Combustion behavior of single iron particles:Part II: A theoretical analysis based on a zero-dimensional model

Following the ignition and solid-to-liquid phase transition of a fine (on the order of 10–100 µm in diameter) iron particle, the self-sustained combustion of a liquid-phase droplet of iron and its oxides takes place. The objective of the current work is to develop an interpretive and explanatory model for the liquid-phase combustion of a single fine iron particle. A zero-dimensional physicochemical model is developed assuming fast internal processes, such that the combustion rate is limited by the rate of external oxygen (O 2) transport. The model considers a particle covered by a shell of liquid-phase FeO enclosing a core of liquid-phase Fe. Stefan flow and diffusion are considered for the gas-transport of O 2, while the gas-transport of gas-phase Fe and FeO are calculated via diffusion only. The outward gas-phase Fe and FeO consume inward-transported O 2 to stoichiometrically form hematite (Fe 2O 3), and the remaining oxygen that reaches the particle surface is entirely consumed to form liquid-phase FeO. The time history of simulated particle temperature shows consistent overprediction of the peak particle temperature when compared to experimental temperature measurements, indicating that the assumption of fast internal kinetics may be incorrect. The model is also unable to capture the apparent slow cooling rate observed in experiments. A further analysis is performed through a heuristic model with a calibrated reaction-rate law, where the internal diffusion of reactive Fe and O ions may become rate-limiting. The calibration of the pre-exponential factor in the Arrhenius term to match the experimental peak temperature yielded good agreement of time to peak temperature, as well as the slow cooling rate. The heuristic model considering internal diffusion predicts a plateau in peak temperature with increasing oxygen concentration. Possible uncertainties of the models, as well as future work, are discussed.