Surface tension breaking a liquid jet into droplets — fastest mode at kR ≈ 0.697
Lord Rayleigh (1879) showed that a liquid jet of radius R is unstable to axisymmetric perturbations with kR < 1 (wavelength λ > 2πR). Surface tension drives growth: longer wavelengths reduce surface area. Growth rate σ(kR) peaks at kR ≈ 0.697 (Rayleigh's result for inviscid jet), giving fastest-growing wavelength λ* ≈ 9R. Plateau (1873) showed stability requires wavelength > circumference. This explains why taps drip and inkjet printers work.