Fragmentation of a drop as it falls in a lighter miscible fluid

Abstract

We report an experimental investigation of the fragmentation process of a heavy drop falling in a lighter miscible fluid. For fixed liquid composition and for different drop sizes, we observe that the fragmentation cascade stops after a few breakups, once each individual droplet has reduced below a critical volume for further splitting. Since each fragmentation is the outcome of a hydrodynamic instability, we expect fluctuations in the size of the fragmented droplets. The main experimental outcomes are the following: ~1! the first breakup time scales with the size separation from the critical volume in a universal way independent of the fluid composition; ~2! in the region intermediate between the first and the last fragmentation, the droplet sizes display multifractal properties, with the average dimension D0 decreasing to a minimum and then increasing again once diffusion prevails; and ~3! the droplet height scales with time with an exponent independent of the drop volume and composition