Permeability of Fractal Aggregates

It is well known that the permeability and density of an aggregate decreases with its size, affecting its settling velocity and coagulation rate (rate of particle capture) with other particles. This change in aggregate density with size can be described by fractal scaling relationships. Two distinctly different fractal scaling approaches, however, have been used to describe aggregate permeability. In one approach (single-particle-fractal model), the permeability is calculated by assuming primary particles are uniformly distributed in the aggregate. In the other approach (cluster-fractal model), it is assumed that aggregates are composed of primary particles separated into individual clusters that are less permeable than the aggregate. The overall permeability of the aggregate is dependent on the number and sizes of these clusters. Using three different permeability correlations (Brinkman, Happel and Carmen–Kozeny), it is demonstrated through comparison with aggregate settling velocity data that the single-particle-fractal model does not provide realistic predictions of settling velocity as a function of aggregate size. In addition, it is shown that the Carmen–Kozeny permeability equation does not produce realistic settling velocity relationships. The transport settling velocity and capture rate of sinking aggregates in natural and engineered environments should therefore only be calculated using the Happel or Brinkman equations and a cluster-fractal model.