TY - JOUR
T1 - Challenges and opportunities concerning numerical solutions for population balances
T2 - a critical review
AU - Singh, Mehakpreet
AU - Ranade, Vivek
AU - Shardt, Orest
AU - Matsoukas, Themis
N1 - Publisher Copyright:
© 2022 The Author(s). Published by IOP Publishing Ltd.
PY - 2022/9/23
Y1 - 2022/9/23
N2 - 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.
AB - 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.
KW - grids
KW - nonlinear integro-partial differential equations
KW - numerical methods
KW - particles
KW - population balance equation
UR - http://www.scopus.com/inward/record.url?scp=85139143438&partnerID=8YFLogxK
U2 - 10.1088/1751-8121/ac8a42
DO - 10.1088/1751-8121/ac8a42
M3 - Review article
AN - SCOPUS:85139143438
SN - 1751-8113
VL - 55
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
IS - 38
M1 - 383002
ER -