Settling Velocities of Fractal Aggregates

Aggregates generated in water and wastewater treatment systems and those found in natural systems are fractal and therefore have different scaling properties than assumed in settling velocity calculations using Stokes' law. In order to demonstrate that settling velocity models based on impermeable spheres do not accurately relate aggregate size, porosity and settling velocity for highly porous fractal aggregates, we generated fractal aggregates by coagulation of latex microspheres in paddle mixers and analyzed each aggregate individually for its size, porosity, 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 of particles within an aggregate. Fractal dimensions (D) derived from size−porosity relationships for the three batches of aggregates were 1.78 ± 0.10, 2.19 ± 0.12 and 2.25 ± 0.10. ...