The natural breakup length of laminar jets: first parameter-free solution in 200 years — Rayleigh–Plateau instability with thermal noise

The breakup length of laminar capillary jets is set by initial surface disturbances amplified through the Rayleigh–Plateau instability. For about two centuries, this process was attributed to external vibrations, nozzle imperfections, or turbulence. We show instead that the instability is seeded by unavoidable thermal capillary waves: surface fluctuations of Ångström amplitude intrinsically limit jet length. The Langevin equation emerges as an effective description of the early growth of unstable modes, yielding the first parameter-free prediction of the natural breakup length, including viscous corrections. The resulting formula matches experiments and simulations over seven orders of magnitude, from nanoscale to macroscopic jets.