Plateau-Rayleigh instability

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.

The driving force of the Plateau-Rayleigh instability is that liquids, by virtue of their surface tensions, tend to minimize their surface area.

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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]

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

See also

• Plateau-Rayleigh Instability - a 3D lattice kinetic Monte Carlo simulation
• An MIT lecture on falling fluid jets, including the Plateau -Rayleigh instability Pdf form, quite mathematical.