作者: Alireza Hosseini , Ala Eldin Bouaswaig , Sebastian Engell
DOI: 10.1016/J.CES.2012.11.021
关键词: Statistical physics 、 Kernel (statistics) 、 Stochastic differential equation 、 Probability distribution 、 Discretization 、 Population balance equation 、 Mathematics 、 Population 、 Fokker–Planck equation 、 Inverse problem
摘要: Abstract A recent investigation on the homopolymerization of styrene ( Hosseini et al., 2012a ) showed that classical population balance models are incapable predicting evolution breadth experimental particle size distributions correctly when a high resolution discretization method is used to suppress numerical errors. Also by re-tuning model parameters predictions did not fit results which points structural inadequacy conventional deterministic growth in describing experimentally observed broadening phenomenon. Two novel approaches suggested this work improve predictions. In first approach, possibly dependent stochastic term added kernel account for inhomogeneities process. The probability distribution resulting differential equation evolves over time based Fokker–Planck equation. (possibly dependent) dispersion as tuning results. second extracted from characteristics transient distributions. described terms states system affect advantages and disadvantages both highlighted.