Plateau-Rayleigh Instability

jet breakup · droplet formation · surface tension wins

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Physics: A cylindrical jet of radius R is unstable to perturbations with wavelength λ > 2πR (Plateau 1873, Rayleigh 1879). Growth rate: σ² = (γ/ρR³)·x(1−x²) where x = kR = 2πR/λ. Maximum growth at kR ≈ 0.697, corresponding to λ/R ≈ 9.02 — the preferred droplet spacing. Rayleigh (1879) added inertia to Plateau's surface-tension analysis. Used in inkjet printing (precise droplet control at ~30 kHz). A dripping faucet is Plateau-Rayleigh with gravity; Savart (1833) took first photographs of jet breakup.