Transport and evaporation of exhaled respiratory droplets: An analytical model

Abstract

An important vector for host-to-host infectious disease transmission is given by the transport of tiny pathogen-laden droplets. These are commonly exhaled by individuals while breathing, speaking, coughing, or sneezing. Depending on their size and ambient conditions, they may follow different paths, either settling on surfaces where the pathogen can be further transmitted by contact, or remaining airborne after evaporation where the pathogen can be inhaled. Our understanding of pathogen transmission from the fluid mechanics perspective is still somewhat limited, especially in quantitative terms. In the current work, starting from the fundamental laws of fluid mechanics and diffusion, a detailed analytical model of droplet transport and evaporation in humid air streams is presented and successfully validated against available data in the literature finding remarkable agreement. The model implements closed-form analytical solutions of the equations of transport, evaporation, and energy balance, and an algebraic model to account for the droplet chemical composition. It also features an analytical model of droplet transport within the buoyant exhaled breath cloud based on momentum conservation addressing both jet and puff phases and is able to handle periodic respiratory events. Turbulent dispersion is modeled with a discrete random walk approach. A simple inhalation model is also proposed. Such a model may help in better understanding droplets' fluid dynamic behavior and may be used to assess the risks associated with pathogen transmission under different scenarios for any type of respiratory event. Overall, the computational cost is relatively low, allowing extensive simulation campaigns to be performed easily.