The Self-Preserving Size Distribution Theory: I. Effects of the Knudsen Number on Aerosol Agglomerate Growth

Abstract

Gas-phase synthesis of fine solid particles leads to fractal-like structures whose transport and light scattering properties differ from those of their spherical counterparts. Self-preserving size distribution theory provides a useful methodology for analyzing the asymptotic behavior of such systems. Apparent inconsistencies in previous treatments of the self-preserving size distributions in the free molecule regime are resolved. Integro-differential equations for fractal-like particles in the continuum and near continuum regimes are derived and used to calculate the self-preserving and quasi-self-preserving size distributions for agglomerates formed by Brownian coagulation. The results for the limiting case (the continuum regime) were compared with the results of other authors. For these cases the finite difference method was in good in agreement with previous calculations in the continuum regime. A new analysis of aerosol agglomeration for the entire Knudsen number range was developed and compared with a monodisperse model; Higher agglomeration rates were found for lower fractal dimensions, as expected from previous studies. Effects of fractal dimension, pressure, volume loading and temperature on agglomerate growth were investigated. The agglomeration rate can be reduced by decreasing volumetric loading or by increasing the pressure. In laminar flow, an increase in pressure can be used to control particle growth and polydispersity. For Df=2, an increase in pressure from 1 to 4 bar reduces the collision radius by about 30%. Varying the temperature has a much smaller effect on agglomerate coagulation.