Hydrodynamic radius of fractal clusters.

The Kirkwood-Riseman theory has been used to derive an analytical formula for the evaluation of the hydrodynamic radii of fractal clusters. The proposed relation is based on knowledge of the particle-particle correlation function and can be applied to clusters containing any number of particles larger than 4. The calculated values of the hydrodynamic radius are compared with the results of other theoretical approaches proposed in the literature, as well as several experimental data. Finally, the developed relation has been used in connection with a population balance equation model that computes the clusters' mass distribution to estimate the average hydrodynamic radius for a population of fractal clusters of different sizes. The obtained results have been compared to suitable experimental data for a silica colloidal suspension aggregating under reaction-limited conditions.