The conventional multi-scale modelling approach that predicts carbon nanotube (CNT) growth region in heterogeneous flame environment is computationally exhaustive. Thus, the present study is the first attempt to develop a zero-dimensional model based on existing multi-scale model where mixture fraction z and the stoichiometric mixture fraction zst are employed to correlate burner operating conditions and CNT growth region for diffusion flames. Baseline flame models for inverse and normal diffusion flames are first established with satisfactory validation of the flame temperature and growth region prediction at various operating conditions. Prior to developing the correlation, investigation on the effects of zst on CNT growth region is carried out for 17 flame conditions with zst of 0.05 to 0.31. The developed correlation indicates linear ( zlb=1.54zst +0.11) and quadratic ( zhb=zst(7-13zst )) models for the zlb and zhb corresponding to the low and high boundaries of mixture fraction, respectively, where both parameters dictate the range of CNT growth rate (GR) in the mixture fraction space. Based on the developed correlations, the CNT growth in mixture fraction space is optimum in the flame with medium-range zst conditions between 0.15 and 0.25. The stronger relationship between growth-region mixture-fraction (GRMF) and zst at the near field region close to the flame sheet compared to that of the far field region away from the flame sheet is due to the higher temperature gradient at the former region compared to that of the latter region. The developed models also reveal three distinct regions that are early expansion, optimum, and reduction of GRMF at varying zst.

Although flame synthesis promises economic benefit and rapid synthesis of carbon nanotube (CNT), the lack of control and understanding of the effects of flame parameters (e.g., temperature and precursor composition) impose some challenges in modelling and identifying CNT growth region for obtaining better throughput. The present study presents an investigation on the types of carbon precursor that affect CNT growth region on nickel catalyst particles in an ethylene inverse diffusion flame. An established CNT growth rate model that describes physical growth of CNT is utilised to predict CNT length and growth region using empirical inputs of flame temperature and species composition from the literature. Two variations of the model are employed to determine the dominant precursor for CNT growth which are the constant adsorption activation energy (CAAE) model and the varying adsorption activation energy (VAAE) model. The carbon precursors investigated include ethylene, acetylene, and carbon monoxide as base precursors and all possible combinations of the base precursors. In the CAAE model, the activation energy for adsorption of carbon precursor species on catalyst surface E a,1 is held constant whereas in the VAAE model, E a,1 is varied based on the investigated precursor. The sensitivity of the growth rate model is demonstrated by comparing the shifting of predicted growth regions between the CAAE model and the VAAE model where the CAAE model serves as a control case. Midpoint-based and threshold-based techniques are employed within each model to quantify the predicted CNT growth region. Growth region prediction based on the midpoint-VAAE approach demonstrates the importance of acetylene and carbon monoxide to some extent towards CNT growth. Ultimately, the threshold-VAAE model shows that the dominant precursor for CNT growth is the mixture of acetylene and carbon monoxide. A simplified reaction mechanism is proposed to describe the surface chemistry for precursor reactions with nickel catalyst where decomposition of the ethylene fuel source into acetylene and carbon monoxide is accounted for by chemisorption.