Large time solution for collisional breakage model: Laplace transformation based accelerated homotopy perturbation method

Abstract

The behavior of several particulate processes, such as cell interaction, blood clotting, bubble formation, grain breakage, and cheese formation from milk, have been studied using coagulation and fragmentation models (Fogelson and Guy, 2008 [1]; Pazmiño et al., 2022 [2]; Chen et al., [3]). Various studies utilize the linear fragmentation model to simplify the underlying physics. However, in real-life scenarios, particles form due to the collision of two particles, leading to a non-linear collisional breakage model. Unfortunately, the collisional breakage model is less explored due to its complex behavior. While analytical solutions are difficult to compute and are still missing in the literature, this article proposes an approximate solution for the model using the Laplace-based accelerated homotopy perturbation method. Further, coupling with Padé approximant, the accuracy of the solution is extended for the longer time. Considering various physically relevant kernels, the approximate series solutions are compared with the well known finite-volume solutions to measure the accuracy in terms of qualitative and quantitative errors. The article also encompasses theoretical convergence analysis and error estimations to enhance comprehension of the proposed formulation.