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Vortex Loops
March 11, 2013
When I starting working in
industrial research, more than thirty years ago, about one in five of my colleagues were
tobacco smokers. Everyone of them was smart enough to know that smoking was
harmful to their health, and every year the number of smokers was reduced. One year, there was a
betting pool among a few smokers to determine who could refrain from smoking the longest. The winner got a little money, but he started smoking again shortly thereafter.
When I left the
labs after thirty years, not a single person was a smoker. The health benefit was an obvious motivation, but numerous obstacles were imposed over the years. No smoking was allowed in any corporate building, and any outside smoking was not allowed within thirty
feet of a building entrance. Perhaps it should have been thirty
meters for the
research buildings.
When I was younger, I would see a few skilled smokers blowing
smoke rings. There were even
television cartoons, so old that they were in
black and white, showing a
cartoon character blowing smoke rings. Nowadays, a smoke ring is an uncommon sight. Just as for
coffee rings, there's a bit of
physics behind smoke rings, more properly called
vortex loops, since they exist in more
media than
smoke in
air.[1-3] I wrote about coffee rings in a
recent article (Coffee Ring Physics, February 11, 2013).
"Wreaths of Tobacco Smoke" by Adriaen Brouwer (1605-1638)
Brouwer was a Flemish painter who apparently spent much of his time in alehouses. Notably, Rembrandt and Rubens possessed a number of his works, and his art was popular enough to be counterfeited in his own time.
(From the article, "Studies of Vortex Rings" by Andrien Guébhard, in The Popular Science Monthly, vol. 20, p. 176, via Wikimedia Commons.)
The movement of a vortex loop is real. It's not like a
wave, the motion of which is only apparent. As can be seen in the example of a smoke ring, the entrapped particles in the vortex travel farther than if they were just in a
cloud. This long distance movement is enabled by the
rolling interface between the loop and the surrounding
fluid, since a vortex loop is a tube of fluid, spinning on the tube
axis. The movement is usually in the direction
orthogonal to the
plane of the loop.
Vortex loops interested
William Thompson (Lord Kelvin) in the
mid-nineteenth century as a way to explain
atoms. He
conjectured that atoms were
knotted loops of the
Aether, with the number and type of knot giving the
elements their particular
properties.[2] The vortex loop atomic theory was wrong, but it inspired research on vortices.
Hermann von Helmholtz published a
mathematical analysis of vortex loops in 1858.[4]
Although linked and knotted vortex loops have been described in
theory since that time, they had never been created in the
laboratory.
Physicists from the
University of Chicago have now developed a technique for generation of vortex loops, including knotted loops, in a
water tank.[1-3] Their apparatus is quite ingenious, as the photographs, below, show. The loops are generated by the rapid movement of
gas bubble coated
airfoils in water.
Electrolytic generation of microbubbles.
Some of the hydrogen and oxygen bubbles stick to the airfoil to allow vortex loop creation.
(Still image from a YouTube Video by UChicago Creative/Robert Kozloff/University of Chicago.)
Postdoc Dustin Kleckner holding a 3D-printed loop airfoil.
(Still image from a YouTube Video by UChicago Creative/Robert Kozloff/University of Chicago.)
The airfoils are created using a
3D printer, and they become coated with
microbubbles of
hydrogen and
oxygen generated by the
electrolysis of water. The 3D printing proved invaluable, since it took many iterations of airfoil shape to generate the desired vortices.[1] When subjected to a 100
g acceleration, the bubbles detach from the airfoil and produce a propagating vortex loop, which is tracked with a
high speed camera (see figure).
Temporal evolution of an air bubble vortex loop in water. The first frame shows the initial state after detachment from the airfoil. (Still images from a Robert Kozloff/University of Chicago video.)
These
experiments have yielded interesting results.
Dustin Kleckner, a
postdoctoral scientist at the
James Franck Institute of the University of Chicago and coauthor of the vortex studies, notes that vortex knots, once thought to be persistent and stable, are not.
Says Kleckner, "They seem to break up in a particular way. They stretch themselves, which is a weird behavior."[2] Their decomposition culminates in
reconnection events in which parts of the vortices
annihilate each other to produce unknotted loops from those that were originally knotted.[2]
Knotted structures are thought to occur in
turbulence,
plasmas,
fluids, both
quantum and
classical, and
superfluids, but are nearly impossible to observe.[1-2] In many systems, the degree of
knottedness has been thought to be a
conserved quantity, and these experiments have shown that this might not always be the case.[2]
These results are published online in
Nature Physics in an article notable for its many freely-available supplementary
videos.[1] This research was funded by the
Alfred P. Sloan Foundation, the
Packard Foundation, and the
National Science Foundation.[2]
References:
- Dustin Kleckner and William T. M. Irvine, "Creation and dynamics of knotted vortices," Nature Physics, Published Online March 3, 2013, doi:10.1038/nphys2560.
- Steve Koppes, "Vortex loops could untie knotty physics problems," University of Chicago Press Release, March 4, 2013.
- Daniel P. Lathrop and Barbara Brawn-Cinani, "News and Views - Fluid dynamics: Lord Kelvin's vortex rings," Nature Physics, Published Online March 3, 2013, doi:10.1038/nphys2577.
- H. von Helmholtz, "On Integrals of the hydrodynamical equations, which express vortex-motion," (1867 English Translation of original 1858 paper), Philosophical Magazine, Series 4 (1851–1875), vol. 33, no. 226.
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