Fragmentation from inertial detachment of a sessile droplet: implications for pathogen transport

Various modes of fluid fragmentation inherent to foliar disease transmission have been linked to the average-wetting dominating most crop leaves (Gilet and Bourouiba 2015). One of such modes is the inertial detachment: Upon impact from rain, irrigation, or dew drops, the motion of a compliant leaf locally transfers its impulse to the sessile contaminated drop residing on it. The resulting fragmentation of  the sessile contaminated drop is particularly interesting for the application domain for its ability to produce highly contaminated ejected droplets not undergoing any dilution and typically producing a primary tip drop. Inertial detachment is also interesting as a fundamental fragmentation process on its own merit, in which it is the asymmetric stretching under impulsive axial forcing that shapes the fragmentation of the initially sessile drop. Although the related filament end-pinching phenomenon is well studied, the wetting at the liquid-solid interface significantly complicates the dynamics. Nevertheless, in a controlled analog experimental system to that of leaves, we find that the radius, $R_{tip}$,  of the tip drop ejected for $Bo>1$ become insensitive to the Bond number value itself. Here, the Bond number quantifies the inertial effects via the relative axial impulsive acceleration compared to capillary effects. This insensitivity to the Bond number is also recovered for the time of tip drop breakup, $t_{tip}$. In a combined experimental and theoretical study we investigate these results, to decipher what sets the primary drop radius and its sensitivity to the surface-wetting and foot dynamics on the substrate.  Asymptotic theory in the large $Bo$ limit for which the thin-film/slender-jet approximation holds and a reduced physical model enable further insights, including prediction of the properties of the ejected primary tip drop, consistent with experiments. Combined with numerical simulations which are developed and validated against the experiments and theory, the results also enable to shed light on how physical properties of pathogens (e.g., their wetting) within the sessile contaminated drop affect their distribution in the primary tip drop and secondary drops.