Abstract
Population balance modeling is an established framework to describe the dynamics of particle populations in disperse phase systems found in a broad field of industrial, civil, and medical applications. The resulting population balance equations account for the dynamics of the number density distribution functions and represent (systems of) partial differential equations which require sophisticated numerical solution techniques due to the general lack of analytical solutions. A specific class of solution algorithms, so-called moment methods, is based on the reduction of complex models to a set of ordinary differential equations characterizing dynamics of integral quantities of the number density distribution function. However, in general, a closed set of moment equations is not found and one has to rely on approximate closure methods. In this contribution, a concise overview of the most prominent approximate moment methods is given.
Highlights
Disperse phase systems are a core part of many industrial processes, such as crystallization, granulation, drying, and fermentation, but are encountered in biomedicine, astrophysics, and meterology
The resulting models represent partial differential equations, so-called population balance equations (PBEs), that account for the change of the particle number density distribution
(II) In contrast, the bottom-up approach is based on detailed first-principle modeling of the individual particle behavior, e.g., ordinary or stochastic differential equations, which is adapted to single-particle experimental data
Summary
Disperse phase systems are a core part of many industrial processes, such as crystallization, granulation, drying, and fermentation, but are encountered in biomedicine, astrophysics, and meterology They are characterized by a population of individuals (particles) that interact with their environment and with each other. The resulting models represent (systems of) partial differential equations, so-called population balance equations (PBEs), that account for the change of the particle number density distribution. Thereby, focus is on methods that aim to solve directly for the moments without having to calculate the full distribution first Techniques of the latter class, which are applied, e.g., in relation to the solution of the Fokker–Planck equation [58,59], would be a worthwhile topic for a stand-alone manuscript and are not included in this review. Algorithms for multivariate PBEs are discussed and further needs of development are identified
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