Solution of bivariate aggregation population balance equation: a comparative study

The present work shows a comparative study of two different numerical methods for solving bivariate aggregation population balance equations. In particular, we summarize the cell average technique (Kumar et al. in Comput Chem Eng 32(8):1810–1830, 2008) and the finite volume scheme (Singh et al. in J Comput Appl Math 308:83–97, 2016) for solving pure aggregation population balance equation. The qualitative and quantitative numerical results of various order moments and number density functions are compared with the exact results for analytically tractable kernels. The results reveal that the finite volume scheme approximates the results more accurately and efficiently as compared to the cell average technique. With respect to mixed moments, in particular, the total variance of excess solute (Matsoukas et al. in AIChE J 52(9):3088–3099, 2006), the finite volume scheme is superior to the cell average technique. Additionally, it is also shown that bicomponent moments are more sensitive to the selection of the grid and require finer discretization to reduce errors.