Two-dimensional mathematical framework for evaporation dynamics of respiratory droplets

In majority of pandemics in human history, respiratory bio-aerosol is the most common route of transmission of diseases. These tiny droplets ejected through mouth and nose from an infected person during exhalation process like coughing, sneezing, speaking, and breathing consist of pathogens and a complex mixture of volatile and nonvolatile substances. A cloud of droplets ejected in such an event gets transmitted in the air, causing a series of coupled thermo-physical processes. Contemplating an individual airborne droplet in the cloud, boundary layers and wakes develop due to relative motion between the droplet and the ambient air. The complex phenomenon of the droplet's dynamics, such as shear-driven internal circulation of the liquid phase and Stefan flow due to vaporization or condensation, comes into effect. In this study, we present a mathematical description of the coupled subprocesses, including droplet aerodynamics, heat, and mass transfer, which were identified and subsequently solved. The presented two-dimensional model gives a complete analysis encompassing the gas phase coupled with the liquid phase responsible for the airborne droplet kinetics in the ambient environment. The transient inhomogeneity of temperature and concentration distribution in the liquid phase caused due to the convective and diffusive transports are captured in the 2D model. The evaporation time and distance traveled by droplets prior to nuclei or aerosol formation are computed for major geographical locations around the globe for nominal-windy conditions. The model presented can be used for determining the evaporation timescale of any viral or bacterial laden respiratory droplets across any geographical location.