Growth of respiratory droplets in cold and humid air

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 are critical. Here we employ direct numerical simulations (DNS) of a turbulent respiratory vapour 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 William F. Wells (1934). Indeed, cold and humid environments diminish the ability of air to hold water vapour, thus causing the respiratory vapour puff to super-saturate. Consequently, the super-saturated vapour 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 quasi-stationary jet. Our model correctly predicts super-saturated 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.Significance StatementInfluence of environmental conditions on airborne diseases transmission is an important issue, especially during the pandemic of COVID-19. Human-to-human transmission is mediated by the transport of virus-laden respiratory droplets. Here we investigate the problem from a fluid mechanics perspective by conducting numerical simulations to quantify the fate of respiratory droplets in a warm humid coughing puff under different ambient conditions. We reveal a non-intuitive regime with considerable growth of respiratory droplets, dominated by a super-saturated vapour field, preferentially occurring in cold and humid environments. We further propose a theoretical model that accurately predicts the condition for droplet growth. Our work should inform socializing policies and ventilation strategies for controlling indoor ambient conditions to mitigate dispersion of droplets from asymptomatic individuals.