A model to predict the short-term turbulent indoor dispersion of small droplets and droplet nuclei released from coughs and sneezes

Abstract

We propose a simple model to predict the short-term indoor turbulent dispersion of the aerosol cloud produced by violent expiratory events. Once the air injection ceases, the turbulent jet transitions to a thermal puff that progressively decays due to viscous effects. According to recent literature, the expelled liquid droplets of saliva and sputum smaller than 20–30 μm in diameter stay afloat within this decaying turbulent puff. In contrast, droplets larger than 100 μm tend to leave the puff following quasi-ballistic trajectories and landing on the floor at relatively short times after release. The model presented here is capable of providing good estimates for the shape and dimensions of the cloud composed of the lighter fraction of droplets as a function of the intensity and the duration of the flow injection and the density difference between the exhaled and the ambient air. Predictions agree with Direct Numerical Simulations and experiments reported in the literature. This model can be used as an operational tool to determine the short-term spatial range of expelled droplets and provides realistic initial conditions for simulations of long-term dispersion of pathogen-laden clouds in indoor environments with forced and natural ventilation.