On the fractal dimension of carbon black particles in pyrolysis flow reactors

This study presents a numerical approach for simulating the internal morphology of carbon black particles formed in a pyrolysis reactor. The simulation process involves a two-step approach using population balance models (PBM) and detailed population balance models (DPBM), solved via sectional and stochastic methods, to simulate the arrangement of primary particles within aggregates to allow determination of their fractal dimension (FD). The outcome is a novel introduction of simulating real flow reactors that for the first time provides the fractal dimension of particles as an output, rather than an assumed input. The results of this study have practical implications for optimizing the synthesis processes in carbon black production. The effects of various production parameters, including aggregation efficiency, temperature, pressure, and acetylene concentrations, on the fractal dimension values of carbon black particles are examined. It is observed that higher temperatures lead to the formation of larger fractal shapes with lower fractal dimensions and larger primary particle diameters. Moreover, increased reactor pressure and higher aggregation efficiency enhance the formation of carbon black aggregates, but also have a time-based effect with higher compactness at longer residence times. The time-based effect reveals the importance of sintering, where high loads of small particles enhance the overall sintering of the aggregates. These findings provide insights into the interplay between temperature, pressure, and particle morphology, highlighting the dynamic nature of carbon black nanoparticles and their response to synthesis process conditions.