On the theory of the coagulation of noninteracting particles in brownian motion

The theory for coagulation of particles in Brownian motion is reviewed. The effects of heterogeneity in particle size, and of particle motion in a rarefied medium are examined using numerical solutions of the coagulation equations. Heterogeneity and increased values of the ratio of the mean free path of the medium to the particle radius (the Knudsen number for particles) increased the rate of coagulation. According to the results of the numerical experiments, a self-preserving function for the size distribution develops after dimensionless coagulation times of about 3. The self-preserving spectrum was found to be independent of the initial distribution after a sufficiently long time. The shape of the asymptotic distribution varied with the ratio of the mean free path of the medium to the particle radius (λ/r₁). A cumulative distribution rapidly formed which was insensitive to time, to initial conditions, and to variations in λ/r₁ up to one. The average cumulative distribution compared fairly well with an experimentally determined distribution.