Modeling the Viral Load Dependence of Residence Times of Virus‐laden Droplets from COVID‐19‐infected Subjects in Indoor Environments

In the ongoing COVID-19 pandemic situation, exposure assessment and control strategies for aerosol transmission path are feebly understood. A recent study pointed out that Poissonian fluctuations in viral loading of airborne droplets significantly modifies the size spectrum of the virus-laden droplets (termed as "virusol") (Anand and Mayya, 2020). Herein we develop the theory of residence time of the virusols, as contrasted with complete droplet system in indoor air using a comprehensive "Falling-to-Mixing-Plate-out" model that considers all the important processes namely, indoor dispersion of the emitted puff, droplet evaporation, gravitational settling, and plate out mechanisms at indoor surfaces. This model fills the existing gap between Wells falling drop model (Wells, 1934) and the stirred chamber models (Lai and Nazarofff, 2000). The analytical solutions are obtained for both 1-D and 3-D problems for non-evaporating falling droplets, used mainly for benchmarking the numerical formulation. The effect of various parameters is examined in detail. Significantly, the mean residence time of virusols is found to increase nonlinearly with the viral load in the ejecta, ranging from about 100 to 150 s at low viral loads (<104 /ml) to about 1100-1250 s at high viral loads (>1011 /ml). The implications are discussed.