Analytical approach for solving population balances: a homotopy perturbation method. (26th August 2019)

• Record Type: Journal Article
• Authors: Kaur, Gurmeet; Singh, Randhir; Singh, Mehakpreet; Kumar, Jitendra; Matsoukas, Themis
• Is Part Of: Journal of physics. Volume 52:Number 38(2019)
• Publication Date: 2019-08-26
• Subjects: particles -- population balance equation -- homotopy perturbation method -- analytical solution; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/ab2cf5
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: In the present work, a new approach is proposed for finding the analytical solution of population balances for aggregation and fragmentation process. This approach is relying on the idea of the homotopy perturbation method (HPM). The HPM solves both linear and nonlinear initial and boundary value problems without nonphysical restrictive assumptions such as linearization and discretization. It gives the solution in the form of series with easily computable solution components. The outcome of this study reveals that the proposed method can avoid numerical stability problems which often characterize in general numerical techniques related to this area. Several examples including Austin's kernel, available in literature, are examined to demonstrate the accuracy and applicability of the proposed method. In addition, the analytical solution to two new kernels (the power-law kernel in fragmentation and the Ruckenstein/Pulvermacher kernel in aggregation) are also introduced.