Dispersion of free-falling saliva droplets by two-dimensional vortical flows

Abstract: The dispersion of respiratory saliva droplets by indoor wake structures may enhance the transmission of various infectious diseases, as the wake spreads virus-laden droplets across the room. Thus, this study analyzes the interaction between vortical wake structures and exhaled multi-component saliva droplets. A self-propelling analytically described dipolar vortex is chosen as a model wake flow, passing through a cloud of micron-sized evaporating saliva droplets. The droplets' spatial location, velocity, diameter, and temperature are traced, coupled to their local flow field. For the first time, the wake structure decay is incorporated and analyzed, which is proved essential for accurately predicting the settling distances of the dispersed droplets. The model also considers the nonvolatile saliva components, adequately capturing the essence of droplet-aerosol transition and predicting the equilibrium diameter of the residual aerosols. Our analytic model reveals non-intuitive interactions between wake flows, droplet relaxation time, gravity, and transport phenomena. We reveal that given the right conditions, a virus-laden saliva droplet might translate to distances two orders of magnitude larger than the carrier-flow characteristic size. Moreover, accounting for the nonvolatile contents inside the droplet may lead to fundamentally different dispersion and settling behavior compared to non-evaporating particles or pure water droplets. Ergo, we suggest that the implementation of more complex evaporation models might be critical in high-fidelity simulations aspiring to assess the spread of airborne respiratory droplets.