Geoscientific Model Development Discussions www.geosci-model-dev-discuss.net 1991-9611 1991-962X 3 3 2010 10.5194/gmdd-3-1089-2010 http://www.geosci-model-dev-discuss.net/3/1089/2010/ http://www.geosci-model-dev-discuss.net/3/1089/2010/gmdd-3-1089-2010.html http://www.geosci-model-dev-discuss.net/3/1089/2010/gmdd-3-1089-2010.pdf 1089 1104 2010-07-13 An analytical solution to calculate bulk mole fractions for any number of components in aerosol droplets after considering partitioning to a surface layer D. Topping david.topping@manchester.ac.uk National Centre for Atmospheric Science, Leeds, UK Centre for Atmospheric Science, University of Manchester, Manchester, UK 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. Predictions made by the model across a range of surface active properties should be tested against measurements. 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. Booth, A. M., Topping, D. O., McFiggans, G., and Percival, C. J.: Surface tension of mixed inorganics and dicarboxylic acid aqueous solutions at 298.15 K and their importance for cloud activation predictions, Phys. Chem. Chem. Phys., 11(36), 8021–8028, 2009. Fainerman, V. B., Miller, R., and Aksenenko, E. V.: Simple model for prediction of surface tension of mixed surfactant solutions, Adv. Col. Int. Sci., 96(1–3), 339–359, 2002. Fainerman, V. B. and Miller, R.: Simple method to Estimate Surface tension of Mixed Surfactant Solutions, J. Phys. Chem. B, 105, 11432–11438, 2001. Fainerman, V. B., Wustneck, R., and Miller, R.: Surface tension of mixed surfactant solutions, Tenside Surfact Det., 38(4), 224–229, 2001. Hallquist, M., Wenger, J. C., Baltensperger, U., Rudich, Y., Simpson, D., Claeys, M., Dommen, J., Donahue, N. M., George, C., Goldstein, A. H., Hamilton, J. F., Herrmann, H., Hoffmann, T., Iinuma, Y., Jang, M., Jenkin, M. E., Jimenez, J. L., Kiendler-Scharr, A., Maenhaut, W., McFiggans, G., Mentel, Th. F., Monod, A., Prévôt, A. S. H., Seinfeld, J. H., Surratt, J. D., Szmigielski, R., and Wildt, J.: The formation, properties and impact of secondary organic aerosol: current and emerging issues, Atmos. Chem. Phys., 9, 5155–5236, doi:10.5194/acp-9-5155-2009, 2009. Hu, Y. F. and Lee, H.: Prediction of the surface tension of mixed electrolyte solutions based on the equation of Patwardhan and Kumar and the fundamental Butler equations, J. Col. Int. Sci., 269(2), 442–448, 2004. Kokkola, H., Sorjamaa, R., Peraniemi, A., Raatikainen, T., and Laaksonen, A.: Cloud formation of particles containing humic-like substances, Geophys. Res. Lett., 33, L10816, doi:10.1029/2006GL026107, 2006. McFiggans, G., Topping, D. O., and Barley, M. H.: The sensitivity of secondary organic aerosol component partitioning to the predictions of component properties - Part 1: A systematic evaluation of some available estimation techniques, Atmos. Chem. Phys. Discuss., 10, 15379–15415, doi:10.5194/acpd-10-15379-2010, 2010\blackbox\bf reference updated!OK?. Laaksonen, A., McGraw, R., and Vehkamaki, H: Liquid-drop formalism and free-energy surfaces in binary homogeneous nucleation theory, J. Chem. Phys.,111, 2019–2027, 1999. Li, Z., Williams, A. L., and Rood, M. J.: Inluence of soluble surfactant properties on the activation of aerosol particles containing inorganic solute, J. Atmos. Sci., 55, 1859–1866, 1998. Li, Z. B. and Lu, B. C. Y.: Surface tension of aqueous electrolyte solutions at high concentrations representation and prediction, Chem. Eng. Sci., 56(8), 2879–2888, 2001. Sorjamaa, R., Svenningsson, B., Raatikainen, T., Henning, S., Bilde, M., and Laaksonen, A.: The role of surfactants in Köhler theory reconsidered, Atmos. Chem. Phys., 4, 2107–2117, doi:10.5194/acp-4-2107-2004, 2004. Topping, D. O., McFiggans, G. B., and Coe, H.: A curved multi-component aerosol hygroscopicity model framework: Part~2 - Including organic compounds, Atmos. Chem. Phys., 5, 1223–1242, doi:10.5194/acp-5-1223-2005, 2005.