A predictive thermodynamic framework of cloud droplet activation for chemically unresolved aerosol mixtures, including surface tension, non-ideality, and bulk–surface partitioning
Authors: Prisle Nønne L. 
Published: November 2021

Abstract. This work presents a thermodynamically consistent framework
that enables self-contained, predictive Köhler calculations of droplet growth and activation
with considerations of surface adsorption, surface tension reduction, and non-ideal water activity for chemically complex and unresolved surface-active aerosol mixtures.
The common presence of surface-active species
in atmospheric aerosols is now well-established. However, the impacts of different effects driven by surface activity, in particular bulk–surface partitioning and resulting bulk depletion and/or surface tension reduction, on aerosol hygroscopic growth and cloud droplet activation remain to be generally established.
Because specific characterization of key properties, including water activity and surface tension, remains exceedingly
challenging
for finite-sized activating droplets,
a self-contained and thermodynamically consistent model framework is needed to resolve the individual effects of surface activity during droplet growth and activation.
Previous frameworks have achieved this for simple aerosol mixtures, comprising at most a few well-defined chemical species.
However, atmospheric aerosol mixtures and more realistic laboratory systems are typically chemically more complex and not well-defined (unresolved). Therefore, frameworks which require specific knowledge of the concentrations of all chemical species in the mixture and their composition-dependent interactions cannot be applied.
For mixtures which are unresolved or where specific interactions between components are unknown, analytical models based on retrofitting can be applied, or the mixture can be represented by a proxy compound or mixture with well-known properties. However, the surface activity effects evaluated by such models cannot be independently verified.
The presented model
couples Köhler theory with the Gibbs adsorption and Szyszkowski-type surface tension equations. Contrary to previous thermodynamic frameworks, it is formulated on a mass basis to obtain a quantitative description of composition-dependent properties for chemically unresolved mixtures.
Application of the model is illustrated by calculating
cloud condensation nuclei (CCN) activity of aerosol particles comprising
Nordic aquatic fulvic acid (NAFA),
a chemically unresolved and strongly surface-active model atmospheric humic-like substance (HULIS), and NaCl, with dry diameters of 30–230 nm and compositions spanning the full range of relative NAFA and NaCl mixing ratios.
For comparison with the model presented, several other predictive Köhler frameworks, with simplified treatments of surface-active NAFA, are also applied.
Effects of NAFA surface activity are gauged via a suite of properties evaluated for growing and activating droplets.
The presented framework predicts a similar influence of surface activity of the chemically complex NAFA on CCN activation as was previously shown for single, strong surfactants. Comparison to experimental CCN data shows that NAFA bulk–surface partitioning is well-represented by Gibbs adsorption thermodynamics. Contrary to several recent studies, no evidence of significantly reduced droplet surface tension at the point of activation was found.
Calculations with the presented thermodynamic model show that throughout droplet growth and activation, the finite amounts of NAFA in microscopic and submicron droplets
are strongly depleted from the bulk, due to bulk–surface partitioning, because surface areas for a given bulk volume are very large.
As a result, both the effective hygroscopicity and ability of NAFA to reduce droplet surface tension are significantly lower in finite-sized activating droplets than in macroscopic aqueous solutions of the same overall composition.
The presented framework enables the influence of surface activity on CCN activation for other chemically complex and unresolved aerosol mixtures, including actual atmospheric samples, to be systematically explored. Thermodynamic input parameters can be independently constrained from measurements, instead of being either approximated by a proxy or determined by retrofitting, potentially confounding several mechanisms influenced by surface activity.