Plateau-Rayleigh Instability in Water Stream

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.


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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.
[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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