Collision frequencies between fractal aggregates and small particles in a turbulently sheared fluid

Three groups of aggregates with fractal dimensions of 1.89 ±0 0.06, 2.21 ± 0.06, and 2.47 ± 0.10 were generated by coagulation of latex microspheres (2.85 μm) in a Jartest (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 environment 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 (O) affected the collision frequency function (β) between fractal aggregates and small particles, resulting in β ~ G(1-0.33D). According to this relationship, as D → 0, the aggregates become infinitely porous and β becomes proportional to G¹ 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.