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Plateau-Rayleigh Instability in Water Stream

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When water pours from a faucet, instead of keeping a cylindrical flow, the fluid tends to break into drops due to surface tension; Joseph Plateau studied this phenomenon, and it was explained theoretically by Rayleigh.

Contributed by: Enrique Zeleny (April 2014)
Open content licensed under CC BY-NC-SA

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Details

In the simplest approximation, the radius of the stream along the axis at an intermediate stage before breaking into drops is given by

,

where is the radius of the strand, is the wave number, and the are the amplitudes of the perturbations.

References

[1] Wikipedia. "Plateau–Rayleigh Instability." (Apr 28, 2014) en.wikipedia.org/wiki/Plateau% E2 %80 %93 Rayleigh_instability.

[2] V. Y. Chen. Surface Tension: Plateau Rayleigh Instability [Video]. (Apr 28, 2014) www.youtube.com/watch?v=ml4KEy4N0gc.

[3] U. Miyamoto, "Curvature Driven Diffusion, Rayleigh–Plateau, and Gregory–Laflamme." arxiv.org/pdf/0804.1723v2.pdf.

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