Simultaneous Particle and Molecule Modeling (SPAMM): An Approach for Combining Sectional Aerosol Equations and Elementary Gas-Phase Reactions

ABSTRACT

A method for writing the sectional aerosol equations in a form suitable for combination with a detailed kinetic model for gas-phase reactions has been developed. The sectional equations are given for arbitrary values of d, the ratio of molecular weights of adjacent bin boundaries, and are solved for d ≥ 2 for three different cases of the intra-bin distribution: (1) constant mass density w.r.t. ln(v), where v = molecular weight; (2) constant number density w.r.t. ln(v), or alternately, constant mass density w.r.t. v; (3) constant number density w.r.t. v. All the solutions given conserve mass; the extent of deviation from conservation of particle number is evaluated. An example of the approach is given for soot formation in combustion. The aerosol sections describe mass above 400 amu, with d = 2. Aerosol reactions are: bin-bin coagulation; addition of C₂H₂; addition of polycyclic aromatic hydrocarbons (PAH) with 2 to 10 benzenoid rings; oxidation via OH attack. The set of aerosol reactions is appended to a detailed elementary-step kinetic mechanism describing the gas-phase chemistry, including growth of PAH up to C₃₂H₁₄ (398 amu). The method also directly calculates the effect of the soot aerosol upon concentrations of gas-phase species such as PAH—a new capability for soot formation models. Predictions for a given set of conditions for the three cases of the intrabin distribution show striking changes not only in the particle size distribution but also in predictions of total aerosol mass and number concentrations. The extent of deviation from conservation of particle number for the three cases is shown to have a direct effect upon the predicted aerosol dynamics.