From rupture to structure: the physical character of flocs.

The paper focuses on the physical character of flocs. This is developed through analysis of the impact of hydrodynamic stress on floc size. Theory is developed on the basis of an energy criterion which balances the turbulent kinetic energy against the energy expenditure associated with rupture. For turbulence, the kinetic energy per unit volume is modelled by the velocity scale (nu epsilon)1/4 and the d/eta ratio in which nu, epsilon, eta refer to the kinematic viscosity, the rate of energy dissipation per unit mass and the Kolmogorov length respectively. The distance scale, d, is equivalent to the maximum floc size. In its most rudimentary form, floc structure is based on the model S [symbol, see text] k[symbol, see text]/d3 in which k is the number of bonds broken and [symbol, see text] the potential energy expenditure per bond broken. With appropriate development, this transforms to S = So (d/d(o))D-3 in which d(o) is the primary particle size, D--the fractal dimension, and So--a scaling factor controlling the mechanical strength. From the energy criterion, analytical expressions are derived for d in the form d = gammadelta(-m2) in which gamma and m are constants. Beside the proposal of a model for S, a valuable advance is the development of rupture theory for the continuous domain of d/eta consistent with the Kolmogorov description of turbulence. Theory is compared with a number of published data sets in which there exists knowledge of parameters gamma, m and D. The paper demonstrates how the model can be used as an analytical tool for dissecting the factors such as raw water quality or floc aids which control So.