Abstract
We show that the dynamics of the expiratory cloud ejected during human respiratory events can be modeled by extending the theory of buoyant vortex rings with an initial momentum. We embed the integral conservation laws that govern the cloud’s motion into the model of an expanding vortex to determine the velocity field inside and outside the cloud. We then apply a Lagrangian particle-tracking model to calculate the trajectories of the mucosalivary droplets suspended within the cloud. Our results show very good agreement with the available experimental data. The vortex is shown to have a significant effect on suspending the droplets present in the cloud, increasing the time they remain airborne and extending their range further than predicted by the existing models. We also study the role that initial conditions have on the maximum streamwise range of the droplets, finding that decreasing the angle of projection can reduce the spread of the droplets by an order of meters. Finally, we discuss the importance of these findings in the context of informing public health policies and global information campaigns to slow down the spread of respiratory viruses.
Highlights
In this paper, we develop a physico-mathematical characterization of the vortex dynamics of expiratory clouds based on experimental evidence and quantify how this dynamics affects the fate of the droplets ejected during human respiratory events.The ongoing Coronavirus Disease 2019 (COVID-19) pandemic caused by the Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) has shown how respiratory viruses are able to spread across an entire continent, leaving us unprepared
We show that the dynamics of the expiratory cloud ejected during human respiratory events can be modeled by extending the theory of buoyant vortex rings with an initial momentum
We develop a physico-mathematical characterization of the vortex dynamics of expiratory clouds based on experimental evidence and quantify how this dynamics affects the fate of the droplets ejected during human respiratory events
Summary
We develop a physico-mathematical characterization of the vortex dynamics of expiratory clouds based on experimental evidence and quantify how this dynamics affects the fate of the droplets ejected during human respiratory events. The moist atmosphere of the cloud dramatically slows down evaporation and increases the lifetime of the droplets by a factor 1000, from fractions of a second to minutes.1,6 The dynamics of this turbulent flow is much more complex than the dichotomic droplet model and is still poorly understood. The recent work of Busco et al. shows that the flow dynamics of violent human respiratory events is analogous to that of fluid ejection from sprayers. Motivated by this analogy, we conducted experiments with a nozzle sprayer to visualize the vortex dynamics of the ejected cloud. The vortex present in the cloud is shown to have a significant effect on the droplet suspension, recirculating them within the cloud to varying degrees and extending their range further than previously predicted
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