A Semi-Empirical Model to Estimate Maximum Floc Size in a Turbulent Flow

The basic model for agglomerate breakage under the effect of hydrodynamic stress (d(max) = C.G(−)(γ)) is only applicable for low velocity gradients (<500 s(−1)) and is often used for shear rates that are not representative of the global phenomenon. This paper presents a semi-empirical model that is able to predict mean floc size in a very broad shear range spanning from aggregation to floc fragmentation. Theoretical details and modifications relating to the orthokinetic flocculation output are also provided. Modelling changes in turbidity in relation to the velocity gradient with this model offer a mechanistic approach and provide kinetic agglomeration and breakage index k(a) and k(b). The floc breakage mode is described by the relationship between the floc size and the Kolmogorov microscale. Shear-related floc restructuring is analysed by monitoring the fractal dimension. These models, as well as those used to determine floc porosity, density and volume fraction, are validated by the experimental results obtained from several flocculation operations conducted on ultrafine kaolin in a 4-litre reactor tank compliant with laws of geometric similarity. The velocity gradient range explored was from 60 to 6000 s(−1).