Internal and external viscous effect on drop inertial pinching

The motion of a single pendant droplet, from the moment of ejection through a nozzle, starts with a constant downwards expansion caused due to a continuous feeding at the top of the nozzle. Eventually, the weight of the volume of fluid exceeds the surface tension forces holding it upwards, and a detachment is seen. The breakup of low viscosity liquid drop, when surrounded by air or submerged in water, display fascinating dynamics. Initially, the filament thinning is dictated by the ‘Capillary-Inertial Regime’ power law, before transitioning into other regimes upon approaching the fragmentation of the liquid filament. Within the confines of our research, the pinching is observed, and its effects studied, when both internal and external viscosity are varied. By slightly increasing either droplet viscosity, or that of the surrounding fluid, we show a novel Transitional Inertial Regime that slows down the thinning of the droplet through a reduction in the axial velocity at the filament neck. Through our analysis of the data for both Liquid-in-Air and Liquid-in-Liquid, we derived a simple universal scaling law predicting the value of the ‘Inertial Regime’ Prefactor for both cases, as a function of the axial velocity at the filament neck showing an excellent agreement with both experimental and numerical data.