Journal ArticleDOI
Quadrature method of moments for aggregation-breakage processes.
Daniele Marchisio,R. Dennis Vigil,Rodney O. Fox +2 more
- Vol. 258, Iss: 2, pp 322-334
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TLDR
The quadrature method of moments (QMOM) has already been validated for crystal growth and aggregation; here the method is extended to include breakage and performance is tested for 10 different cases in which the competition between aggregation and breakage leads to asymptotic solutions.Abstract:
Investigation of particulate systems often requires the solution of a population balance, which is a continuity statement written in terms of the number density function. In turn, the number density function is defined in terms of an internal coordinate (e.g., particle length, particle volume) and it generates integral and derivative terms. Different methods exist for numerically solving the population balance equation. For many processes of industrial significance, due to the strong coupling between particle interactions and fluid dynamics, the population balance must be solved as part of a computational fluid dynamics (CFD) simulation. Such an approach requires the addition of a large number of scalars and the associated transport equations. This increases the CPU time required for the simulation, and thus it is clear that it is very important to use as few scalars as possible. In this work the quadrature method of moments (QMOM) is used. The QMOM has already been validated for crystal growth and aggregation; here the method is extended to include breakage. QMOM performance is tested for 10 different cases in which the competition between aggregation and breakage leads to asymptotic solutions.read more
Citations
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Journal ArticleDOI
Solution of population balance equations using the direct quadrature method of moments
Daniele Marchisio,Rodney O. Fox +1 more
TL;DR: The direct quadrature method of moments (DQMOM) is formulated, validated, and tested and shown to be an efficient and accurate method for tracking the moments of the particle size distribution (PSD) in a CFD simulation.
Journal ArticleDOI
Quadrature method of moments for population‐balance equations
TL;DR: In this work the quadrature method of moments (QMOM) is tested for size-dependent growth and aggregation and is validated by comparison with both Monte Carlo simulations and analytical solutions using several functional forms for the aggregation kernel.
Journal ArticleDOI
Application of the direct quadrature method of moments to polydisperse gas–solid fluidized beds
TL;DR: In this article, the direct quadrature method of moments (DQMOM) is implemented in a multi-fluid CFD code to simulate particle aggregation and breakage in a fluidized-bed (FB) reactor.
Journal ArticleDOI
Modeling of Bubble Column Reactors: Progress and Limitations
TL;DR: In this article, the progress reported in the literature during the past decade regarding the use of averaged Eulerian multifluid models and computational fluid dynamics (CFD) to model vertical bubble-driven flows is reviewed.
Journal ArticleDOI
From Form to Function: Crystallization of Active Pharmaceutical Ingredients
TL;DR: The physical properties of the active pharmaceutical ingredient (API) including crystal form, size and shape have the potential to impact bioperformance, particularly for low-solubility compounds, where the rate-limiting step in drug uptake may be the dissolution of the API in the gut.
References
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Journal ArticleDOI
Some problems in particle technology: A statistical mechanical formulation
H.M. Hulburt,S. Katz +1 more
Journal ArticleDOI
On the collision of drops in turbulent clouds
TL;DR: In this paper, a theory of collisions between small drops in a turbulent fluid which takes into account collisions between equal drops was proposed, and it was shown that the collision rate due to the spatial variations of turbulent velocity is N = 1.30(r_1 + r_2)^2(n_1n_2)(e | v)^(1/2), valid for r_1|r_2 between one and two.
Journal ArticleDOI
Description of Aerosol Dynamics by the Quadrature Method of Moments
TL;DR: The quadrature method of moments (QMOM) as mentioned in this paper was proposed to determine the evolution of the lower-order moments of an unknown aerosol distribution without requiring that the size distribution or growth law maintain any special mathematical form.
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