Abstract
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 a 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 the 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.
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