Floc rupture and turbulence: a framework for analysis

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 moulded by the velocity scale (νε)^1/4 and the d/η ratio in which ν, ε, η 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∝k?/d³ in which k is the number of bonds broken and ? the potential energy expenditure per bond broken. With appropriate development, this transforms to S=S₀(d/d₀)^D−3 in which d₀ is the primary particle size, D the fractal dimension, and S₀ is a scaling factor controlling the mechanical strength. From the energy criterion, analytical expressions are derived for d in the form d=γε^−m/2 in which γ and m are constants. Beside the proposal of models for S, a valuable advance is the development of rupture theory for the whole domain of d/η. Theory is examined using a number of published data sets in which there exists knowledge of parameters γ, m and D. The paper demonstrates how the model can be used as an analytical tool for dissecting the factors which control S₀. The theory establishes a framework which can be developed further, and applies to flows containing fractal aggregates in both industry and the natural environment.