Rotary Fragmentation and Atomization of Viscous and Viscoelastic Liquids

In rotary atomization liquid ligaments are formed around a spinning cup, with a repeatable geometrical spacing, due to the destabilizing action of the centripetal acceleration (also known as Rayleigh-Taylor instability). The resulting filaments then follow a geometrical path-line that is described by the involute of a circle. We provide a simple theoretical prediction for the average droplet sizes in this fragmentation process. We also investigate the resulting droplet size distributions and show that the appearance of satellite droplets in the pinch-off events leads to the emergence of bimodal size distributions. These double-peaked distributions are precisely described by the superposition of two separate Gamma distributions. For weakly viscoelastic test fluids, we show that the liquid viscoelasticity has a negligible effect on the average droplet size. However, as viscoelastic effects become increasingly important, the thinning dynamics in the ligaments are delayed by nonlinear elastic effects and this leads to broader droplet size distributions. The ratio of the main to the satellite droplet size increases monotonically with viscosity and viscoelasticity, and this variation can be captured by a simple physical model for both Newtonian and viscoelastic liquids.