A discrete-sectional model for particulate production by gas-phase chemical reaction and aerosol coagulation in the free-molecular regime

Abstract

A universal correlation (self-preserving map) for gas-phase production of powders is derived from first principles. A dimensionless discrete-sectional model for free-molecular aerosol coagulation is developed and systematically validated by examining the effects of section spacing and numerically conserved aerosol property (particle number, volume, and volume squared concentration) used in computing the evolution of the particle size distribution. Discrete-sectional models that numerically conserve the highest moment of the distribution (here, volume squared) most accurately predict the particle size distribution. This υ 2-based model is used to develop a self-preserving map in the process parameter space of dimensionless time for chemical reaction, θ, and dimensionless process residence time, X. The self-preserving map defines a priori conditions for generation of powders having their asymptotic self-preserving size distribution. If the reaction is nearly instantaneous (θ ⩽ 0.25), the time required for the distribution to become self-preserving is four times the characteristic time for monomer coagulation ( X ≈ 4); however, as the reaction becomes slower (θ ⩾ 0.25), the time for the distribution to become self-preserving is approximately 15 times the characteristic time for chemical reaction ( X ≈ 15 θ). The predictions of the present discrete-sectional model are compared against moment models for aerosol coagulation that assume that the particle size distribution remains monodisperse, self-preserving, or lognormally shaped throughout the process.