AN APPROXIMATE EXPLICIT EXPRESSION FOR THE COMBUSTION-RATE OF A SMALL CARBON PARTICLE

The combustion of a carbon particle in an oxidizing environment is studied theoretically. Chemical reactions considered include the surface C-O2 and C-CO2 reactions and the gas-phase CO-O2 reaction. Generalized coupling functions are use d and three limiting solutions describing frozen, flame-detached, and flame-attached combustion modes are investigated. Explicit expressions for the combustion rate of a carbon particle have been obtained for the three limiting situations in terms of the transfer number, which is related to the reduced surface Damkohler numbers and the ambient oxidizer concentrations. It is shown that the present explicit expressions not only agree with the exact theoretical combustion rate in the diffusion-controlled regime, but also include the conventional expression based on the resistances for reaction and mass transfer. By investigating the critical particle size for ignition of a CO flame over a burning carbon particle, and by comparing predictions with experimental data from the literature, it is determined that the expression for frozen mode combustion has practical utility for small particles.