On the solution of the population balance equation: From global to local constrained maximum entropy method

01.Aug.2019

​We propose continuous approximations to the population balance equation based on maximization of the Shannon entropy subject to the expected properties of the particle size distribution (PSD). This solution is used to close the source term of the PBE with careful sampling of the PSD at prescribed points as roots of the Nth-degree Legendre polynomial. Being a maximum entropy functional, the solution is unique and converges to the exact solution as the number of sampling points increases with accurate calculation of PSD integral properties. The accuracy and efficiency of the method are demonstrated by trying different analytical case studies (particle aggregation, aggregation and growth, and particle breakage) where we show it is not restricted to prespecified particle kinetics and functional forms. As practical case study, we modelled the coupled hydrodynamics and mass transfer in different liquid extraction columns and compared the calculated results with published steady state experimental data.

https://www.researchgate.net/publication/335359232_On_the_solution_of_the_population_balance_equation_From_global_to_local_constrained_maximum_entropy_method​