Steady burning of a solid particle

We consider the quasi-steady burning of a carbon particle which undergoes gasification at its surface by chemical reactions, followed by a homogeneous reaction in the gas phase. The burning rate M is found as a function of the gas phase Damkohler number $D_g $ for the whole range $0 < D_g < \infty $. The monotonic $M( D_g )$ curve, obtained for relatively very hot or very cold particles, describes the gradual transition from frozen flow to equilibrium. For moderate particle temperatures the transition is abrupt and the $M( D_g )$ curve is either S-shaped or Z-shaped. In the former the burning is enhanced at ignition while in the latter it is slowed down; this depends on the relative importance of the two competitive surface reactions. At extinction, the reverse is true; burning is slowed down in the case of an S curve and is enhanced in the case of a Z curve.