Collision Frequencies between Fractal Aggregates and Small Particles in a Turbulently Sheared Fluid

Three groups of aggregates with fractal dimensions of 1.89 ± 0.06, 2.21 ± 0.06, and 2.47 ± 0.10 were generated by coagulation of latex microspheres (2.85 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 in the turbulent shear environ ment of the paddle mixer at mean shear rates of 2.1, 7.3, and 14.7 s - 1 . Collision frequencies were 5 orders of magnitude higher than predicted by a curvilinear model but 2 orders of magnitude lower than predicted by a rectilinear model. Collision frequencies much higher than predicted by the curvilinear collision kernel were attributed to significant flow through the interior of the fractal aggregates. The fluid shear rate ( G ) and the aggregate fractal dimension ( D ) affected the collision frequency function (β) between fractal aggregates and small particles, resulting in β ∼ G 1 - 0.33 D . According to this relationship, as D → 0, the ag gregates become infinitely porous and β becomes proportional to G 1 as described by a rectilinear collision model based on aggregates sweeping out all fluid within their pathway. As aggregates become less fractal and D → 3, β becomes relatively insensitive to the magnitude of G as predicted by a curvilinear model.