Collision Frequencies of Fractal Aggregates with Small Particles by Differential Sedimentation

Two groups of aggregates with fractal dimensions of 1.81 ( 0.09 and 2.33 ( 0.07 were generated by coagulation of latex microspheres (2.84 μm) in a Jar-test (paddle-mixing) device. The collision rates between these fractal aggregates (200-1000 μm) and small (1.48 μm) particles were measured for individual aggregates that had settled through a suspension of the small particles. Aggregate permeabilities calculated from measured settling velocities were 3 orders of magnitude greater than predicted by a permeability model based on a homogeneous distribution of primary particles within the aggregates. Collision frequencies were 1 order of magnitude higher than predicted by a curvilinear model and about 2 orders of magnitude lower than predicted by a rectilinear collision model. The capture efficiencies of small particles by settling aggregates were <0.2% based on the total volume of water swept out by an aggregate. Fluid collection efficiencies, collision frequencies, and particle capture efficiencies of the fractal aggregates decreased with the magnitude of fractal dimensions. A fractal permeability model was developed by modifying the Brinkman correlation to describe the permeability as a function of aggregate size. This model was used in conjunction with a filtration model to predict capture rates and capture efficiencies of small particles by settling fractal aggregates. Based on these experiments and models, it is argued that the high aggregate permeabilities and the low overall particle capture efficiencies of fractal aggregates can be explained by flow through macropores formed between large clusters within the aggregates.