Population balance discretization for growth, attrition, aggregation, breakage and nucleation

• A new discretization method to solve the one-dimensional PBE is proposed.
• The method is valid for different size change mechanisms and discretization grids.
• The method accuracy is proved by comparing the numerical and analytical solutions.
• The method is based on the moving pivot technique of Kumar and Ramkrishna.
• Special care is taken to numerically handle the growth and attrition terms.

This paper presents a new discretization method to solve one-dimensional population balance equations (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.The developed strategy is based on the moving pivot technique of Kumar and Ramkrishna and the cell-average method of Kumar et al. A novel contribution is proposed to numerically handle the growth and attrition terms, for which a new representation of the number density function within each size class is developed. This method allows describing the number particle fluxes through the class interfaces accurately by preserving two sectional population moments.By comparing the numerical particle size distributions with analytical solutions of one-dimensional PBEs (including different size change mechanisms and particle-size dependent kinetics), the accuracy of the proposed numerical method was proved.