A numerical framework is introduced for solving the population balance equation (PBE) based on conserving (selectively) the total number and volume concentrations of the population. The key idea in this work is to represent the distribution by a secondary particle capable of conserving two low-order moments of the distribution. The mean position of the particle is related algebraically to the total volume and number concentrations. In the framework of the SQMOM (Attarakih et al., 2008) the secondary particle coincides exactly with the primary particle. The resulting discrete model for the PBE consist of two continuity equations for the total number and volume concentrations in the most general case. These equations are found exact as those derived from the continuous PBE for many popular breakage, aggregation and growth functions. The accuracy of the method could be easily increased by increasing the number of primary particles if needed. The method could be considered as an efficient engineering tool for modeling physical and engineering problems having a discrete and multi-scale nature.
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