TITLE:
Application of the Method of Characteristics to Population Balance Models Considering Growth and Nucleation Phenomena
AUTHORS:
Shahzadi Mubeen ur Rehman, Shamsul Qamar
KEYWORDS:
Population Balance Modeling, Batch Crystallization, Method of Characteristics, Nucleation and Growth
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.13,
July
7,
2014
ABSTRACT: The population
balance modeling is regarded as a universally accepted mathematical framework
for dynamic simulation of various particulate processes, such as
crystallization, granulation and polymerization. This article is concerned with
the application of the method of characteristics (MOC) for solving population
balance models describing batch crystallization process. The growth and
nucleation are considered as dominant phenomena, while the breakage and aggregation
are neglected. The numerical solutions of such PBEs require high order accuracy
due to the occurrence of steep moving fronts and narrow peaks in the solutions.
The MOC has been found to be a very effective technique for resolving sharp
discontinuities. Different case studies are carried out to analyze the accuracy
of proposed algorithm. For validation, the results of MOC are compared with the
available analytical solutions and the results of finite volume schemes. The
results of MOC were found to be in good agreement with analytical solutions and
superior than those obtained by finite volume schemes.