Hydrodynamic properties of rigid fractal aggregates of arbitrary morphology.

The hydrodynamic properties of rigid fractal aggregates are key ingredients in understanding the governing mechanism of their motion and the properties of their suspensions. In the present work we outline explicit equations for the estimation of the complete set of hydrodynamic properties of arbitrary shaped aggregates made of uniform sized spherical primary particles. The rigid body motion equations are coupled to Stokesian dynamics model to derive hydrodynamic rigid body properties. A wide library of clusters consisting of fractal aggregates of different morphologies (d(f)=1.8-3.0) and spheroidal clusters of different axes ratios with broad range of number of constitutive spheres (N(sphere)=10-1000) was used. Using the developed hydrodynamic rigid body properties' equations quantities such as the hydrodynamic radii of translational (R(H)) and rotational (R(ω)) motion, and all hydrodynamic information for each cluster, contained in its grand resistance matrix, are found. Furthermore, the relations between different hydrodynamic properties of average clusters and their morphology are investigated. In the effort to introduce a simplified model that accurately reproduces the complex hydrodynamic behavior of a fractal cluster, two approaches are discussed, namely, an equivalent sphere model and an equivalent ellipsoid model. The predicted hydrodynamic properties from both approaches, which can be computed exactly, closely match those of the clusters, for all cluster masses and morphologies, with the equivalent ellipsoid model being more effective whenever the cluster anisotropy is crucial. Therefore, this simplified approach provides an effective tool to predict the behavior of any cluster with complex structure.