College of Engineering, The University of Utah

Thermodynamical Modeling of Organic Aerosols

While considerable progress has been made in understanding the physical and chemical properties of inorganic aerosols, our knowledge of organic aerosols remains limited due to their chemical complexity. The concentration of organic particulate matter in the atmosphere is determined in large part by the absorptive partitioning between the gas and PM phases. In particular, when the organic PM contains a significant amount of water and/or primary, non-polar organic compounds, phase separation to two liquid phases can occur, with one phase relatively more polar and the other relatively less polar. Such phase separation is expected to increase the stability of the system, leading to higher total organic PM concentrations. It is therefore of considerable interest to have a modeling tool that is capable of predicting liquid-liquid equilibria in organic aerosols.
The first-generation organic models treated each organic component independently and neglected the interactions between organic and inorganic components. The second-generation organic models assumed that the organic species form a solution. In this description, the organic species can partition into the aerosol phase even if their gas phase concentrations are below their saturation levels. One can also find models for the organic PM formation which assume the a priori existence of two liquid phases, one organic phase (with no associated water) and one aqueous phase. They also placed a non-thermodynamic phase lock by allowing hydrophobic compounds to partition only to the organic phase and hydrophilic compounds to partition only to the aqueous phase. Then that phase lock has been relaxed by allowing all modeled organic compounds to partition from the gas phase to both the higher polarity (hydrophilic) and lower polarity (hydrophobic) phases. However, water was still confined to the hydrophilic phase.

Recently, we have developed a primal-dual interior-point algorithm for the efficient solution of the phase equilibrium problem. In this study, our goal is to develop a general modeling tool that is capable of predicting effectively liquid-liquid and gas-liquid equilibria, liquid phase stability and separation of organic aerosol particles. The model to be developed will be incorporated in overall gas/particle partitioning of semi-volatile organic compounds to mixed organic and inorganic particles. The principle features of our primal-dual interior-point algorithm can be summarized as follows:

The algorithm applies Newton's method to the Karush-Kuhn-Tucker (KKT) system at each step to find the next primal-dual approximation of the solution.
To ensure that the algorithm converges to a stable equilibrium rather than any other first order optimality point such as a maximum, a saddle point, or an unstable local minimum, a technique of deflating is implemented by keeping positive definite the reduced Hessian matrix of the Gibbs free energy at each phase.
For a finite termination of the interior-point method, an active phase identification procedure is incorporated for the correct detection of phases whose total number of substances reaches the lower bound, e.g., zero, at the solution.

The more precise description of the method can be found in the note "An Optimization Problem related to the Modeling of Atmospheric Organic Aerosols".

The UHAERO module 2 software for thermodynamical equilibrium of organic aerosols can be found here.

This project will be continued by focusing on the mixtures of inorganic and organic aerosols to compute the thermodynamical equilibriumof atmospheric aerosols involving liquid-liquid and liquid-gas-solid chemical reactions and phases equilibrium. This topic is illustrated [here]

http://www.tlc2.uh.edu/uhaero/Research/Project2/index_html