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.

Additional recommended knowledge

How to quickly check pipettes?

How to ensure accurate weighing results every day?

Daily Visual Balance Check

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.