Evolution of aggregate size and fractal dimension during Brownian coagulation

Fractal aggregate coagulation is described within a general framework of multivariate population dynamics. The effect of aggregate morphology on the coagulation rate, is taken into account explicitly, introducing in addition to aggregate particle size, the aggregate fractal dimension, as a second independent variable. A simple constitutive law is derived for determining the fractal dimension of an aggregate, resulting from a coagulation event between aggregates with different fractal dimensions. An efficient Monte Carlo method was implemented to solve the resulting bivariate Brownian coagulation equation, in the limits of continuum and free molecular flow regimes. The results indicate that as the population mean fractal dimension goes from its initial value towards its asymptotic value, the distribution of fractal dimension remains narrow for both flow regimes. The evolution of the mean aggregate size in the continuum regime is found to be nearly independent of aggregate morphology. In the free molecular regime however, the effects of aggregate morphology, as embodied in its fractal dimension, become more important. In this case the evolution of the aggregate size distribution cannot be described by the traditional approach, that employs a constant fractal dimension.