Plateau-Rayleigh instability
- Plateau-Rayleigh instability
The Plateau-Rayleigh instability, often just called the "Rayleigh instability", explains why and how a falling stream of fluid breaks up into smaller packets with the same volume but less surface area. It is related to the Rayleigh–Taylor instability. This fluid instability is exploited in the design of a particular type of ink jet technology whereby a jet of liquid is perturbed into a steady stream of droplets.
The driving force of the Plateau-Rayleigh instability is that liquids, by virtue of their surface tensions, tend to minimize their surface area.
History
The Plateau-Rayleigh instability is named for Joseph Plateau and Lord Rayleigh. In 1873, Plateau found experimentally that a vertically falling stream of water will break up into drops if its length is greater than about 3.13 to 3.18 times its diameter. [ [http://arxiv.org/abs/math/9701214 Retardation of Plateau-Rayleigh Instability: A Distinguishing Characteristic Among Perfectly Wetting Fluids] by John McCuan. Retrieved 1/19/2007.] Later, Rayleigh showed theoretically that a vertically falling column of non-viscous liquid with a circular cross-section should break up into drops if its length exceeded its circumference, or Pi times its diameter. [ [http://sundoc.bibliothek.uni-halle.de/diss-online/05/05H104/t3.pdf See page 23 of this pdf] Retrieved 1/19/2007. ]
Water dripping from a faucet
A special case of this is the formation of small droplets when water is dripping from a faucet. When a segment of water begins to separate from the faucet, a neck is formed and then stretched. If the diameter of the faucet is big enough, the neck doesn't get sucked back in, and it undergoes a Plateau-Rayleigh instability and collapses into a small droplet.
Notes
ee also
* [http://www.roentzsch.org/Rayleigh/index.html Plateau-Rayleigh Instability - a 3D lattice kinetic Monte Carlo simulation]
* [http://web.mit.edu/1.63/www/Lec-notes/Surfacetension/Lecture5.pdf An MIT lecture on falling fluid jets, including the Plateau -Rayleigh instability] Pdf form, quite mathematical.
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