Hydrodynamics of Fractal Aggregates with Radially Varying Permeability

TLDR: It is shown that a reasonable estimate of the fluid drag force on a fractal aggregate may be obtained by assigning a constant volume-averaged porosity to the aggregate and using any of the expressions available in the literature for aggregates with uniform permeability.

Abstract: Hydrodynamic properties of fractal aggregates with radially varying permeability are investigated in terms of two parameters: radius of equivalent solid sphere experiencing the same drag as the aggregate (Ω*radius of aggregate) and fluid collection efficiency (η) of the aggregate. Resistance to the fluid flow through the aggregate is predicted to increase with increasing fractal dimension, while the fluid collection efficiency is expected to decrease. It is shown that a reasonable estimate of the fluid drag force on a fractal aggregate may be obtained by assigning a constant volume-averaged porosity to the aggregate and using any of the expressions available in the literature for aggregates with uniform permeability. The two hydrodynamic parameters, Ω and η, are used to modify the existing expressions for interactions between solid spheres to account for the porous nature of aggregates and thus calculate the collision rate kernels for interacting aggregates. The ratio of hydrodynamic radius of an aggregate to its radius of gyration predicted by the proposed model was in reasonable agreement with an experimental value reported in the literature.