(128i) Modelling the Breakage of Solid Aggregates in Turbulent Flows

The breakage of solid aggregates suspended in a turbulent flow is considered. The aggregates are assumed to be small with respect to the Kolmogorov length scale, and it is assumed that breakage is caused by hydrodynamic stresses acting on the aggregates. Breakage is therefore assumed to follow a first order kinetic where KB(x) is the breakage rate function and x is the aggregate mass. To model KB(x), it is believed that an aggregate breaks instantaneous when the surrounding flow is violent enough to create a hydrodynamic stress that exceeds a critical stress required to break the aggregate. For aggregates smaller than the Kolmogorov length scale the hydrodynamic stress is determined by the viscosity and local energy dissipation rate whose fluctuations are highly intermittent. Hence, the first order breakage kinetics are governed by the frequency the local energy dissipation rate exceeds a critical value (that corresponds to the critical stress). A multifractal model is adopted to describe the statistical properties of the local energy dissipation rate, and a power law relation is used to relate the critical energy dissipation rate above which breakage occurs to the aggregate mass. The model leads to an expression for KB(x) that is zero below a limiting aggregate mass, and that diverges for x going to infinity. To test the model the expression for KB(x) is implemented into a population balance model that aims at describing the aggregation of fully distabilized particles in a turbulent flow. The population balance model account thereby for both aggregation and breakage. These two mechanism lead eventually to a steady state in the cluster mass distribution, and model predictions and are compared to experimental data from the literature for the aggregation of a polystyrene latex in a stirred tank. The model is able to predict the flattening of the decrease of the steady state aggregate size with decreasing solid volume fraction of the suspension. The increase of the steady state mean aggregate size with increasing solid volume fraction requires that the flow field heterogeneity present in stirred tanks is accounted for.