Abstract
In this paper, the statistical distributions of the position and the size of the evaporating droplets after a cough are evaluated, thus characterizing the inherent stochasticity of respiratory releases due to turbulence. For that, ten independent realizations of a cough with realistic initial conditions and in a room at 20 °C and 40% relative humidity were performed with large eddy simulations and Lagrangian tracking of the liquid phase. It was found that although turbulence decreases far from the emitter, it results in large variations in the spatial distribution of the droplets. The total suspended liquid mass after 60 s from the cough is in good agreement with that estimated by a one-dimensional model accounting for settling and evaporation under quiescent conditions, while deposition times of droplets in the 10–100 μm range are found to vary significantly, reflected in the mass of liquid, and hence the virus content, potentially inhaled by a receptor. The high variability between events is due to the local fluctuations of temperature, humidity, and velocity on droplet evaporation and motion. The droplet distribution suggests that, in the absence of face coverings, an unprotected cough is not safe at 2 m away from the emitter even outdoors. The results indicate that mitigation measures, such as ventilation to address long-range transmission, can be based on the total suspended liquid content evaluated from reduced-order models. However, the large variability of viral content in the near field produces wide variations in estimates of risk; therefore, a stochastic approach is needed for evaluating short-range transmission risk.
Highlights
The ongoing pandemic caused by SARS-CoV-2 (COVID-19) has reinforced the need to better understand the fluid mechanics controlling the spread of airborne diseases
The exhaled flow has two distinct phases:[2] the initial phase during which the flow is exhaled like a turbulent jet, and a second phase when the exhaled jet becomes a turbulent puff of finite duration that grows by entraining air from the surroundings
The stochasticity of the flow associated with a cough and its impact on short-range droplet distribution and, by consequence, disease transmission is discussed
Summary
The ongoing pandemic caused by SARS-CoV-2 (COVID-19) has reinforced the need to better understand the fluid mechanics controlling the spread of airborne diseases. The exhaled flow contains pathogen-carrying droplets of varying sizes, and their trajectory is governed by their initial size, the influence of gravity, the local and ambient temperatures and relative humidity, and the gas velocities. The small droplets can stay suspended in the air for a long time and can carry the pathogens over significantly long distances, whereas the larger droplets follow a ballistic trajectory and tend to settle down quickly under the influence of gravity.[11] The distinction between large ballistic droplets and small droplets is usually assumed to be $100 lm, while the cutoff for droplets that remain suspended in air for long times is typically considered as 10 lm,[12] it is still inconclusive whether that is the case.[13]
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