Aggregate structure and size distribution at steady state shear aggregation

The competition between aggregation and fragmentation at the steady state of the shear aggregation is analyzed. Aggregation probability is formulated based on the Smoluchowski theory, modified to take into account the fractal morphology of flocs. A formula for fragmentation probability is proposed such to guarantee a higher aggregation probability for smaller aggregates and a higher fragmentation probability for larger ones. This is done in order to follow a bell-shaped distribution observed, being the effect of simultaneously occurring aggregation and fragmentation. The mass balance between produced and fragmented aggregates makes it possible to calculate the interdependence between fractal dimension and geometric SD of the aggregate radius for the lognormal distribution. This dependence well corresponds with experimental data. The obtained curve represents the possible equilibrium states. The actual equilibrium parameters depend mainly on shear and shear history, but the range of geometric standard deviation of the aggregate radius distribution by number, 1.5–1.7, may be regarded as expected for the steady state of shear aggregation.