A new framework for numerical modeling of population balance equations: Solving for the inverse cumulative distribution function

Population balance equations (PBE) are a class of integro-partial differential equations with applications spanning a broad range of engineering disciplines. When the state of a population (e.g. droplet size distribution) dictates the mechanical properties of its transporting fluid, modeling tools for solving PBEs must provide good accuracy at very low computational cost. The quadrature method of moments scheme (QMOM) is a popular numerical strategy for many applications, but it has a number of significant weaknesses including the possibility of converging to an incorrect solution. Motivated by limitations of QMOM, this paper introduces a new numerical framework, miCDF, in which standard PBE equations are transformed to solve for the inverse cumulative distribution function. This transformation is straightforward, making use of the triple product rule, and it can be implemented using simple finite difference methods. Through sample calculations, we discuss the advantages and limitations of miCDF relative to QMOM. (c) 2022 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http:// creativecommons.org/licenses/by/4.0/).

Automated summary

Population balance equations are a type of integro-partial differential equations widely used in engineering disciplines. This paper introduces a new numerical framework, miCDF, which transforms the standard PBE equations to solve for the inverse cumulative distribution function. It provides a straightforward and low-cost method for solving PBEs.