What determines the breakup length of a jet?

Abstract

The breakup of a capillary jet into drops is believed to be governed by initial disturbances on the surface of the jet that grow exponentially. The disturbances are often assumed to be due to external sources of noise, to turbulence, or to imperfections of the nozzle. However, even in conditions where external perturbations are minimal, the jet's length cannot grow indefinitely, suggesting that its fragmentation cannot be entirely attributed to such factors. Here we show that the initial disturbances are thermal capillary waves. By extrapolating the observed growth of the instability back in time, we demonstrate that the initiating disturbances must be of the order of an {\aa}ngstr\"om, consistent with fluctuations induced by thermal noise. Further, by performing many experiments with different nozzles, we find no significant variation in breakup length linked to nozzle type, shape or inner roughness. By systematically varying the jet diameter and velocity, and the surface tension, viscosity, and density of the fluid, we validate our thermal disturbance model over four orders of magnitude in jet length; seven orders of magnitude if simulations of nanojets are included.