Challenges and opportunities concerning numerical solutions for population balances: a critical review

Mehakpreet Singh, Vivek Ranade, Orest Shardt, Themis Matsoukas

Research output: Contribution to journalReview articlepeer-review

25 Scopus citations


Population balance models are tools for the study of dispersed systems, such as granular materials, polymers, colloids and aerosols. They are applied with increasing frequency across a wide range of disciplines, including chemical engineering, aerosol physics, astrophysics, polymer science, pharmaceutical sciences, and mathematical biology. Population balance models are used to track particle properties and their changes due to aggregation, fragmentation, nucleation and growth, processes that directly affect the distribution of particle sizes. The population balance equation is an integro-partial differential equation whose domain is the line of positive real numbers. This poses challenges for the stability and accuracy of the numerical methods used to solve for size distribution function and in response to these challenges several different methodologies have been developed in the literature. This review provides a critical presentation of the state of the art in numerical approaches for solving these complex models with emphasis in the algorithmic details that distinguish each methodology. The review covers finite volume methods, Monte Carlo method and sectional methods; the method of moments, another important numerical methodology, is not covered in this review.

Original languageEnglish (US)
Article number383002
JournalJournal of Physics A: Mathematical and Theoretical
Issue number38
StatePublished - Sep 23 2022

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modeling and Simulation
  • Mathematical Physics
  • General Physics and Astronomy


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