Estimates of the stochasticity of droplet dispersion by a cough

Abstract

In this paper, the statistical distributions of the position and the size of the evaporating droplets after a cough are evaluated, thus characterising the inherent stochasticity of respiratory releases due to turbulence. For that, ten independent realisations of a cough with realistic initial conditions and in a room at 20ºC 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 is 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 meters away from the emitter even outdoors. 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.