Mobility of permeable aggregates: effects of shape and porosity

Hydrodynamic resistances of spheroidal porous agglomerates are calculated theoretically for circumstances when the flow is directed either parallel or perpendicular to their symmetry axes. Expressions for the equivalent mobility radii of oblate and prolate spheroids are calculated and generalized for wide ranges of particle porosities, sizes and fractal dimensions Df. Aggregate shape and permeability are shown to have competitive effects on their mobility. Permeability has the strongest effect on the mobility radii of agglomerates with shapes close to spherical and for extremely porous structures. For fractal-like agglomerates, permeability has the strongest effects for low Df structures, composed of about several hundreds of elementary particles. Mobility radii of these agglomerates are found to have fractal dimensions about 10% higher than the one that could be obtained from the geometrical size analysis. Large fractal agglomerates behave like impermeable bodies even if their average porosity is large. A similar behavior is characteristic of very small agglomerates, because their porosity is normally low. The calculated mobility radii are used for correlating the size-dependent free fall velocity of porous ice crystals.