Trajectories of large respiratory droplets in indoor environment: A simplified approach

Abstract

The recent pandemic of COVID-19 has brought about tremendous impact on every aspect of human activities all over the world. The main route of transmission is believed to be through coronavirus-bearing respiratory droplets. The respiratory droplets have a wide spectrum in droplet size, ranging from very small droplets (aerosol droplets) to large droplets of tens and even hundreds of μm in size. The large droplets are expected to move like projectiles under the action of gravity force, buoyancy force and air resistance. Droplet motion is complicated by droplet evaporation, which reduces droplet size in its trajectory and affects the force acting on it. The present work attempts to determine the trajectories of the large droplets by using a simplified single-droplet approach. It aims at providing a clear physical picture to elucidate the mechanics involved in single droplet motion and the various factors affecting the range. Assuming an indoor environment with an air temperature of 18 °C and relative humidity of 50%, the horizontal range Lx of large respiratory droplets (diameter 120 μm–200 μm) in common respiratory activities are as follows: Speaking, Lx ≈ 0.16 m–0.68 m, coughing, Lx ≈ 0.58 m–1.09 m, and sneezing, Lx ≈ 1.34 m–2.76 m. For the smaller droplets (diameter < 100 μm), the droplets are reduced to aerosol droplets (≤5 μm) due to evaporation, and will remain suspended in the air instead of falling onto the ground like a projectile.