-Tooth Instability
A viscous fluid inside a horizontally rotating circular cylinder forms a shark-tooth-like pattern along the fluid’s free surface. This is one of several patterns observed depending on the fluid’s viscosity and surface tension and the rotational rate of the cylinder. (Photo credit: S. Thoroddsen and L. Mahadevan; for more, see Thoroddsen and Mahadevan 1996 and 1997)
Falling Oil
A drop of silicone oil falling through a liquid with lower surface tension distorts into multiple vortex rings connected by thin films. This behavior is caused by the interaction between viscous and capillary forces and is observable for only a narrow range of oil viscosities. (Photo credit: A. Felce and T. Cubaud)
The Fluid Dynamical Sewing Machine
Anyone who has poured a viscous fluid like honey or syrup will have noticed its tendency to coil like rope. A similar effect is observed when a viscous fluid stream falls onto a moving belt. The photos above show some of the patterns seen in these “fluid-mechanical sewing machines” depending on the height of the thread and the speed of the moving belt. Notice how some of the patterns are doubles of another (i.e. two coils per side instead of one). This period doubling behavior is often seen in systems on their way to chaos. (Photo credits: S. Chiu-Webster and J. Lister)
Honey Coiling
The liquid rope coiling effect occurs in viscous fluids like oil, honey, shampoo, or even lava when they fall from a height. The exact behavior of the coil depends on factors like the fluid viscosity, the height from which the fluid falls, the mass flow rate, and the radius of the falling jet. Here Destin of the Smarter Every Day series outlines the four regimes of liquid coiling behavior commonly observed. As with many problems in fluid dynamics the regimes are described in terms of limits, which can help simplify the mathematics. The viscous regime (2:34 in the video) exists in the limit of a small drop height, whereas the inertial regime (3:15) exists in the limit of large drop height. Many complicated physical problems, including those with nonlinear dynamics, are treated in this fashion. For more on the mathematics of the coiling effect, check out Ribe 2004 and Ribe et al. 2006. (Video credit: Destin/Smarter Every Day; submitted by inigox5)
Reader Question: Creeping Flow
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David asks:
I’m taking an undergraduate fluid dynamics course, and I’m having trouble understanding what a Creeping Flow exactly is. The only thing I understand about that is that the Re should be 0 or close to 0 for the flow… Could you post an example of a creeping flow please? Thank you!
Absolutely! Creeping flow, also called Stokes flow, is, like you said, a very low Reynolds number flow. It would be hard to say that the Reynolds number is zero because that would seem to imply no flow at all. Think of it instead as a Reynolds number much, much less than one. When the Reynolds number is very low, it means that viscous forces are dominating the flow. The video above shows creeping flow around a cylinder; notice how the streamlines stay attached all the way around the surface of the cylinder. There’s no separation, no turbulent wake, no von Karman vortex street. Viscosity is so dominant here that it’s damped out all of that inertial diffusion of momentum.
We’ve posted some other great examples of creeping flow, as well, though not by that name. There are the reversible laminar flow demos and various experiments in Hele-Shaw cells, all of which qualify as creeping flow because of their highly viscous nature. If you have the time, there’s also a great instructional video from the 1960s called “Low Reynolds Number Flow” (Parts 1, 2, 3, 4) starring G. I. Taylor (a famous fluid dynamicist) that is full of one demo after another.
Reversing a Flow
The reversibility of laminar mixing often comes as a surprise to observers accustomed to the experience of being unable to separate two fluids after they’ve been combined. As you can see above, however, inserting dye into a highly viscous liquid and then mixing it by turning the inner of two concentric cylinders can be undone simply by turning the cylinder backwards. This works because of the highly viscous nature of Stokes flow: the Reynolds number is much less than 1, meaning that viscosity’s effects dominate. In this situation, fluid motion is caused only by molecular diffusion and by momentum diffusion. The former is random but slow, and the latter is exactly reversible. Reversing the rotation of the fluid undoes the momentum diffusion and any distortion remaining is due to molecular diffusion of the dye.
