Bänsch E, Pflug L, Schikarski T (2023)
Publication Type: Journal article
Publication year: 2023
Book Volume: 190
Pages Range: 814-828
Supersaturation as the thermodynamic driving force of particulate precipitation couples the mixing of solute compounds with the solid formation consisting of nucleation and molecular growth. Because the process spans many orders of magnitude in space and time, gathering spatio-temporal information by experiments is hardly achievable. Numerical simulation of the nonlinear, non-local balance equations for mass, momentum and dispersed phase provide detailed solution information in space and time. We here introduce a novel, highly accurate and very efficient numerical formulation of the population balance equations for the dispersed phase coupled to the concentration and velocity field. We reformulate the problem in terms of a fixed-point equation solving the population balance equation along Lagrangian paths with the recently developed exact Method of Moments (eMoM, Pflug et al., 2020) coupled to the concentration field (Eulerian frame). The analytical reformulation provides the information about the full particle size distribution while the computational effort remains in the order of classical moment methods and is much less than numerical schemes approximating the full particle size distribution such as finite volume methods. Furthermore, we explore the difference between an Euler-Euler and Euler-Lagrange coupling considering moderate to large P é clet numbers for the solutes and particles. It turns out that the mean particle size as a solution of the population balance is much more sensitive to the numerical discretization of the advection term than the approximation of the number density function. Based on this finding, we eventually explore the impact of particle diffusion on the solid formation process and give guidelines, when particle diffusion should be taken into account.
Bänsch, E., Pflug, L., & Schikarski, T. (2023). Highly accurate and numerical tractable coupling of nanoparticle nucleation, growth and fluid flow. Chemical Engineering Research & Design, 190, 814-828. https://dx.doi.org/10.1016/j.cherd.2022.12.029
Bänsch, Eberhard, Lukas Pflug, and Tobias Schikarski. "Highly accurate and numerical tractable coupling of nanoparticle nucleation, growth and fluid flow." Chemical Engineering Research & Design 190 (2023): 814-828.