Architecture of a self-fragmenting droplets cascade

We report quantitative imaging experiments describing the three-dimensional (3D) bursting cascade of droplets from a liquid melt reacting with the oxygen of air which explode sequentially to produce ever smaller fragments. The 3D space-time resolved trajectories of the fragmenting drops reveal an arborescent structure of branchings defining the cascade steps, each random in direction and shortening along the cascade, in a way we determine. The phenomenon is a unique and prototypical illustration of the so-called Richardson regime, namely, an accelerated cascade towards smaller scales. The phenomenon, which coincides with the early time dispersion period of a Brownian motion, featuring here ever shrinking steps, is well captured by a Langevin dynamics.