Cake resistance of aggregates formed in the diffusion-limited-cluster-aggregation (DLCA) regime

The ideal aggregate characterized by the quadratically increasing permeability κ(r)=k2r2κ(r)=k2r2 is investigated to estimate the specific cake resistance (i.e., inverse permeability) of a cake layer composed of deposited aggregates formed in the diffusion-limited-cluster-aggregation (DLCA) regime. Happel’s cell model is employed in this study by embedding the ideal aggregate in the center of a spherical cell of tangential stress-free surface. The specific resistance is analytically calculated as a function of the occupancy fraction and then compared to those of conventional cake layers of equal-sized spherical colloids and uniformly porous spheres. The DLCA cake layer provides significantly less specific resistance and therefore shows the remarkable potential of aggregate-enhanced membrane filtration (AEMF) as a new protocol for colloidal filtration. The settling velocity of a swarm of the ideal aggregates is investigated as a by-product and experimental verification of this theory.