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Abstract
Ignition and combustion of metal particles are strongly influenced by the interference of a persistent layer of condensed metal oxide covering the metal fuel, thereby shielding it from the gaseous oxidizer. The existence of this surface cover sets metals apart from other condensed fuels for which ignition can be described by the theory of surface inflammation, as formulated by Frank-Kamenetzkii. The paper investigates the stability of the stationary oxide layer, which is assumed to be liquid so that the equations of a model can be used, as was published earlier. It is shown that global ignition, which is defined to result from globally uniform removal of the oxide layer, occurs when the control parameters attain critical values. In the present case, control parameters are the ambient temperature T ∞ , the ambient oxidizer concentration C g , and the particle radius R. The ignition model is derived in the form of an expansion in a small parameter ε = h 0 /R, where h 0 is a reference thickness of the oxide layer. In the first order of approximation in ε, the critical ambient temperature and the critical particle temperature are shown to be independent of R, while depending on the oxidizer concentration, whereas the critical oxide layer thickness turns out to be proportional to R. A comparison with published experimental data on ignition (mostly for boron, but some for aluminum also) is used to support these predictions of the model. Global ignition is a special case of the more general concept of local ignition, which involves the appearance and subsequent widening of punctures and ruptures in the oxide layer. It is shown to be strongly influenced by the oxidizer content in the ambient atmosphere. In particular, a reduction in oxidizer concentration is found to greatly enhance the tendency for ruptures and punctures to spread.