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.
ABSTRACT
To mitigate the COVID-19 pandemic, it is key to slow down the spreading of the life-threatening coronavirus (SARS-CoV-2). This spreading mainly occurs through virus-laden droplets expelled at speaking, screaming, shouting, singing, coughing, sneezing, or even breathing [1-7]. To reduce infections through such respiratory droplets, authorities all over the world have introduced the so-called "2-meter distance rule" or "6-foot rule". However, there is increasing empirical evidence, e.g. through the analysis of super-spreading events [6, 8-11], that airborne transmission of the coronavirus over much larger distances plays a major role [1-3, 7, 12-15], with tremendous implications for the risk assessment of coronavirus transmission. It is key to better and fundamentally understand the environmental ambient conditions under which airborne transmission of the coronavirus is likely to occur, in order to be able to control and adapt them. Here we employ direct numerical simulations of a typical respiratory aerosol in a turbulent jet of the respiratory event within a Lagrangian-Eulerian approach [16-18] with 5000 droplets, coupled to the ambient velocity, temperature, and humidity fields to allow for exchange of mass and heat [19] and to realistically account for the droplet evaporation under different ambient conditions. We found that for an ambient relative humidity of 50% the lifetime of the smallest droplets of our study with initial diameter of 10 {micro}m gets extended by a factor of more than 30 as compared to what is suggested by the classical picture of Wells [20, 21], due to collective effects during droplet evaporation and the role of the respiratory humidity [22], while the larger droplets basically behave ballistically. With increasing ambient relative humidity the extension of the lifetimes of the small droplets further increases and goes up to 150 times for 90% relative humidity, implying more than two meters advection range of the respiratory droplets within one second. Smaller droplets live even longer and travel further. Our results may explain why COVID-19 superspreading events can occur for large ambient relative humidity such as in cooled-down meat-processing plants [10] or in pubs with poor ventilation. We anticipate our tool and approach to be starting points for larger parameter studies and for optimizing ventilation and indoor humidity controlling concepts, which in the upcoming autumn and winter both will be key in mitigating the COVID-19 pandemic.
