Coagulation of aerosol agglomerates in the transition regime

Abstract

Aerosol agglomerates are produced by homogeneous nucleation and Brownian coagulation. Coagulation models developed previously for spheres may be applicable to the initial stages of growth in which the colliding particles coalesce rapidly. Particles larger than a critical size d_1 are expected not to coalesce, leading to the formation of fractal-like agglomerates of dense primary particles. To describe coagulation in such systems, it is necessary to predict the mobilities, collision diameters, and mean free paths of agglomerate particles having sizes comparable to the gas mean free path λ. Using existing data on particle mobility and structure, these quantities are obtained for model agglomerates with fractal dimensions D_f in the range 1 < D_f < 3. For D_f ∼ 1.8, the resulting coagulation-frequency function K is found to be significantly higher than for spheres with the same mobility and material density ρ, in part because of the low effective density of the agglomerates. Numerical solutions of the coagulation equation show that as the aerosol grows from coalescing particles past the critical primary-particle size d1, both the width of the size distribution, σ_g, and the coagulation rate increase. For aerosols where the average particle is much larger than f_1, both σg and the coagulation rate are reduced. Although the growth is affected by D_f, f_1, λ, and ρ, results for large agglomerates are consistent with similarity solutions using a simplified collision-frequency function. For the simplified coagulation-frequency function it is assumed that the agglomerates are smaller than λ but much larger than the agglomerate mean free paths.