Breakage rate of colloidal aggregates in shear flow through stokesian dynamics

We study the first breakage event of colloidal aggregates exposed to shear flow by detailed numerical analysis of the process. We have formulated a model, which uses stokesian dynamics to estimate the hydrodynamic interactions among the particles in a cluster, van der Waals interactions and Born repulsion to describe the normal interparticle interactions, and the tangential interactions through discrete element method to account for contact forces. Fractal clusters composed of monodisperse spherical particles were generated using different Monte Carlo methods, covering a wide range of cluster masses (N(sphere) = 30-215) and fractal dimensions (d(f) = 1.8-3.0). The breakup process of these clusters was quantified for various flow magnitudes (γ), under both simple shear and extensional flow conditions, in terms of breakage rate constant (K(B)), mass distribution of the produced fragments (FMD, f(m,k)), and critical stable aggregate mass (N(c)), defined as the largest cluster mass that does not break under defined flow conditions. The breakage rate K(B) showed a power law dependence on the product of the aggregate size and the applied stress, with values of the corresponding exponents depending only on the aggregate fractal dimension and the type of flow field, whereas the prefactor of the power law relation also depends on the size of the primary particles comprising a cluster. The FMD was fitted by Schultz-Zimm distribution, and the parameter values showed an analogous dependence on the product of the aggregate size and the applied stress similar to the rate constant. Finally, a power law relation between the applied stress and corresponding largest stable aggregate mass was found, with an exponent value depending on the aggregate fractal dimension. This unique and detailed analysis of the breakage process can be directly utilized to formulate a breakage kernel used in solving population balance equations.