Water evaporation from solute-containing aerosol droplets: effects of internal concentration and diffusivity profiles and onset of crust formation

Saliva is primarily composed of water, but additionally includes a variety of organic and inorganic substances such as salt, proteins, peptides, mucins, virions, etc. The presence of such solutes affects the evaporation time of respiratory droplets that are sedimenting in air, and thereby the airborne transmission of infections. From solutions of the coupled heat-conduction and water-diffusion equations within the droplet and in the ambient vapor phase, we find that the solute-induced water vapor-pressure reduction considerably slows down the evaporation process and dominates the solute-concentration dependence of the droplet evaporation time. The evaporation-induced solute-concentration gradient near the droplet surface, which is accounted for using a two-stage evaporation model, is found to further intensify the slowing down of the drying process. On the other hand, the presence of solutes is found to reduce evaporation cooling of the droplet, which causes a slight decrease in the evaporation time. Overall, the first two effects are dominant, meaning that the droplet evaporation time increases in the presence of solutes. The solute-concentration dependence of the water diffusivity inside the droplet does not significantly change the evaporation time. Finally, crust formation on the droplet surface is found to increase the final equilibrium size of the droplet.