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Most of the works on the dispersion of droplets and their COVID-19(Coronavirus disease) implications address droplets' dynamics in quiescentenvironments. As most droplets in a common situation are immersed in externalflows (such as ambient flows), we consider the effect of canonical flowprofiles namely, shear flow, Poiseuille flow, and unsteady shear flow on thetransport of spherical droplets of radius ranging from 5$\mu$m to 100 $\mu $m,which are characteristic lengths in human talking, coughing or sneezingprocesses. The dynamics we employ satisfies the Maxey-Riley (M-R) equation. Anorder-of-magnitude estimate allows us to solve the M-R equation to leadingorder analytically, and to higher order (accounting for the Boussinesq-Bassetmemory term) numerically. Discarding evaporation, our results to leading orderindicate that the maximum travelled distance for small droplets ($5\mu m$radius) under a shear/Poiseuille external flow with a maximum flow speed of$1m/s$ may easily reach more than 250 meters, since those droplets remain inthe air for around 600 seconds. The maximum travelled distance was alsocalculated to leading and higher orders, and it is observed that there is asmall difference between the leading and higher order results, and that itdepends on the strength of the flow. For example, this difference for dropletsof radius $5\mu m$ in a shear flow, and with a maximum wind speed of $5m/s$, isseen to be around $2m$. In general, higher order terms are observed to slightlyenhance droplets' dispersion and their flying time.

Drops in the wind: their dispersion and COVID-19 implications