Water droplets shoot out of a nozzle one after another, like cyclists on a narrow track. The faster ones catch up with the slower ones and merge into larger drops. This simple mechanism is called ballistic aggregation, and until now it had only been observed on cosmic scales: this is how dust particles stick together to form planets.
The laws turned out to be remarkably robust. Air slows droplets unevenly, so fast droplets start lagging behind slow ones — the exact opposite of what happens in a vacuum. But the big picture does not change: the mass distribution (how many small, medium, and large droplets form) follows the same mathematics. Everything is determined by a single parameter — the characteristic length over which droplets manage to meet.
The simple equations that usually describe particle coalescence (the Smoluchowski equations) fail here. They do not account for memory of the direction of motion, but in a jet, each droplet remembers where it came from and how fast it was traveling. It is this memory that creates a special order in the chaos of collisions.
as written by the authors arXiv:2607.21315
Ballistic aggregation is a canonical non-equilibrium process, relevant across scales from granular gases to planetary accretion. Collisions are driven by differences in velocities, building up persistent correlations between neighbors. Here, we provide the first experimental realization of one-dimensional ballistic aggregation in a train of droplets formed by the breakup of a liquid jet. Experiments and simulations confirm the analytically predicted scaling, with the global process shown to be governed by a single length scale. While air drag inverts the sign of neighbor velocity correlations, a 1D ordering constraint protects bulk characteristics of ballistic aggregation such as the scaling exponent and the shape of the large mass tail. More broadly, our results show that Smoluchowski-like mean-field descriptions fail when collisions carry directional memory -- as demonstrated here for jet-generated sprays.
The experiment used a water jet as thin as a human hair — about 70 micrometers. At such scales, droplets behave almost like celestial bodies.