A Two-Dimensional Discrete-Sectional Model for Metal Aerosol Dynamics in a Flame

Aerosol nucleation and growth in a laminar flame or a gas-phase reaction jet were considered in the free-molecular regime. A two-dimensional, axisymmetric, discrete-sectional model was developed based on a species equation. Parabolic conservation equations resulted from the formulation of the governing equations in boundary layer form, neglecting axial diffusion and axial thermophoretic velocities. The source terms of the equations included monomer formation by gas-phase chemical reaction, and growth or reduction by coagulation and condensation among all aerosol particles. A binomial expansion was used to approximate the collision rate. The equations were linearized by Newton’s method and solved with a block tridiagonal solver. The results of the model exhibited reasonable agreement with an aerosol size distribution measured by dynamic light scattering. Spatial transport processes that could influence the aerosol dynamics included convection, diffusion, and thermophoresis. Their impact on the development of the aerosol and its distribution in the flame was investigated; thermophoresis was found to have the greatest impact on the spatial distribution of aerosol mass, although the amount of aerosol was not affected significantly