Analytical solutions for airborne droplet trajectory: Implications for disease transmission

Abstract

Airborne droplets containing viruses from infected persons can present long range disease transmission risks. In this study, we examine the trajectory of an airborne droplet based on a point force model. The interplay between gravity, drag, inertia and deformation are factored in, for drop sizes ranging from micrometer to millimeter size. In particular, we propose an expression for the drag force which enables analytical solutions for cases of practical interest, such as the transient velocity behavior and spreading distances. This allows us to obtain physical insights which are not obvious from direct numerical simulations. Effects such as droplet deformation, breakup and evaporation are also considered. Our analytical solutions compare favorably with numerical and experimental data. The evaporation rate was determined experimentally with a levitating device and some experimental drop velocity versus time data were obtained with falling millimeter sized droplets.