Hydrodynamics of an ideal aggregate with quadratically increasing permeability

In this study, we consider the ideal aggregate with quadratically increasing permeability κ=k2r2 and derive the analytical expression of the stream function within the porous aggregate by incorporating the Brinkman and continuity equations. The hydrodynamic properties of the aggregate are investigated by taking account of the hydrodynamic radius, settling velocity, and fluid collection efficiency, which are found to be solely dependent on the permeability prefactor k2. The fractal dimension Df and prefactor k2 of the ideal aggregate are found to be 5/3 (=1.67) and 0.20, respectively, and well describe the hydrodynamics of aggregates formed in the diffusion-limited-cluster-aggregation (DLCA) regime. More important, hydrodynamic similarity between the ideal aggregate and impermeable solid sphere is discovered in terms of variations of the hydrodynamic radius, settling velocity, and fluid collection efficiency with respect to the aggregate radius.