Determination of water diffusion coefficients in aerosols based on characteristic time analysis

Abstract. The water diffusion coefficient in atmospheric particles is a key parameter characterising particle-phase water transport and is essential for understanding aerosol phase state, phase transitions, and multiphase chemical processes. In this study, we develop a characteristic-time-based method for directly measuring the water diffusion coefficient in an individual droplet. The progress of water diffusion is represented by the relative abundance of H₂O and D₂O within the droplet, which is retrieved from Raman spectra and quantified here as the D₂O fraction. The characteristic time is derived as the time at which the measured D₂O fraction reaches the value predicted by the aqueous-phase diffusion model. Since the characteristic time derived from this model depends only on the water diffusion coefficient and droplet radius, the water diffusion coefficient can be calculated directly from the measured characteristic time and droplet radius. Using this method, water diffusion coefficients in sucrose droplets at 30–45 % RH were determined to be 1×10^-16 to 1×10^-14 m²s^-1. The water diffusion coefficient showed a clear RH dependence, with lower coefficients observed at lower RH. These results are consistent with previous experimental measurements, supporting the reliability of our method. A key advantage of this method is that it does not require tracking the complete H₂O/D₂O exchange process, as measurements are only needed until the characteristic time, thereby shortening the experimental observation time and making the method particularly suitable for diffusion measurements in highly viscous aerosol particles. This method applies to both spherical droplets and non-spherical diffusion systems, which allows it to be adapted to different experimental platforms. It therefore provides a basis for understanding mass transport in aerosols and related atmospheric chemical processes.