Hydrodynamic stress on fractal aggregates of spheres

We calculate the average hydrodynamic stress on fractal aggregates of spheres using Stokesian dynamics. We find that for fractal aggregates of force-free particles, the stress does not grow as the cube of the radius of gyration, but rather as the number of particles in the aggregate. This behavior is only found for random aggregates of force-free particles held together by hydrodynamic lubrication forces. The stress on aggregates of particles rigidly connected by inter-particle forces grows as the radius of gyration cubed. We explain this behavior by examining the transmission of the tension along connecting lines in an aggregate and use the concept of a persistance length in order to characterize this stress transmission within an aggregate.