The Elasticity and Breakage of Colloidal Aggregates In Shear and Turbulent Flows

Recently, we proposed a free energy expansion-based model for the shear modulus of random colloidal aggregates as they are formed in shear and turbulent flows, resorting to the Cauchy-Born theory of solids. Considering only harmonic terms, application of the fundamental relations of linear elasticity yields an expression for the shear modulus of the aggregates which is proportional to the packing fraction, to the bond rigidity and the coordination number n. The latter term is modelled based on statistical mechanical theories of the liquid state. The main assumption of the model is that interparticle bonds are rigid and the particles are multiply connected. n accounts for the short-range liquid-like order which is a good approximation for dense aggregates that have a high fractal dimension (>=2.5) and introduces a further dependence on the packing fraction. However, also empirical scattering data for the structure can be employed. The model has already been validated against data for cohesive packings of beads. We will show how this approach, combined with the most detailed description of breakage rate in turbulent flows and accounting for turbulence intermittency via a multifractal description, is able to predict the experimentally observed asymptotic scaling between size and shear rate in turbulent breakage of aggregates, without any free parameters. Zaccone et al., Journal of Chemical Physics, 2007