Sharp Interface Methods for Simulation and Analysis of Free Surface Flows with Singularities: Breakup and Coalescence

A common feature of many free surface flows—drop/bubble breakup or coalescence and film/sheet rupture—is the occurrence hydrodynamic singularities. Accurately computing such flows with continuum mechanical, multidimensional flow algorithms is a challenging task given these problems’ multiscale nature, which necessitates capturing dynamics occurring over disparate length scales across 5–6 orders magnitude. In drop breakup, thinning fluid threads that form eventually pinch-off must be simulated until thread's radius about 10 nm. When two drops approach one another, thickness film separating them fall below nm before said to have occurred. If initial radii are 1 mm, simulations remain faithful physics as thread falls from −3 m −8 m. Here we review significant findings in interfacial singularities spearheaded by sharp interface algorithms. These can achieve resolution date has only been possible use simple 1D evolution equations.