Modelling the effects of equivalence ratio on carbon nanotubes diameter in premixed flame based on a semi-empirical approach

In combustion-based synthesis, controlling the morphological properties of carbon nanotubes (CNTs) to meet specific requirements for technological applications remains challenging. This study examines the effect of the equivalence ratio on CNT diameter via flame temperature in a premixed flat flame, using a computational approach validated by experimental data. The overall flame temperature varies from 1 to 2 in increments of 0.2. For each of the six cases, the predicted premixed flat flame temperature from computational fluid dynamics (CFD) is within 10% of the measured value, demonstrating comprehensive validation. A semi-empirical correlation between CNT diameter and flame temperature is established by using the computed temperature as the dependent variable in an empirical correlation based on existing experimental data. The results show that reducing the equivalence ratio from 2 to 1 increases the average flame temperature, leading to CNT diameter increases of 5% and 20%, respectively. Additionally, the influence of temperature on CNT diameter becomes noticeable only within 6 mm downstream of the flame. Microscopy showed that CNTs with larger diameters (36 − 46 nm) are expected in high-temperature regions (T > 1300 K), whereas smaller diameters (29 − 41 nm) are observed in lower-temperature areas (T < 1300 K) within the flame.