Unsteady sheet fragmentation: droplet sizes and speeds

Abstract

Understanding what shapes the drop size distributions produced from fluid fragmentation is important for a range of industrial, natural and health processes. Gilet & Bourouiba (J. R. Soc. Interface, vol. 12, 2015, 20141092) showed that both the size and speed of fragmented droplets are critical to transmission of pathogens in the agricultural context. In this paper, we study both the size and speed distributions of droplets ejected during a canonical unsteady sheet fragmentation from drop impact on a target of comparable size to that of the drop. Upon impact, the drop transforms into a sheet which expands in the air bounded by a rim on which ligaments grow, continuously shedding droplets. We developed high-precision tracking algorithms that capture all ejected droplets, measuring their size and speed, as well as the detachment time from, and link to, their ligament of origin. Both size and speed distributions of all ejected droplets are skewed. We show that the polydispersity and skewness of the distributions are inherently due to the unsteadiness of the sheet expansion. We show that each ligament sheds a single drop at a time throughout the entire sheet expansion by a mechanism of end-pinching. The droplet-to-ligament size ratio $R\approx 1.5$ remains constant throughout the unsteady fragmentation, and is robust to change in impact Weber number. We also show that the population mean speed of the fragmented droplets at a given time is equal to the population mean speed of ligaments one necking time prior to detachment time.