Solution of bivariate population balance equations with high-order moment-conserving method of classes |
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| Affiliation: | 1. Department of Physics, Chinese Jiliang University, Hangzhou 310028, China;2. The State Key Laboratory of Nonlinear Mechanics, Chinese Academy of Sciences, Beijing 100090, China;3. Institute for Mechanical processes Engineering and Mechanics, Karlsruhe Institute of Technology, Germany;1. Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur 721302, India;2. Thermal Process Engineering, Institute for Process Engineering, Otto von Guericke University, Magdeburg 39106, Germany;1. Department of Biotechnology and Chemical Technology, School of Chemical Technology, Aalto University, Espoo, Finland;2. Institute of Chemical Engineering, Department of Applied Science and Technology, Politecnico di Torino, Torino, Italy |
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| Abstract: | In this work the high-order moment-conserving method of classes (HMMC) (Alopaeus et al., 2006) is extended to solve the bivariate Population Balance Equation (PBE). The method is capable of guaranteeing the internal consistency of the discretized equations for a generic moment set, including mixed-order moments of the distribution. The construction of the product tables in the case of aggregation, breakage and convection in internal coordinate space are discussed. Eventually, several test cases are considered to assess the accuracy of the method. The application to a realistic mass transfer problems in a liquid–liquid system is preliminarily discussed. The comparison with analytical solutions of pure aggregation problems shows that the proposed method is accurate with only a limited number of categories. |
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| Keywords: | Population balance High-order moment-conserving method of classes (HMMC) Bivariate Two-component aggregation Particulate processes Numerical methods |
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