The effect of radial diffusion on nanoparticle formation in laminar flow reactors

Abstract The present work examines two-dimensional effects during nanoparticle formation in laminar flow reactors using two approaches: a 2D model and a simplified 1D model. The investigated cases consist of carbon nanoparticle synthesis via ethylene pyrolysis in laminar flow. The simplified 1D simulations are conducted using the 1D plug flow solver Nano PFR, while the 2D simulations have been performed using CoFlame in an axisymmetric configuration. Both models utilize a sectional population balance model coupled with gas-phase chemistry to simulate detailed particle formation processes. The effects of radial diffusion of the 2D approach are analyzed in a reference case of an isothermal reactor by comparing a diffusion model against a no-diffusion model. Results show that radial diffusion sufficiently mixes the gas phase species along the radius to approximate plug flow. While radial diffusion effects are apparent in particle formation, it is not nearly enough to develop a uniform radial profile for the primary particle and agglomerate number densities and volume fraction. Next, experimental data from the literature are simulated, examining the suitability, differences, and limitations between the 1D and 2D domains. Both models perform similarly in prediction accuracy for the gas-phase species, including fuel pyrolysis and PAH formation. Moreover, by integrating particle mass across several regions (i.e. radial integration approach), the 1D model can achieve accuracy on par with the 2D model for particle formation predictions. Both models can adequately capture SMPS measurements for particle volume fraction, number densities, and size distributions. Ultimately, within the range of experimental conditions typically found in current laminar flow reactor studies for carbon nanoparticle formation, a modified 1D approach can sufficiently describe the gas-phase chemistry and particle formation processes with lower computational costs than the 2D approach.