Subtle interplay of rim and bag instabilities in drop atomization

Research on liquid drop atomization until now has assumed different deforming segments of a fragmenting fluid drop to be influenced by instabilities which either act independent of each other or occur one after the other. The inherent coupling between the instabilities though evident, has been largely overlooked. In this work we investigate the breakup of a single drop as it deforms into a bag bounded by a rim upon being subjected to aerodynamic forces emanating from an air nozzle. Our analysis reveals the hidden interplay of instabilities acting along the rim and the bag as we observe a close relationship between the thickness of the rim, bag and the radial extent of the deformed drop based on fundamental laws of conservation. This interdependence helps us determine the exact relation between the wavelength of instabilities acting on the bag and the rim which we extend to predict the resulting drop sizes and establish their dependence on the aerodynamic disruptive forces. The scaling laws derived from these calculations and verified by our experimental observations show that the rim drop sizes weakly depend on the oncoming air flow while the bag sizes are dominantly affected by it.