Bridging Macro- and Mesoscopic Methodologies for the Modeling of Nanoparticle Synthesis and Population Dynamics

The present work aims for the development of new classes of multiscale simulation models for gas-phase nanoparticle synthesis processes that are tailored for application with computational fluid dynamics (CFD). Directly coupled CFD approaches developed in the context of large-eddy simulation (LES) of turbulent flames, or for laminar synthesis processes in hot-wall and microwave-plasma reactors, are therefore presented. The particle dynamics models were designed to be independent of the synthesis application for suitable nucleation and growth mechanisms (i.e., nucleation from vapor phase, kinetically based growth, etc.). After explaining the basic theory of reactive and particle-laden flows and their numerical treatment, published and unpublished models that originated as parts of this work are presented.

The first of the three published papers presents a novel model for simulating heterogeneous particle systems. It is able to simulate the deposition of Pt-particles on Al2O3 carrier-particles formed by spray-flame synthesis. A multiclass model based on the extensively extended sectional approach has been developed to simulate the heterogeneous particle system. It includes size distributions for particles in the gas phase and on the surface of the carrier particles, which can grow by deposition, direct collision and collision on the surface. The tabulated chemistry approach used includes a new formulation for the nucleation process that allows the nucleated mass to be calculated at any location and time. This work involves the first simulation of spray flame synthesis of heterogeneous nanoparticles and provides promising results for further applications and extensions.

A novel CFD model using the sectional representation of the particle size distribution (PSD) is the subject of the second publication. It is designed for application in the context of synthesis processes of silicon nanoparticles in microwave-plasma reactors. The particle dynamics model presented involves a direct coupling with the gas phase through nucleation, condensation and evaporation. The simulations show a good agreement with the experimental data from the presented measurements and correctly describe unique process features, such as local particle zones and particle growth in the recirculation zone. In a further investigation, it was found that thermophoresis has a decisive effect on the trajectories of the particles in the present case: Thermophoresis causes nanoparticles to drift away from the hot zones where they would otherwise evaporate. This is a new finding showing that thermophoresis inhibits particle evaporation in the present case.

The third paper presents a bivariate approach for modeling particle dynamics developed for cases with complex nucleation and growth kinetics. The model was applied in simulations of low-temperature synthesis processes from monosilane (SiH4) in hot-wall reactors. The monodisperse formulation of the particle phase is linked to the gas phase by a series of of inception, condensation and surface reaction processes coupled with the gas phase. Due to the high volatile content that may be present in such particles, an additional conservation equation balances the volatile fraction in the particle phase, while an internal reaction describes the emission of these substances into the gas phase. The results of the model agree well with the measured values of a zero-dimensional validation case from the literature. The detailed simulations of a pilot-scale hot-wall reactor describe strong recirculation zones in the reactor that mix particles with different residence times, explaining the evolution of the complex particle morphology. The simulation results are again in good agreement with experimentally determined data and contribute significantly to the understanding of the process.

The first of the two unpublished models combines the monodisperse particle phase representation with nucleation, condensation, and evaporation formulations allowing full coupling to the gas phase. Due to the monodisperse assumption, the implementation of evaporation is critical, though, thus the new approach includes a transition function that prescribes the fractions of shrinkage and disappearance of the particles. The model has been shown to provide good accuracy compared to the sectional approach at a lower computational cost and also allows the prediction of particle morphology.

The second model, the "Digital Clone Probability Weighted Monte-Carlo Method" was developed to achieve detailed modeling of the particle system. The model is capable of simulating hundreds of thousands of individual particles in combination with gas-phase and surface kinetics in a stand-alone 0D simulation or in one-way coupling with CFD simulations. Very good agreement with established data from the literature is achieved for particle sizes and gas phase concentrations, confirming the good accuracy of the method. Images of artificially generated 3D models of the calculated aggregates are presented for visual comparison with TEM images from the experiments. For this study, the new simulation software "Another Nano-Tool" (ANT) was developed by the author, which now serves as a stochastic nanoparticle in-house code.

The results presented confirm the success of the novel classes of coupled multiscale simulation models, as all cases considered could be successfully reproduced by CFD simulations when the crucial interfaces between the gas and particle phases were included. This approach is now being discussed in other research groups and has led to collaborations and co-author publications. The latter are presented in the appendix of this work.


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