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2007-15

An efficient numerical technique for solving population balance equation involving aggregation, breakage, growth and nucleation

by Kumar, J., Peglow, M., Warnecke, G. Heinrich, S..


Series: 2007-15, Preprints

MSC:
65R99 None of the above, but in this section
65M99 None of the above, but in this section

Abstract:
A new discretization for simultaneous aggregation, breakage, grwoth and nucleation is presented. The new dicretization is an extension of the cell average technique developed by the authors (J. Kumar et al.; 2006, Chem. Eng. sci.; 61, 3327-3342). It is shown that the cell average scheme enjoys the major advantage of simplicity for solving combined problems over other existing schemes. This is done by a special coupling of the different processes that treats all processes in a similar fashion as it handles the individual process. It is demonstrated the the new coupling makes the technique mores useful by being not only more accurate but also computationally less expensive. At first, the coupling is performed for combined aggregation and breakage problems. Furhtermore, a new idea that considers the growth process as aggregation of existing particle with new small nuclei is presented. In that way the resulting discretization of the growth process becomes very simple and consistent with the first two moments exactly without any computational difficulties like appearance of negative values or instability etc.
The numerical scheme proposed in this work is consistent only with the first two moments but it can easily be extended to the consistency with any two or more than two moments. Finally, the discretization of pure and coupled problems is tasted on several analytical solvable problems.

Keywords:
Population balance; Aggregation; Breakage; Growth; Nucleation; Particle; Batch.