A note on the analytical approach and its efficiency for solving multivariate breakage population balance equations

Breakage population balance equations are of significant importance in powder technology, specifically in the processes which involve reduction of particle size, milling, granulation and material refinement. The dynamics of breakage process can be captured well by multivariate formulations but are challenging to solve due to strong non-linearity and contributions from internal and external coordinates. To address these challenges, a semi-analytical technique based on the homotopy of functions is employed to solve linear and collisional breakage equations in a multivariate framework. Accuracy and computational performance of the proposed method are validated with respect to the Adomian decomposition method and finite volume method. Numerical results show that the proposed homotopy-based method outperforms both the existing techniques in terms of computational accuracy. Thus, homotopy analysis method can be considered as a robust and powerful tool to solve intricate multivariate particulate problems arising in scientific research and industrial applications.

Subjects

35Q70

45K05

Primary 34A12

Secondary 35F10

DDC Class

660.284: Chemical Reactors

660.2: Chemical Engineering

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A note on the analytical approach and its efficiency for solving multivariate breakage population balance equations