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Updated: Jan 2, 2026

Ligand-Mediated Nucleation and Growth of Palladium Metal Nanoparticles
Published on: June 25, 2018
Mass-based finite volume scheme for aggregation, growth and nucleation population balance equation
Mehakpreet Singh1, Hamza Y Ismail1, Themis Matsoukas2
1Department of Chemical Sciences, Bernal Institute, University of Limerick, V94 T9PX Limerick, Ireland.
Abstract:
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.
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