Characterisation, scaling and analysis of steady state floc size distribution using a mass balance approach

A framework is developed for describing the steady state floc size distribution Ψ(u) in terms of a scaling ratio u = d/d_L in which d is a representative aggregate diameter and d_L, the corresponding arithmetic average value across the distribution. Flocs were treated as objects of simple fractal structure, such that the floc solids mass (m) complied with the scaling m∝d^D in which D is the fractal dimension. From integration of the solids mass across the size distribution, it was shown that the overall solids concentration (M) followed the dependence M∝NA′d^D_L S(D) in which N is the number of flocs per unit volume, A′ is a packing factor and S(D) a shape factor. Theory was developed to enable estimation of the foundation size distribution for situations in which data on the smallest floc sizes was missing as a result of the lower resolution limit of a measuring system. The framework was used to analyse five data sets displaying different features. Under conditions of varying shear, it was found that the mass scaling dependence shown above could not be explained on the basis of fixed values of A′ or D; this was attributed to a kinetic dependence of the floc solids concentration on shear and beyond the impact of shear on floc size. For the data sets analysed it was shown that the distribution responds to changes in shear and M in a complex way and there were several pointers to the lack of self-similarity.