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

Mehakpreet Singh,Ashish Kumar,Vivek Ranade,Saeed Shirazian,Gavin Walker

doi:10.3390/pharmaceutics12121152

Mehakpreet Singh, Ashish Kumar + Show 3 more

Open Access

https://doi.org/10.3390/pharmaceutics12121152

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Abstract

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 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 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 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.

Highlights

Population balance equations (PBEs) describe the behavior of particle properties’ changes due to phenomena such as nucleation, growth, aggregation and breakage [1]
This emphasizes the need for accurate prediction of particle size distribution evolution, which depends on the selection of a suitable numerical scheme to solve the PBEs and aggregation
We focus on the relevance of different numerical schemes for multivariate PBE solution in terms of their capability to capture the degree of mixing during aggregation

Summary

Introduction

Population balance equations (PBEs) describe the behavior of particle properties’ changes due to phenomena such as nucleation, growth, aggregation and breakage [1]. The aggregation mechanism is caused by the mixing-driven presence of liquid binder in the system For such processes, the ability to mechanistically characterize aggregation requires consideration of the degree of mixing between particles and the binder phase. The study concluded that the scaling of the variance indicates that the mixing of components is not characterized by a time scale but by a size scale. This emphasizes the need for accurate prediction of particle size distribution evolution, which depends on the selection of a suitable numerical scheme to solve the PBEs and aggregation

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