Journal Article10.1002/AIC.10228
High resolution algorithms for multidimensional population balance equations
TL;DR: In this article, high-resolution finite volume methods developed for compressible gas dynamics have been applied to aerodynamics, astrophysics, detonation waves, and related fields where shock waves occur.
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Abstract: Population balance equations have been used to model a wide range of processes including polymerization, crystallization, cloud formation, and cell dynamics. Rather than developing new algorithms specific to population balance equations, it is proposed to adapt the high-resolution finite volume methods developed for compressible gas dynamics, which have been applied to aerodynamics, astrophysics, detonation waves, and related fields where shock waves occur. High-resolution algorithms are presented for simulating multidimensional population balance equations with nucleation and size-dependent growth rates. For sharp distributions, these high-resolution algorithms can achieve improved numerical accuracy with orders-of-magnitude lower computational cost than other finite difference and finite volume algorithms. The algorithms are implemented in the ParticleSolver software package, which is applied to batch and continuous processes with one and multiple internal coordinates. © 2004 American Institute of Chemical Engineers AIChE J, 50: 2738 –2749, 2004
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Citations
Crystal Shape Engineering
Michael A. Lovette,Andrea R. Browning,Derek W. Griffin,Jacob P. Sizemore,Ryan C. Snyder,Michael F. Doherty +5 more
TL;DR: In this paper, the state-of-the-art in modeling crystallization processes over a range of length scales relevant to nucleation through process design is discussed, as well as opportunities for continued research and specific areas where significant advancements are needed.
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A comparative study of high resolution schemes for solving population balances in crystallization
Shamsul Qamar,Shamsul Qamar,Martin Peter Elsner,I. A. Angelov,Gerald Warnecke,Andreas Seidel-Morgenstern,Andreas Seidel-Morgenstern +6 more
TL;DR: In this article, the authors demonstrate the applicability and usefulness of high-resolution finite volume schemes for the solution of population balance equations (PBEs) in crystallization processes.
176
Simulation of Mixing Effects in Antisolvent Crystallization Using a Coupled CFD-PDF-PBE Approach
TL;DR: In this paper, a turbulent computational fluid dynamics (CFD) code was coupled with a multienvironment probability density function (PDF) model, which captured the micromixing in the subgrid scale, and the population balance equation, which models the evolution of the crystal size distribution.
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Recent progress of continuous crystallization
TL;DR: In this article, the development of continuous crystallization in recent years, including novel crystallizers, control strategies, models and some assistive technologies, is summarized, and the authors conclude that continuous crystallisation is still not as universal as batch crystallization due to the existence of the drawbacks, such as blockage and encrustation.
119
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