Fractal Dimensions of Aggregates Determined from Steady-State Size Distributions

Aggregates formed by Brownian motion, shear coagulation, and differential sedimentation have fractal geometries. In order to model coagulation of fractal aggregates, we have derived a set of collision functions containing a fractal dimension for use in a general coagulation equation. These collision functions predict greater collision frequencies than models based on aggregates with Euclidean properties. Assuming only one mechanism of aggregate formation is dominant for a range of particle sizes, we also incorporated a fractal dimension in a dimensional analysis of steady-state particle-size distributions. Using particle-size distributions observed in marine systems, we calculated that aggregates formed by shear coagulation had fractal dimensions greater than 2.4, whereas aggregates formed from differential sedimentation had lower fractal dimensions in the range of 1.6-2.3. Reported fractal dimensions for many biological aggregates from bioreactors and marine systems are in the range expected for differential sedimentation. Fractal dimensions of inorganic colloidal aggregates are in the range expected for aggregation by Brownian motion and shear coagulation.