Solution of the bivariate dynamic population balance equation in batch particulate systems: Combined aggregation and breakage

This paper presents a study on the application of an extended sectional grid technique for the solution of the dynamic bivariate population balance equation (PBE) in batch particulate systems. Specifically, particulate processes operating under the action of constant particle aggregation as well as the combined action of constant particle aggregation and an idealized linear breakage mechanism are examined. In order to solve the bivariate PBE an extended sectional grid technique is developed with improved computational efficiency. The performance of the extended sectional grid technique in terms of numerical accuracy and stability is assessed by a direct comparison of the calculated bivariate particle size distributions and/or distribution moments to available analytical solutions. For combined aggregation and breakage processes it is observed that the time required for the computed bivariate PSDs to evolve towards a steady-state distribution is considerably longer than the time required for the univariate number distributions and volume moments to reach steady-state.