A Theoretical Analysis on the Final Sizes of Human Respiratory Droplets in Different Relative Humidities

The final sizes of human respiratory droplets are important for understanding disease transmission and indoor environments. This study develops a simple method to estimate the final sizes of human respiratory droplets in different humidities. The droplet was treated as a sodium chloride solution mixed with insoluble fine spheres. The water in droplet would reach equilibrium with vapor in air at the final size for a suspended droplet, and the solute effect and Kelvin effect on the equilibrium were taken into consideration. The final sizes were estimated at both low relative humidity, which were the sizes of the crusts formed by crystallized sodium chloride and insoluble fine spheres, and at high relative humidity, which were the sizes of the droplets at equilibrium. The final sizes and critical relative humidity were also found to be significantly related to the initial sodium chloride concentration c and initial volume ration of the spheres Φi. When c = 0.9% and Φi = 1.8%, the critical relative humidity was found to be 70%. The final size was 32% of the original size, if relative humidity < 70%. The final size might be much larger than the original size, if relative humidity > 70%, e.g. 61% of the original size at relative humidity = 95%.