BREAKDOWN OF SCALING IN DROPLET FISSION AT HIGH REYNOLDS-NUMBER

In this paper we address the shape of a low-viscosity fluid interface near the breaking point. Experiments show that the shape varies dramat ically as a function of fluid viscosity. At low viscosities, the inter face develops a region with an extremely sharp slope, with the steepne ss of the slope diverging with vanishing viscosity. Numerical simulati ons demonstrate that this tip forms as a result of a convective instab ility in the fluid; in the absence of viscosity this instability resul ts in a finite time singularity of the interface far before rupture (i n which the interfacial curvature diverges). The dynamics before the i nstability roughly follow the scaling laws consistent with predictions based on dimensional analysis, though these scaling laws are violated at the instability. Since the dynamics after rupture is completely de termined by the shape at the breaking point, the time dependences of r ecoiling do not follow a simple scaling law. In the process of demonst rating these results, we present detailed comparisons between numerica l simulations and experimental drop shapes with excellent agreement. ( C) 1997 American Institute of Physics.