Approximate solutions of aggregation and breakage population balance equations

The work aims to present a semi-analytical approach based on the homotopy analysis method for finding closed-form solutions and approximate solutions to aggregation and breakage population balance equations. The population balance equations are specific integro-partial differential equations. In this work, we first transform both the aggregation and breakage models into integral equations. Then the resulting integral equations are solved by the homotopy analysis method (HAM) to get the series solution, which in particular cases eventually converges to the exact solution. The semi-analytical solutions for various benchmark aggregation kernels like the Ruckenstein/Pulvermacher kernel and breakage kernels such as the Austin kernel are provided using HAM.