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Lim, Y.I., Lann, J-M.L., Meyer, X.M., Joulia, X., Lee, G. and Yoon, E.S. (2002) On the Solution of Population Balance Equation (PBE) with Accurate Front Tracking Method in Practical Crystallization Processes. Chemical Engineering Science, 57, 3715-3732.
http://dx.doi.org/10.1016/S0009-2509(02)00236-1

has been cited by the following article:

• 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.