Viral air load due to sedimenting and evaporating droplets produced by speaking

The effect of evaporation on droplet sedimentation times is crucial for estimating the risk of infection from virus-containing airborne droplets. For droplet radii in the range 100 nm < R < 60 {\mu}m, 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 the significant effect of evaporation cooling. Evaporation makes the time for 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 air load of more than 10^4 virions. In a mid-size closed room, this leads to a viral inhalation frequency of at least 2.5 per minute. Low relative humidity, as encountered inside buildings in winter and in airliners, speeds evaporation and thus keeps initially larger droplets suspended in air.