How far droplets can move in indoor environments - revisiting the Wells evaporation-falling curve

A large number of infectious diseases are believed to be transmitted between people via large droplets and by airborne routes. An understanding of evaporation and dispersion of droplets and droplet nuclei is not only significant for developing effective engineering control methods for infectious diseases but also for exploring the basic transmission mechanisms of the infectious diseases. How far droplets can move is related to how far droplet-borne diseases can transmit. A simple physical model is developed and used here to investigate the evaporation and movement of droplets expelled during respiratory activities; in particular, the well-known Wells evaporation-falling curve of droplets is revisited considering the effect of relative humidity, air speed, and respiratory jets. Our simple model considers the movement of exhaled air, as well as the evaporation and movement of a single droplet. Exhaled air is treated as a steady-state non-isothermal (warm) jet horizontally issuing into stagnant surrounding air. A droplet is assumed to evaporate and move in this non-isothermal jet. Calculations are performed for both pure water droplets and droplets of sodium chloride (physiological saline) solution (0.9% w/v). We calculate the droplet lifetimes and how droplet size changes, as well as how far the droplets travel in different relative humidities. Our results indicate that a droplet's size predominately dictates its evaporation and movement after being expelled. The sizes of the largest droplets that would totally evaporate before falling 2 in away are determined under different conditions. The maximum horizontal distances that droplets can reach during different respiratory activities are also obtained. Our study is useful for developing effective prevention measures for controlling infectious diseases in hospitals and in the community at large.