Solutions of Mixed Population Balance Equation With Nonlinear Multivariate Aggregation, Breakage and Growth

ABSTRACT

The mixed population balance equation including aggregation, collision‐induced breakage, and growth has significant usage in particulate modeling. These models are highly nonlinear and difficult to solve accurately. Discretization‐based sectional methods often lead to complex, grid‐dependent formulations. This reduces computational efficiency and may affect numerical stability. Extending these approaches to multivariate models is also challenging. To overcome these issues, a semi‐analytical mesh‐free method based on a homotopy approach is proposed. The method is further developed to handle multivariate models in a systematic way. Temimi‐Ansari method [Comput. Math. Appl., 2011, 61(2), 203‐210] is also applied to the same problem to examine the performance of the proposed approach. The accuracy is evaluated through the prediction of the solution and the associated moment functions. Numerical examples based on equi‐partition of kinetic energy (EKE) kernels, relevant to droplet behavior, are considered. The results show that the proposed method is simple, efficient, and provides accurate solutions.