  We formulate a model for the dynamics of respiratory droplets and use it to
study their airborne lifetime in turbulent air representative of indoor
settings. This lifetime is a common metric to assess the risk of respiratory
transmission of infectious diseases, with longer lifetime correlating with
higher risk. We consider a simple momentum balance to calculate the droplets
spread, accounting for their size evolution as they undergo vaporization via
mass and energy balances. The model shows how an increase in relative humidity
leads to higher droplet settling velocity, which shortens the lifetime of
droplets and can therefore reduce the risk of transmission. Emulating indoor
air turbulence using a stochastic process, we numerically calculate probability
distributions for the lifetime of droplets, showing how an increase in the air
turbulent velocity significantly enhances the range of lifetimes. The
distributions reveal non-negligible probabilities for very long lifetimes,
which potentially increase the risk of transmission.
