The paper focuses on the physical character of floes. 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 4 associated with rupture. For turbulence, the kinetic energy per unit volume is moulded by the velocity scale (nuepsilon)(1/4) and the d/n 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 floe size. In its most rudimentary form, floe structure is based on the model S proportional to kphi/d(3) in which k is the number of bonds broken and phi the potential energy expenditure per bond broken. With appropriate development, this transforms to S = S-0(d/d(0))(D-3) in which d(0) is the primary particle size, D the fractal dimension, and S-0 is a scaling factor controlling the mechanical strength. From the energy criterion, analytical expressions are derived for d in the form d = gammaepsilon(-m/2) in which gamma 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/eta. Theory is examined using 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 which control So. The theory establishes a framework which can be developed further, and applies to flows containing fractal aggregates in both industry and the natural environment. (C) 2004 Elsevier Ltd. All rights reserved.