A model of a growing, coagulating aerosol: Fid-Bau Portal

A model of a growing, coagulating aerosol

Wadden, R.A. / Quon, J.E. / Hulburt, H.M.

Abstract A continuously reinforced aerosol, undergoing change by particle growth and coagulation, and particle removal at some selected large size, is described by a number balance equation. For the steady state condition, the number balance equation was solved numerically for the distribution of particle concentrations as a continuous function of particle volume. The particle growth rate, $Φ(v)$ , was based on rate data describing the Mn²⁺, Fe³⁺, and non-catalyzed aqueous phase conversion of $SO 2 (g)$ to H2SO4(aq). The catalyst and the H2SO4 were assumed to be contained in drops, which grew with acid production, due to the accretion of water vapor. The number balance equation without growth was also solved. Calculations on the Mn²⁺ catalyzed systems resulted in distributions which reflected detectable effects of both growth and coagulation. For sufficiently large values of $Φ(v) (> 10$ ⁻¹⁰ μ³ min ⁻¹), corresponding to $SO 2 (g)$ concentrations of 0.1–10 ppm. the resulting distributions were found to display two regions, one dominated by growth and the other by coagulation. The particle size distribution in the growth region (small $v$ ) is similar in shape to $1/Φ(v)$ , while in the coagulation region (large $v$ ) the particle distribution is a straight line on a log-log plot. The shape of the input distribution did not have an effect on the shape of the calculated distribution. The neutralizing effects of $NH 3 (g)$ on the Mn²⁺ catalyzed aqueous phase reaction were also checked and the resulting distribution has a shape similar to those at high $SO 2 (g)$ concentrations (10 ppm). The Fe³⁺ catalyzed and non-catalyzed systems $(Φ(v) ≦ 10$ ⁻¹²μ³ min ⁻¹) displayed only a coagulation region. At large values of $v$ , calculated distributions for all systems displayed a power law relationship between particle concentration and volume with a slope of − 1.3 to −1.5. The H2SO4 or (NH4)2SO4 composition of the particles was found not to be a function of size.