scholarly journals Mass-based finite volume scheme for aggregation, growth and nucleation population balance equation

2019 ◽  
Vol 475 (2231) ◽  
pp. 20190552 ◽  
Author(s):  
Mehakpreet Singh ◽  
Hamza Y. Ismail ◽  
Themis Matsoukas ◽  
Ahmad B. Albadarin ◽  
Gavin Walker
Keyword(s):  
Finite Volume ◽  
Balance Equation ◽  
Population Balance ◽  
Distribution Functions ◽  
Population Balance Equation ◽  
Finite Volume Scheme ◽  
Number Density ◽  
Finite Volume Schemes ◽  
One Dimensional ◽  
Number Distribution

In this paper, a new mass-based numerical method is developed using the notion of Forestier-Coste & Mancini (Forestier-Coste & Mancini 2012, SIAM J. Sci. Comput. 34 , B840–B860. ( doi:10.1137/110847998 )) for solving a one-dimensional aggregation population balance equation. The existing scheme requires a large number of grids to predict both moments and number density function accurately, making it computationally very expensive. Therefore, a mass-based finite volume is developed which leads to the accurate prediction of different integral properties of number distribution functions using fewer grids. The new mass-based and existing finite volume schemes are extended to solve simultaneous aggregation-growth and aggregation-nucleation problems. To check the accuracy and efficiency, the mass-based formulation is compared with the existing method for two kinds of benchmark kernels, namely analytically solvable and practical oriented kernels. The comparison reveals that the mass-based method computes both number distribution functions and moments more accurately and efficiently than the existing method.

scholarly journals Characterization of Simultaneous Evolution of Size and Composition Distributions Using Generalized Aggregation Population Balance Equation

Pharmaceutics ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 1152
Author(s):  
Mehakpreet Singh ◽  
Ashish Kumar ◽  
Saeed Shirazian ◽  
Vivek Ranade ◽  
Gavin Walker
Keyword(s):  
Finite Volume ◽  
Balance Equation ◽  
Numerical Scheme ◽  
Population Balance ◽  
Population Balance Equation ◽  
Finite Volume Scheme ◽  
Average Technique ◽  
Volume Scheme ◽  
Density Prediction ◽  
Cell Average

The application of multi-dimensional population balance equations (PBEs) for the simulation of granulation processes is recommended due to the multi-component system. Irrespective of the application area, numerical scheme selection for solving multi-dimensional PBEs is driven by the accuracy in (size) number density prediction alone. However, mixing the components, i.e., the particles (excipients and API) and the binding liquid, plays a crucial role in predicting the granule compositional distribution during the pharmaceutical granulation. A numerical scheme should, therefore, be able to predict this accurately. Here, we compare the cell average technique (CAT) and finite volume scheme (FVS) in terms of their accuracy and applicability in predicting the mixing state. To quantify the degree of mixing in the system, the sum-square χ2 parameter is studied to observe the deviation in the amount binder from its average. It has been illustrated that the accurate prediction of integral moments computed by the FVS leads to an inaccurate prediction of the χ2 parameter for a bicomponent population balance equation. Moreover, the cell average technique (CAT) predicts the moments with moderate accuracy; however, it computes the mixing of components χ2 parameter with higher precision than the finite volume scheme. The numerical testing is performed for some benchmarking kernels corresponding to which the analytical solutions are available in the literature. It will be also shown that both numerical methods equally well predict the average size of the particles formed in the system; however, the finite volume scheme takes less time to compute these results.

scholarly journals Finite volume approximation of nonlinear agglomeration population balance equation on triangular grid

2019 ◽  
Vol 137 ◽  
pp. 105430 ◽  
Author(s):  
Mehakpreet Singh ◽  
Hamza Y. Ismail ◽  
Randhir Singh ◽  
Ahmad B. Albadarin ◽  
Gavin Walker
Keyword(s):  
Finite Volume ◽  
Balance Equation ◽  
Population Balance ◽  
Population Balance Equation ◽  
Triangular Grid ◽  
Volume Approximation ◽  
Finite Volume Approximation

Discrete finite volume approach for multidimensional agglomeration population balance equation on unstructured grid

2020 ◽  
Vol 376 ◽  
pp. 229-240 ◽  
Author(s):  
Mehakpreet Singh ◽  
Randhir Singh ◽  
Sukhjit Singh ◽  
Gavin Walker ◽  
Themis Matsoukas
Keyword(s):  
Finite Volume ◽  
Balance Equation ◽  
Unstructured Grid ◽  
Population Balance ◽  
Population Balance Equation ◽  
Finite Volume Approach

Finite volume approximations of breakage population balance equation

2016 ◽  
Vol 110 ◽  
pp. 114-122 ◽  
Author(s):  
Jitraj Saha ◽  
Jitendra Kumar ◽  
Andreas Bück ◽  
Evangelos Tsotsas
Keyword(s):  
Finite Volume ◽  
Balance Equation ◽  
Population Balance ◽  
Population Balance Equation

scholarly journals Conservative Finite Volume Schemes for Multidimensional Fragmentation Problems

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 635
Author(s):  
Jitraj Saha ◽  
Andreas Bück
Keyword(s):  
Finite Volume ◽  
Three Dimensional ◽  
Test Problems ◽  
Finite Volume Scheme ◽  
Finite Volume Schemes ◽  
One Dimensional ◽  
Volume Scheme ◽  
Multidimensional Problems ◽  
Conservative Form ◽  
Fragmentation Equation

In this article, a new numerical scheme for the solution of the multidimensional fragmentation problem is presented. It is the first that uses the conservative form of the multidimensional problem. The idea to apply the finite volume scheme for solving one-dimensional linear fragmentation problems is extended over a generalized multidimensional setup. The derivation is given in detail for two-dimensional and three-dimensional problems; an outline for the extension to higher dimensions is also presented. Additionally, the existing one-dimensional finite volume scheme for solving conservative one-dimensional multi-fragmentation equation is extended to solve multidimensional problems. The accuracy and efficiency of both proposed schemes is analyzed for several test problems.

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