Modelling the dispersion of airborne respiratory particles

Abstract

The outbreak of the COVID-19 virus has increased the interest in respiratory droplet dispersion in the built environment. The dispersion of these droplets is inseparable from transmission risk. Sneezing, coughing and breathing can be modelled in many ways. In this study several models of increasing complexity are proposed and compared.
Three different models are distinguished. The first is a simple ballistic model, where the trajectories of particles of different sizes are simulated, given an initial velocity and particle diameter. This simulation gives a first insight in the movement of particles from Newton’s second law.
Model 2 works by releasing particles in a turbulent jet. Mean properties of turbulent jets have been derived from experiments and computer modelling. By means of particle tracking, the dispersion of three different sizes of particles are monitored. The turbulent behaviour of the jet is captured by applying a stochastic discontinuous random walk model (DRW) in Model 2. The smallest particles (10 μm) are airborne, while the large (100 μm) particles fall out of the turbulent jet and settle on the ground. Medium size particles (50 μm) have the widest range of dispersion. The effect of evaporation has been studied in this research as well. Both relative humidity and relative velocity (the velocity between the surrounding air and the particle) influence the evaporation speed. The medium size particles are affected the most by evaporation. Depending on the ambient conditions, the medium size particles either behave more like the large particles or as the small particles.
The third model contains the effect of an ambient crossflow, representing ventilation flows. Trajectories of bent jets have been calculated. Eulerian solutions for dilution have been found for such bent jets. No mean properties in literature have been found for bent jets and hence the Langrangian particle tracking model could not be used.
Based on the results of model 2 we conclude that ventilation flows will have a tremendous impact on the dispersion of respiratory droplets, in particular the particles with initial diameter 75 - 100 μm. These droplets become airborne and will follow the ventilation flow. In dryer air droplets evaporate faster and will become airborne more quickly.
Future research could be done to create a CFD model to generate analytical formulas for jets in ambient crossflows. More detailed room conditions like the stratification of air temperature can be taken into account.