The analytical method and exact solutions of the population balance equation involving growth and breakage processes are investigated in this paper. Partial symmetries, group invariant solutions and reduced integro-ordinary differential equations of the population balance equation are found by scaling transformation group analysis. Explicit exact solutions of the population balance equation are obtained by solving the reduced integro-ordinary differential equations with the method of trial function. The dynamic behavior of explicit exact solutions is analyzed. The obtained group invariant solutions can provide interpretation for the physical processes model, on the other hand, these obtained exact solutions can also be used to verify the correctness and accuracy of numerical solutions.
Fubiao LIN, Qianhong ZHANG. Analysis of scaling transformation group and explicit exact solutions of the population balance equation involving breakage and growth processes. Journal of Zhejiang University (Science Edition), 2022, 49(1): 36-40.
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