A quantitative theory for heterogeneous combustion of nonvolatile metal particles in the diffusion-limited regime

The paper presents an analytical theory quantitatively describing the heterogeneous combustion of nonvolatile (metal) particles in the diffusion-limited regime. It is assumed that the particle is suspended in an unconfined, isobaric, quiescent gaseous mixture and the chemisorption of the oxygen takes place evenly on the particle surface. The analytical solution of the particle burn time is derived from the conservation equations of the gas-phase described in a spherical coordinate system with the utilization of constant thermophysical properties, evaluated at a reference film layer. This solution inherently takes the Stefan flow into account. The approximate expression of the time-dependent particle temperature is solved from the conservation of the particle enthalpy by neglecting the higher order terms in the Taylor expansion of the product of the transient particle density and diameter squared. Coupling the solutions for the burn time and time-dependent particle temperature provides quantitative results when initial and boundary conditions are specified. The theory is employed to predict the burn time and temperature of 10–100 $\mu$m iron particles, which are then compared with measurements, as the first validation case. The theoretical burn time agrees with the experiments almost perfectly at both low and high oxygen levels. The calculated particle temperature matches the measurements fairly well at relatively low oxygen mole fractions, whereas the theory overpredict the particle peak temperature due to the neglect of evaporation and the possible transition of the combustion regime.

Novelty and significance statement

For the first time, we present a comprehensive and quantitative analytical theory elucidating the heterogeneous combustion of nonvolatile (metal) particles in the diffusion-limited regime. This novel theoretical model exhibits a remarkable capacity for quantitative prediction, obviating the need for supplementary information from numerical simulations or experimental data. The derivation process of analytical solutions for burn time and time-dependent particle temperature from conservation equations is elaborated, offering transparency and insight into the model’s foundations. To demonstrate the practical utility of the theory, we apply it to analyze the combustion of iron particles, providing valuable mathematical perspectives on the underlying processes. The model’s predictions for burn time and temperature align closely with experimental results, offering a partial validation of the theory within the realm of its applicable assumptions. This pioneering work contributes a robust and versatile analytical framework, advancing our understanding of diffusion-limited combustion phenomena of nonvolatile particles.