The breakthrough in understanding how a water jet breaks up into droplets was made by a team consisting of Stefan Kooij, Daniel T. A. Jordan, Cees J. M. van Rijn, and Daniel Bonn from the University of Amsterdam (Van der Waals-Zeeman Institute / Institute of Physics), along with Neil M. Ribe from the Université Paris-Saclay. The study was published in the journal Physical Review Letters.

Small waves, big consequences

In their study, “What Determines the Breakup Length of a Jet?”, the authors convincingly demonstrate that the initial disturbances that lead to the breakup of so-called laminar jets of liquids into droplets, are not primarily caused by external noise, turbulence, or imperfections in the nozzle, as is often assumed. Instead, their extensive experiments, using a wide range of fluids, nozzles, and flow conditions, reveal that the decisive disturbances are caused by intrinsic thermal capillary waves—thermal fluctuations on the scale of angstroms, tenths of a millionth of a millimeter.

The underlying process is similar to Brownian motion, where random molecular movements cause microscopically visible particles to “dance”. The researchers discovered that in the case of liquid jets, similar thermal oscillations on the surface of a water jet are sufficient to eventually cause the jet to break up into droplets. These tiny undulations, just a few angstroms in size, are then amplified by the so-called Rayleigh-Plateau instability, until the jet breaks.

From nanojets to macrojets

The team was able to confirm this hypothesis by image analysis of beam modulations and systematic variation of the parameters, and found a surprisingly good agreement between the experimentally measured length of the pieces in which the beam breaks up (the so-called breakup length) and a model based on thermal noise, valid over seven orders of magnitude — from so-called nanojets up to macroscopically large jets such as those from a faucet.

The work challenges a nearly 200-year-old notion about the importance of external noise in droplet formation, demonstrating that even in carefully isolated setups, the breakup length is ultimately determined by a fundamental thermal mechanism. These insights yield new fundamental knowledge for diverse application areas involving droplet formation, such as inkjet printing, food technology, and aerosol drug delivery.

Publication and further information

What Determines the Breakup Length of a Jet? S. Kooij, D. T. A. Jordan, C. J. M. van Rijn, N. M. Ribe and D. Bonn, Physical Review Letters 135, 214001 (2025), DOI: 10.1103/PhysRevLett.135.214001.

Water jets may break up into droplets thanks to jiggling molecules, news item by Emily Conover for Science News.