Mass–radius relation for fractal aggregates of polydisperse particles

Mass–radius relation for fractal aggregates of polydisperse particles is derived from the Hausdorff measure. The Debye–Brinkman concept of treating polymer coils as uniformly permeable spheres is practically utilized for aggregates composed of not many polydisperse primary particles. The method is based on the calculation of permeability of the system contained inside the sphere circumscribed on the aggregate. The values of normalized hydrodynamic radius for aggregates with log-normal distribution of constituents are close if calculated by the mass–radius relation and by the permeability. Mass–radius relation for aggregates of polydisperse particles is compatible with the aggregation act equation, previously verified by aggregate structure, its dynamics and the aggregation kinetics. It is applicable to describe the free settling velocity of fractal aggregates of polydisperse solids.