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Abstract

The ambient conditions surrounding liquid droplets determine their growth or shrinkage.
However, the precise fate of a liquid droplet expelled from a respiratory puff as dictated
by its surroundings and the puff itself has not yet been fully quantified. From the view of
airborne disease transmission, such as SARS-CoV-2, knowledge of such dependencies is
critical. Here, we employ direct numerical simulations (DNS) of a turbulent respiratory
vapor puff and account for the mass and temperature exchange with respiratory droplets
and aerosols. In particular, we investigate how droplets respond to different ambient
temperatures and relative humidity (RH) by tracking their Lagrangian statistics. We reveal
and quantify that in cold and humid environments, as there the respiratory puff is supersaturated, expelled droplets can first experience significant growth, and only later followed by
shrinkage, in contrast to the monotonic shrinkage of droplets as expected from the classical
view by Wells in 1934. Indeed, cold and humid environments diminish the ability of air to
hold water vapor, thus causing the respiratory vapor puff to supersaturate. Consequently,
the supersaturated vapor field drives the growth of droplets that are caught and transported
within the humid puff. To analytically predict the likelihood for droplet growth, we propose
a model for the axial RH based on the assumption of a quasistationary jet. Our model
correctly predicts supersaturated RH conditions and is in good quantitative agreement with
our DNS. Our results culminate in a temperature-RH map that can be employed as an
indicator for droplet growth or shrinkage.