An analytical solution to calculate bulk mole fractions for any number of components in aerosol droplets after considering partitioning to a surface layer

Calculating the equilibrium composition of atmospheric aerosol particles, using all variations of Köhler theory, has largely assumed that the total solute concentrations define both the water activity and surface tension. Recently however, bulk to surface phase partitioning has been postulated as a process which significantly alters the predicted point of activation. In this paper, an analytical solution to calculate the removal of material from a bulk to a surface layer in aerosol particles has been derived using a well established and validated surface tension framework. The applicability to an unlimited number of components is possible via reliance on data from each binary system. Whilst assumptions regarding behaviour at the surface layer have been made to facilitate derivation, it is proposed that the framework presented can capture the overall impact of bulk-surface partitioning. Demonstrations of the equations for two and five component mixtures are given while comparisons are made with more detailed frameworks capable at modelling ternary systems at higher levels of complexity. Predictions made by the model across a range of surface active properties should be tested against measurements. Indeed, reccomendations are given for experimental validation and to assess sensitivities to accuracy and required level of complexity within large scale frameworks. Importantly, the computational efficiency of using the solution presented in this paper is roughly a factor of 20 less than a similar iterative approach, a comparison with highly coupled approaches not available beyond a 3 component system.