Mechanisms of Airborne Infection via Evaporating and Sedimenting Droplets Produced by Speaking

Abstract

For estimating the infection risk from virus-containing airborne droplets, it is crucial to consider the interplay of all relevant physical-chemical effects that affect droplet evaporation and sedimentation times. For droplet radii in the range 70 nm < R < 60 μm, evaporation can be described in the stagnant-flow approximation and is diffusion-limited. Analytical equations are presented for the droplet evaporation rate, the time-dependent droplet size, and the sedimentation time, including evaporation cooling and solute osmotic-pressure effects. Evaporation makes the time for initially large droplets to sediment much longer and thus significantly increases the viral air load. Using recent estimates for SARS-CoV-2 concentrations in sputum and droplet production rates while speaking, a single infected person that constantly speaks without a mouth cover produces a total steady-state air load of more than 104 virions at a given time. In a midsize closed room, this leads to a viral inhalation frequency of at least 2.5 per minute. Low relative humidity, as encountered in airliners and inside buildings in the winter, accelerates evaporation and thus keeps initially larger droplets suspended in air. Typical air-exchange rates decrease the viral air load from droplets with an initial radius larger than 20 μm only moderately.