SETTLING VELOCITIES OF FRACTAL AGGREGATES

Aggregates generated in water and wastewater treatment systems and tho se found in natural systems are fractal and therefore have different s caling properties than assumed in settling velocity calculations using Stokes' law. In order to demonstrate that settling velocity models ba sed on impermeable spheres do not accurately relate aggregate size, po rosity and settling velocity for highly porous fractal aggregates, we generated fractal aggregates by coagulation of latex microspheres in p addle mixers and analyzed each aggregate individually for its size, po rosity, and settling velocity. Settling velocities of these aggregates were on average 4-8.3 times higher than those predicted using either an impermeable sphere model (Stokes' law) or a permeable sphere model that specified aggregate permeability for a homogeneous distribution o f particles within an aggregate. Fractal dimensions (D) derived from s ize-porosity relationships for the three batches of aggregates were 1. 78 +/- 0.10, 2.19 +/- 0.12 and 2.25 +/- 0.10. These fractal dimensions were used to predict power law relationships between aggregate size a nd settling velocity based on Stokes' law. When it was assumed that th e the drag coefficient, Co, was constant and fixed at its value of C-D = 24/Re for the creeping flow region (Re much less than 1), predicted slopes of size and settling velocity were in agreement with only the data sets where D > 2. As a result, when D < 2, aggregate porosities w ill be overestimated and fractal dimensions will be calculated incorre ctly from settling velocity data and Stokes' law.