Collision frequencies of fractal bacterial aggregates with small particles in a sheared fluid

Bacteria were aggregated in a paddle mixer, producing highly amorphous aggregates of 3-300 μm diameter with an average fractal dimension of D = 2.52. To determine the rate that these types of biological flocs could coagulate with other particles, collision frequencies of these aggregates with small (0.49 μm diameter) fluorescent yellow green (YG) latex microspheres were measured in a paddle mixer at a mean shear rate of 17 s^{- 1}. As the aggregate sizes (<5 μm) approached that of the small YG microspheres, measured collision rates converged to values similar to those predicted by two conventional coagulation models (rectilinear and curvilinear) developed for collisions between spherical particles. Collision frequencies between larger bacterial aggregates (L(a) ~100 μm) and YG microspheres were found to be as much as 2 orders of magnitude smaller than values predicted using a rectilinear coagulation model but 5 orders of magnitude higher than predicted using the curvilinear model. Similar but slightly larger collision frequencies were obtained for aggregates (D = 2.31) made from red-stained microspheres (2.93 μm diameter). These data when combined with other data for larger inorganic aggregates indicate that the collision function increases from 10^-10 to 10^-6 cm³ s^-1 for fractal aggregates 3-1000 μm in size with small particles. These results demonstrate that fractal aggregates of particles collide much more frequently than expected based on spherical-particle coagulation models and suggest that coagulation rates in natural systems are much more rapid than predicted by coagulation models based on impermeable spheres.