Investigating airborne transmission risks: A mathematical model of evaporating droplets with solid residue

The COVID-19 pandemic has spotlit the scientific field of fluid dynamics governing airborne transmission through virus-laden mucosal-salivary droplets. In this work, a mathematical model for airborne droplet dispersion and viral transmission centered on evaporating droplets containing solid residue was proposed. Droplet dynamics are influenced by factors such as initial velocity, relative humidity (RH), and solid residue, in agreement with analytical and experimental results. Interestingly, the maximum droplet dispersion distance depends strongly on initial droplet size and RH, such as 0.8-mm-diameter droplet at 0.3 RH, 1.0 mm at 0.6 RH, and 1.75 mm at 0.9 RH, but only weakly on initial projected velocity. Under realistic conditions, an evaporating sputum droplet can cover a dispersion distance at least three times than that of a pure water droplet. Based on Wells falling curves, the critical droplet size, the largest droplet that can remain suspended in air without settling due to gravity, ranges from 120 μm at 0.3 RH to 75 μm at 0.9 RH. Together, our results highlight the role of evaporation on droplet lifetime, dispersion distance, and transmission risks.