Mixtures of Inorganic/Organic Aerosols

Atmospheric aerosols consist of complex mixtures of inorganic and organic compounds. Organic components may affect the hygroscopic properties of atmospheric aerosols. Conversely, dissolved electrolytes can have appreciable effects on the solubility of organic components in solution. Despite the importance of organic compounds to the behavior of particles in the atmosphere only a few theoretical models for the prediction of the hygroscopic growth of mixed inorganic/organic aerosols have been developed. In this study, we will develop a primal-dual interior-point active-set algorithm for the efficient solution of multiphase and multireaction chemical equilibrium problems arising in modeling atmospheric particles of inorganic and organic mixtures. The algorithm will be implemented in UHAERO module 2, a general inorganic and organic thermodynamic model that will enable us to address the questions such as: (a) which of the equilibrium and dynamic approaches should be used to model mixed organic/inorganic aerosols? (b) how does water absorption by organic components affect the partitioning of inorganic compounds between gas and aerosol phases? The principle features of the proposed primal-dual interior-point active-set algorithm can be summarized as follows: The algorithm applies Newton's method to the perturbed Karush-Kuhn-Tucker (KKT) system of equations at each step to find the next primal-dual approximation of the solution. The interior-point method is applied together with an active phase identification procedure to accurately track the liquid phase formation and separation. The active set method allows to add a solid salt once it reaches saturation, while deleting a solid phase from the active set when its concentration does not satisfy the non-negativeness constraint, Phase stability criteria are incorporated into the algorithm to ensure that the algorithm converges to a stable equilibrium rather than to any other first order optimality point such as a maximum, a saddle point, or a unstable local minimum. The KKT system is decomposed into the liquid-liquid equilibrium and the solid-liquid stoichiometry so that efficient and tailored linear solvers can be applied to the reduced systems.