The Foundation of the Population Balance Equation: A Review

In dispersed multi-phase flow modeling using population balances (PBs), the dispersed phase system is considered as a population of entities of the dispersed phase distributed not only in physical space but also in an abstract property space. Different frameworks exist for the formulation of the population balance equation (PBE): (i) continuum mechanical principles, (ii) statistical Boltzmann-like equation, or (iii) probability principles. The source terms, that is, birth and death of the entities in the population, are defined from mechanistic principles. This article presents a review of the foundation of the PBE.