An open-source computational framework for the solution of the bivariate population balance equation

Singh, Deepak Kumar; Brito-Parada, Pablo R.; Bhutani, Gaurav

doi:10.1016/j.compchemeng.2022.107780

Cited by 2 publications

(2 citation statements)

References 62 publications

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“…The concept of the bidisperse distribution has been extensively used (although it is not recognized as such) by the so-called quadrature methods of moments used for the solution of population balance equations [14,15]. The equation is integrated numerically using the bidisperse distribution to advance four moments of the distribution.…”

Section: Methodsmentioning

confidence: 99%

Approximation of Any Particle Size Distribution Employing a Bidisperse One Based on Moment Matching

Kostoglou,

Karapantsios

2024

Colloids and Interfaces

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Dispersed phases like colloidal particles and emulsions are characterized by their particle size distribution. Narrow distributions can be represented by the monodisperse distribution. However, this is not the case for broader distributions. The so-called quadrature methods of moments assume any distribution as a bidisperse one in order to solve the corresponding population balance. The generalization of this approach (i.e., approximation of the actual particle size distribution according to a bidisperse one) is proposed in the present work. This approximation helps to compress the amount of numbers for the description of the distribution and facilitates the calculation of the properties of the dispersion (especially convenient in cases of complex calculations). In the present work, the procedure to perform the approximation is evaluated, and the best approach is found. It was shown that the approximation works well for the case of a lognormal distribution (as an example) for a moments order from 0 to 2 and for dispersivity up to 3.

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Section: Methodsmentioning

confidence: 99%

Approximation of Any Particle Size Distribution Employing a Bidisperse One Based on Moment Matching

Kostoglou,

Karapantsios

2024

Colloids and Interfaces

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“…Some other ex-istence and uniqueness studies can also be found in [14,15]. Various numerical approaches in 1D and 2D for solving these models have been discussed in detail by [16][17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

A Note on the Volume Conserving Solution to Simultaneous Aggregation and Collisional Breakage Equation

Kharchandy

Das

Thota

et al. 2023

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A new population balance model is introduced, in which a pair of particles can coagulate into a larger one if their encounter is a completely inelastic collision; otherwise, one of them breaks into multiple fragments (two or more) due to the elastic collision. Mathematically, coagulation and breakage models both manifest nonlinearity behavior. We prove the global existence and uniqueness of the solution to this model for the compactly supported kinetic kernels and an unbounded breakage distribution function. A further investigation dealt with the volume conservation property (necessary condition) of the solution.

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An open-source computational framework for the solution of the bivariate population balance equation

Cited by 2 publications

References 62 publications

Approximation of Any Particle Size Distribution Employing a Bidisperse One Based on Moment Matching

Approximation of Any Particle Size Distribution Employing a Bidisperse One Based on Moment Matching

A Note on the Volume Conserving Solution to Simultaneous Aggregation and Collisional Breakage Equation

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