A Simple Surface-Bulk Partitioning Model for Estimating Size-Dependent Surface Tension of Deliquesced Aerosol Particles

Atmospheric aerosols significantly affect climate by scattering solar radiation and acting as cloud condensation nuclei (CCN). According to Köhler theory, aerosol activation into cloud droplets or CCN activity is impacted by aerosol surface tension. However, predicting the surface tension of activating aerosol particles is complicated by the bulk depletion of surfactants, which is sensitive to droplet size. Here, we present a simple surface-bulk partitioning model based on the Langmuir adsorption isotherm, which is capable of predicting bulk depletion and the size-dependent surface tension of microscopic droplets. The present model is validated by comparing our predictions with reported surface tension measurements of microdroplets containing nonionic surfactants and generally agrees with the droplet measurements. More importantly, the model can reproduce the size-dependent surface tension of ∼5-20 μm droplets containing NaCl and sodium dodecyl sulfate (SDS) at a given SDS concentration. Predicted Köhler curves of equilibrium supersaturation versus droplet diameter reveal that the models assuming a constant surface tension of pure water (i.e., classical Köhler theory) or bulk solution containing surfactants may potentially underestimate or overestimate CCN activity, respectively, highlighting the essential role of size-dependent surface tension in accurately representing the effect of surface tension on aerosol-cloud interactions.