A dynamic optimization problem related to organic aerosols

A model that rigorously computes the gas–particle partitioning and liquid–liquid equilibrium for organic atmospheric aerosol particles is presented. The dynamics of the mass transfers between the particle and the gas phase are modeled with differential equations and are coupled with a constrained optimization problem for the thermodynamic equilibrium inside the particle. The nonlinear system composed by the first order optimality conditions coupled with the discretized differential equations is solved with an interior-point method and a Newton method. The resulting linear system is decoupled with sequential quadratic programming techniques. Numerical results and comparisons of time scales show the accuracy and efficiency of our algorithm.