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