Aggregation frequencies of fractal aggregates

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Abstract
The size-specific coagulation frequencies of fractal aggregates formed by the simulation of diffusion-limited cluster-cluster aggregation in two and three dimensions are determined from dynamic-scaling spectra by an inverse-problem approach. The four cases considered are two- and three-dimensional aggregation in which the cluster diffusivity is independent and dependent upon the mass of the cluster. The frequencies dervied from this approach describe the transient simulation results very well, the predictions being better than those with the Smoluchowski Brownian-coagulation frequency [Phys. Z. 17, 557 (1916)] modified by scaling arguments in three dimensions. Furthermore, frequencies are obtained for two-dimensional aggregation for which physical models have been evasive. The validity of the mean-field equation with a time-independent homogeneous frequency is examined. It is found that the mean-field approximation is valid in the range of simulation results but progressively deteriorates with time. The power of the inverse-problem approach here lies in its yielding size-specific aggregation rates of particles whether or not physical models are available.