Modelling polydisperse nanoparticle size distributions as produced via flame spray pyrolysis

The correct description of the particulates produced via the flame spray pyrolysis (FSP) process is essential for scale-up studies and new reactor design. With the combination of computational fluid dynamics (CFD) and population balance models (PBM) it is possible to predict the formation and evolution of nanoparticles in such reactors, and estimate final product characteristics. The solution of such PBM, however, can be very costly, given the fact that the phenomena involved in the process require for a bivariate approach. In this work, the direct quadrature method of moments (DQMoM) is employed in order to obtain a polydisperse solution of the PBM, due to its relatively straight forward adaptation from uni- to bivariate cases. Furthermore, the reacting turbulent multiphase flow of the burning spray is described by an Eulerian-Lagrangian framework and solved with the use of CFD. The production of zirconium dioxide nanoparticles from a solution of zirconium n-propoxide in ethanol and propanol is investigated, and experimental data obtained through transmission electron microscopy (TEM) is used for model validation. Accuracy of about 90% is obtained for the first two moments of the distribution and the number of primary particles per agglomerate show good agreement with experiments. [Display omitted] •A PBM is coupled with CFD to describe nanoparticle formation and evolution.•The DQMoM is employed in order to solve the bivariate PBM.•A polydisperse solution of the PBM allows for the prediction of particle size distribution.•An approximation of the DQMoM with three point of quadrature produces accurate results.