Models of Isotopic Water Diffusion in Spherical Aerosol Particles

Isotopic exchange experiments that utilize D₂O and H₂O have received attention as a method for studying water diffusion in high viscosity aerosol particles. However, the mathematical models used to retrieve diffusion coefficients from these measurements have yet to be critically examined. Here, two models for the isotopic exchange of D₂O and H₂O in spherical particles are analyzed and compared. The primary difference between the two models is the choice of boundary condition at the surface of the spherical particle. In one model, it is assumed that the concentration of D₂O at the surface is fixed, while in the other model, it is assumed that, at the particle surface, the concentration of D₂O in the condensed phase is in equilibrium with D₂O vapor. Closed-form expressions for the two boundary value problems that describe these physical models are found and discussed. Then, specific examples of aqueous droplets containing either sucrose, citric acid, and shikimic acid are examined with both models. It is found that at low relative humidities the choice of boundary condition has a negligible effect on the predicted lifetime of isotopic exchange, while at high relative humidities predicted lifetimes can differ by orders of magnitude. The implication of this result is that the choice of model can greatly affect diffusion coefficients retrieved from experimental measurements under certain conditions. Finally, discrepancies between diffusion coefficients measured using isotopic exchange and water sorption and desorption experiments are discussed.