Plateau-Rayleigh instability

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The Plateau-Rayleigh instability, often 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.

1 History
2 The effect
3 Notes
4 See Also

[edit] 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. ^[1] 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. ^[2]

[edit] The effect

A specialized case of this is the formation of droplets. The Plateau-Rayleigh instability explains why a stream of water will eventually break up into smaller droplets which are approximately the same diameter as the stream itself. In drop formation, as a segment of liquid begins to separate from the faucet, a neck is formed and then stretched. In the situation where 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. A related fact is that liquids, by virtue of their surface tensions, tend to minimize their surface area. Therefore, a cylinder of water will break up into spheres of a certain critical radius where by the volume remains the same, but the surface area is less than the cylinder's.