A Solution to the Problem of Nonequilibrium Acid/Base Gas-Particle Transfer at Long Time Step

A stable numerical solution to the unsolved problem of nonequilibrium growth/evaporation at long time step of multiple dissociating acids (e.g., nitric acid, hydrochloric acid, carbonic acid, sulfuric acid, etc.) and a base (ammonia) is discussed. The solution eliminates most oscillatory behavior observed in previous solutions at long time step. The solution is applicable across the entire relative humidity range, both in the presence and absence of solids and among multiple aerosol size bins and distributions. It involves solving growth/evaporation of semivolatile acids with a dissolutional growth scheme at high liquid water content (LWC), semivolatile acids with a condensational growth scheme at low LWC, involatile acids with a condensation scheme at all LWCs, then equilibrating ammonia and pH simultaneously between gas and solution phases at all LWCs based on updated acid contents, and finally solving internal-aerosol composition, final pH, and LWC with an operator-split equilibrium calculation. The new method at long time step (150–300 s) compares well with, and is 10–60 times faster than, a previous solution at short time step over the entire size distribution. Solutions at short and long time steps converge to equilibrium solutions when unique equilibrium solutions exist, even in the presence of calcium, magnesium, potassium, and carbonate. The new scheme is referred to as PNG-EQUISOLV II, where PNG is Predictor of Nonequilibrium Growth. Analysis with the scheme suggests that, under some conditions of high relative humidity and concentration, some coarse-mode particles (<6 μm diameter) may reach equilibrium on time scales <1 h.