Articles | Volume 5, issue 1
Development and technical paper
04 Jan 2012
Development and technical paper |  | 04 Jan 2012

Partial Derivative Fitted Taylor Expansion: an efficient method for calculating gas/liquid equilibria in atmospheric aerosol particles – Part 2: Organic compounds

D. Topping, D. Lowe, and G. McFiggans

Abstract. A flexible mixing rule is presented which allows the calculation of activity coefficients of organic compounds in a multi-component aqueous solution. Based on the same fitting methodology as a previously published inorganic model (Partial Differential Fitted Taylor series Expansion; PD-FiTE), organic PD-FiTE treats interactions between binary pairs of solutes with polynomials of varying order. The numerical framework of organic PD-FiTE is not based on empirical observations of activity coefficient variation, rather a simple application of a Taylor Series expansion. Using 13 example compounds extracted from a recent sensitivity study, the framework is benchmarked against the UNIFAC model. For 1000 randomly derived concentration ranges and 10 relative humidities between 10 and 99%, the average deviation in predicted activity coefficients was calculated to be 3.8%. Whilst compound specific deviations are present, the median and inter-quartile values across all relative humidity range always fell within ±20% of the UNIFAC value. Comparisons were made with the UNIFAC model by assuming interactions between solutes can be set to zero within PD-FiTE. In this case, deviations in activity coefficients as low as −40% and as high as +70% were found. Both the fully coupled and uncoupled organic PD-FiTE are up to a factor of ≈12 and ≈66 times more efficient than calling the UNIFAC model using the same water content, and ≈310 and ≈1800 times more efficient than an iterative model using UNIFAC. The use of PD-FiTE within a dynamical framework is presented, demonstrating the potential inaccuracy of prescribing fixed negative or positive deviations from ideality when modelling the evolving chemical composition of aerosol particles.