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)
Tag: viscous flow
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.
Pāhoehoe Lava
Lava flows come in many varieties but one of the most captivating is the pāhoehoe flow, meaning “smooth, unbroken lava” in the native Hawaiian. This type of basaltic lava features a smooth or undulating surface formed by the fluid lava beneath a cooler, congealing surface crust. They often feature low viscosity (by the standards of lava) and very high temperatures between 1100 and 1200 degrees Celsius. Here the flow shows features of viscous fluids like honey, including rope-coiling motions.
Viscous Fluid Falling on a Moving Belt
In this video a very viscous (but still Newtonian) fluid is falling in a stream onto a moving belt. Initially, the belt is moving quickly enough that the viscous stream creates a straight thread. As the belt is slowed, the stream begins to meander sinusoidally and ultimately begins to coil. Aside from some transient behavior when the speed of the belt is changed very quickly, the behavior of the thread is very consistent within a particular speed regime. This is indicative of a nonlinear dynamical system; each shift in behavior due to the changing speed of the belt is called a bifurcation and can be identified mathematically from the governing equation(s) of the system. (Video credit: S. Morris et al)
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.
Reader Question: Froude vs. Reynolds
@spooferbarnabas asks: I was wondering what the difference is between Froude’s number and Reynold’s number? they seem very similar
Fluid dynamicists often use nondimensional numbers to characterize different flows because it’s possible to find similarity in their behaviors this way. The Reynolds number is the most common of these dimensionless numbers and is equal to (fluid density)*(mean fluid velocity)*(characteristic length)/(fluid dynamic viscosity). The Reynolds number is considered a ratio of total momentum (or inertial forces) to the molecular momentum (or viscous forces). A small Reynolds number indicates a flow dominated by viscosity; whereas a flow with a large Reynolds number is considered one where viscous forces have little effect.
The Froude number, in contrast, focuses on resistance to flow caused by gravitational effects, not molecular effects. It is defined as (mean fluid velocity)/(characteristic wave propagation velocity). Initially, it was developed to describe the resistance of a model floating in water when towed at a given speed. As the boat’s hull moves through the water, it creates a wave that travels forward (and backward in the form of the wake), carrying information about the boat–much like pressure waves travel before and behind a subsonic aircraft. The speed of the wave created by the boat depends on gravity (see shallow water waves). The closer the boat’s speed comes to the water wave’s speed, the greater the resistance the boat experiences. In this respect, the Froude number is actually analogous to the Mach number in compressible fluids.
I hope that helps explain some of the differences!
Reader Question: National Committee for Fluid Mechanics Films
lazenby asks: Have you seen these guys? http://web.mit.edu/hml/ncfmf.html
Yes, absolutely! Those videos, which date from the 1960s, are so useful that they’re still shown to undergraduates today. (Or at least they showed several of them to us when I was junior!) They can seem a bit slow by current standards, but the films are full of great demonstrations of basic fluid mechanics. If the links on that page don’t work (or, if like me, you can’t stream RealPlayer), a lot of the videos can also be found on YouTube by searching for individual titles. The Low Reynolds Number Flow video is one of my favorites because it’s hosted by G. I. Taylor, one of the the most prolific and influential fluid mechanicians of the 20th century.
Ants as a Fluid
The collective behavior of ants can mirror the flow of a viscous fluid. It would be interesting to see if any such parallels carry over to the flocking of birds or schooling of fish. The latter two behaviors are thought to increase aero- and hydrodynamic efficiency for the group. #
Viscous Fingers
This photo shows the Saffman-Taylor instability in a Hele-Shaw cell. Here a viscous fluid has been placed between two glass plates and a second less viscous fluid inserted, resulting in a finger-like instability as the less viscous fluid displaces the more viscous one. This is an effect that can be easily explored at home using common liquids like glycerin, water, dish soap, or laundry detergent. #
