Properties of the fractal measure describing the hydrodynamic force distributions for fractal aggregates moving in a quiescent fluid

Abstract

Using the Kirkwood-Riseman theory we show that the penetration of the hydrodynamic field for a fractal aggregate (diffusion-limited cluster-cluster aggregate) moving with a constant translational velocity with respect to a fluid can be described in terms of a fractal measure. The spectrum of singularities, f(α) of strength α defined by Halsey et al. has been estimated by scaling the total force distribution and the distribution of force components parallel and perpendicular to the relative velocity for aggregates of different sizes. The scaling of the moments of the force and force component distributions with the cluster mass has also been investigated. Each moment scales with a different exponent which is related to the spectrum f (α ) and the corresponding infinite hierarchy of fractal dimensionalities Dq. © 1987 American Institute of Physics.