Coagulation of a continuously reinforced aerosol

Abstract

The particle size distribution of an aerosol continually reinforced by the introduction of particles (feed) and undergoing Brownian coagulation was calculated by numerically integrating the equations of Smoluchowski modified to include a feed term. A variation of the Adams' method of numerical integration was used. The equations used for the numerical computations were in dimensionless form and results obtained may be sealed for different rates of particle feed. The concentrations of different size particles were computed as a function of time for several functional representations of particle feed and coagulation coefficients. For a constant coagulation coefficient and a feed of unit size particles, the equilibrium size distribution is approximated by a power expression. For the case where the coagulation rate is dependent on the size of the colliding particles, the particle size distribution approaches closely the equilibrium distribution for the constant coagulation coefficient case, the time necessary being dependent on the feed rate and particle size distribution of the feed. The feed rate and size distribution influence the time to reach equilibrium but do not affect the resulting size distribution. The particle concentration is related to the square root of the feed rate. The time to reach equilibrium is inversely proportional to the feed rate. For the aerosol model considered, the highest concentration occurs at the particle size associated with the highest rate of input and the peak size is invariant with time. Equilibrium is promoted more by heterogeneity in the feed particle size than by the size dependency of the coagulation coefficient. Heterogeneity in the feed particle size results in an equilibrium size distribution of a broader size range than in the case of a feed of only one particle size. The ratio of peak concentration for any given particle size to its equilibrium value is approximately 1.1 for the heterogeneous feed and 1.8 for the feed of a single particle size.