σ(k) = (γ/2ρr³)·k²r²(1-k²r²)^(1/2)
Plateau (1873) observed, Rayleigh (1879) analyzed: a fluid cylinder is unstable for perturbations with wavelength λ>2πr.
Fastest-growing wavelength: λ_max = 2π√2·r ≈ 9.01r.
Surface tension drives breakup into droplets to minimize surface area. Competition between wave number selection and viscous dissipation.
Top: Fluid cylinder with growing perturbation
Bottom: Dispersion relation σ(k)