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Two Analytical Approaches for Solution of Population Balance Equations: Particle Breakage Process
Author(s) -
Hasseine Abdelmalek,
Senouci Samra,
Attarakih Menwer,
Bart HandJörg
Publication year - 2015
Publication title -
chemical engineering and technology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.403
H-Index - 81
eISSN - 1521-4125
pISSN - 0930-7516
DOI - 10.1002/ceat.201400769
Subject(s) - breakage , population balance equation , adomian decomposition method , mathematics , population , partial differential equation , mathematical analysis , computer science , demography , sociology , world wide web
Various particulate systems were modeled by the population balance equation (PBE). However, only few cases of analytical solutions for the breakage process do exist, with most solutions being valid for the batch stirred vessel. The analytical solutions of the PBE for particulate processes under the influence of particle breakage in batch and continuous processes were investigated. Such solutions are obtained from the integro‐differential PBE governing the particle size distribution density function by two analytical approaches: the Adomian decomposition method (ADM) and the homotopy perturbation method (HPM). ADM generates an infinite series which converges uniformly to the exact solution of the problem, while HPM transforms a difficult problem into a simple one which can be easily handled. The results indicate that the two methods can avoid numerical stability problems which often characterize general numerical techniques in this area.