FLUID-MECHANICS AND FRACTAL AGGREGATES

The disturbances in uniform creeping flow in the presence of an isolated porous floc are investigated theoretically. Using the Carman-Kozeny equation, the floc permeability is related to its fractal dimension, D. Fluid streamlines, drag coefficient and the fluid collection efficiency of porous aggregates are expressed in terms of D. As D increases, for a fixed packing factor and ratio of primary particle radius to floc radius, the permeability is found to decrease and the fluid mechanics resembles more closely that of an isolated impermeable sphere. As a simplification, it is suggested that a rectilinear model for flow up to an impervious sphere may be a reasonable approximation for aggregate-aggregate and particle-aggregate interactions if D less than or similar 2. Curvilinear models for flow up to an impervious sphere may be accurate approximations for interactions involving aggregates with higher fractal dimensions (D greater than or similar to 2.3).