The Rayleigh-Plateau Instability (Lord Rayleigh 1878, building on Plateau 1849) explains why a water jet breaks into droplets. A cylindrical liquid column is unstable to perturbations with wavelength λ > 2πR (wavenumber kR < 1).
The physics: a long-wavelength sinusoidal perturbation reduces the total surface area (despite seeming to wrinkle it). Surface tension then amplifies the perturbation. The growth rate is σ² = (γ/ρR³) · kR · (1−k²R²) · I₁(kR)/I₀(kR), where I₀, I₁ are modified Bessel functions. The fastest-growing mode occurs at kR ≈ 0.697, setting the natural drop spacing. This principle governs inkjet printing, fiber drawing, and even the breakup of celestial jets.