Tracer studies of high-shear granulation: II. Population balance modeling



A population balance framework developed describes the tracer studies in Part I. A two internal coordinate population balance equation (PBE) links the evolution with time of granule-size and tracer-mass distributions to underlying rate processes. A new analytical PBE was developed for the tracer distribution and novel numerical techniques, including a new discretized population balance equation for breakage or grinding. Also developed is a general differential technique for extracting rate constants from measurements of particle-size distributions. Granulation in a high-shear mixer proceeds after nucleation, not studied here, with very high initial breakage rates but a relatively unchanging aggregation rate constant. The breakage function is bimodal on a mass basis and the selection rate decays exponentially over about 20 s. A heterogeneous strength hypothesis was used to account for this time dependence. Aggregation rates are the highest for interactions between small and large granules and may be quantitatively given by the Equipartition of kinetic energy kernel developed from the theory of collisions between gas molecules. The model can describe granule-size and tracer-mass distributions simultaneously with great accuracy. The need to replace time as a driving force variable in the kinetics for these systems is identified.