Population Balance Discretization for Growth, Attrition, Aggregation, Breakage and Nucleation

Abstract

This paper presents a new discretization method to solve the population balance equation (PBE) for batch and unsteady/steady-state continuous perfectly-mixed systems. The numerical technique is valid for any size change mechanism (i.e., growth, aggregation, attrition, breakage and nucleation occurring alone or in combination) and different discretization grids. Special care is taken to numerically handle the growth and attrition terms, for which a new representation of the number density function within each size class is proposed. This method allows describing the number particles fluxes through the classes interfaces accurately by preserving two sectional population moments. This is accomplished by defining a representative size for each class, which is updated as particles appear and disappear into/from each class. The accuracy of the proposed numerical method is proved by comparing the numerical particle size distributions with available or here developed analytical PBE solutions for different size change mechanisms and particle size dependent kinetics.