Hydrodynamics of Aggregates

The hydrodynamic behavior of fractal aggregates plays an important role in various applications in industry and environment, and has been a topic of interest over the past several decades. Despite this, crucial aspects such as the relationship of the mobility radius, Rm, with respect to the fractal dimension, df, the fluid penetration depth ,d, have largely remained unexplored. Herein, we examine these aspects across a wide range of df, by employing a Stokesian Dynamics Approach. It takes into account all orders of monomer-monomer interactions to construct the resistance matrix for the entire cluster, which is assumed to be rigid. Statistical fractals such as DLA, CCA, Tunable Monte Carlo, and a deterministic fractal (Vicsek) with df varying from 1.76 to 3 and number of monomers ranging from 20 to 10240 are considered. While confirming the expected asymptotic cluster-size independence of the hydrodynamic ratio,B=Rg/Rm (where Rg is  the radius of gyration of the cluster), this study reveals a monotonically increasing trend for B with increasing df. The dependence of the penetration depth with the hydrodynamic ratio is investigated and its behavior with cluster size is compared to the predictions from the mean field theory .