Radial density distribution of fractal clusters

Abstract

The radial density distributions of fractal clusters generated in both DLCA and RLCA conditions by Monte-Carlo off-lattice cluster–cluster aggregation have been investigated. It has been computed by averaging a large number of clusters of same mass to form an average cluster, which is then considered as spherically symmetric. It is found that the radial density distribution, calculated using the mass center of the cluster as the center point, does not follow the fractal scaling, as sometimes assumed in the literature. An empirical model has been proposed to describe the dependence of the radial density distribution on the number of particles in the cluster. The obtained radial density distribution is used to compute permeability profile of the fractal cluster using several literature models, which is then applied to estimate the cluster hydrodynamic radius, R h , by considering the cluster as a porous permeable object and using the solution of Brinkman equations for the fluid flow inside the cluster. The so obtained R h values are compared to those in the literature, computed using the Kirkwood–Riseman (KR) theory. It has been found that, among the five permeability models examined, only the model proposed by Davis (Proceedings of the Institution of Mechanical Engineers Part B 1, 185) provides results in good agreement with those obtained using the KR model. Furthermore, it has been verified that the R h values are insensitive to the model used for the density distribution.