Fragmentation instabilities of a liquid drop falling in a miscible fluid

Abstract

We report a set of experimental investigations on the break-up of a liquid drop when falling in a miscible solvent, with the density difference being positive, or negative, or zero. Non-dimensional numbers, derived from the characteristic times of the drop evolution, account for the hydrodynamic instabilities and the self-similar character of the fragmentation process. The role of the initial surface tension at the air-drop interface is explored, leading to scaling laws for the drop volume V and the various height h reached by the drop before it fragments into smaller droplets. From the first break-up to the onset of diffusion, the fragmentation process is shown to have a fractal structure, which is associated to universal power laws for h and V during the dynamical processes associated to the break-up phenomena