Sectional modelling of TiO₂ particle size distribution and crystallinity in burner-stabilised stagnation flames

<p dir="ltr">The use of flames as heat sources for producing high-quality nanoparticles has gained significant attention due to its one-step, high-throughput nature and the absence of liquid by-products compared to traditional wet chemistry methods. Titanium nanoparticles, such as, Titanium Dioxide (TiO₂ ), have been widely used as photocatalysts for solar cells and semiconductors for gas sensors. Macroscopic properties of the produced TiO₂ are directly influenced by nanoscale characteristics of particles, such as, Particle Size Distributions (PSDs) and crystalline phase composition. Accurate modelling of nanoparticles characteristics is vital for producing high-quality nanomaterials in industrial applications. A mass- and number-density-preserving sectional method, originally developed for soot PSDs, is here extended to compute titanium dioxide nanoparticle size distributions. The gas-phase chemistry combines a detailed C/H/N/O mechanism with a Ti 25-species 65-reaction chemical mechanism for Titanium Tetra-Iso-Propoxide (TTIP) decomposition to Ti(OH)₄ . The mechanism features inception of TiO² particles through barrierless dissociation of Ti(OH)₄ . Coagulation and aggregation using varying primary particle diameters are explored and surface growth is assumed via condensation of Ti(OH)₄ molecules on the particle surface. Crystalline phase transport equations are proposed and integrated with the sectional model to provide the crystalline phase fraction in each section, while two distinct phase identification models are used to determine the boundary conditions. The methodology is applied to the formation of TiO₂ in three sets of laminar, premixed, ethylene-oxygen-argon stagnation flame experimentally studied by Tolmachoff et al. (Proc. Combust. Inst., 2009) and Manuputty et al. (Combust. Flame, 2021 and J. Aerosol Sci, 2019). Results are compared with experimental data for PSDs of TiO₂ and phase composition with TTIP loading from 194 ppm to 1454 ppm. Satisfactory results are obtained for all datasets under fuellean, stoichiometric, and fuel-rich conditions, supporting the applicability of the augmented sectional model in simultaneously predicting both PSDs and crystalline phase fractions.</p>