Effects of product condensation on reaction-enhanced vaporization rates and on the transition from homogeneous to heterogeneous reaction in high-temperature metal oxidation

Abstract

In order to predict the vaporization rate of fume-forming condensed phases into reactant-rich gases it is necessary to account for the strong augmentation of vapor transport rates caused by bulk flow into the reaction-condensation zone. For this purpose a simple film theory is developed based on the idealization of a thin reaction-condensation “front” supplied by convection-diffusion processes normal to the surface, but with condensate removal by convection processes parallel to the vaporizing surface. The steady-state position or “stand-off distance” of the front and, hence, its effect on the observed mass transfer rate, are determined by the demands of local reactant stoichiometry at the front and species conservation throughout the two-part film, subject to the imposed vapor and oxidizer boundary concentrations. As applied to the problem of metal vaporization into reactive atmospheres, it is shown that while we recover the results of Turkdogan, Grieveson, and Darken in highly dilute isothermal systems (i.e., metals far from their boiling points vaporizing into dilute oxygen-inert gas mixtures) appreciable additional effects due to the condensation process are predicted in the limit of oxidizer-rich ambient gases. Combining this extended theory with the notion that there is an upper limit to the attainable magnitude of the vaporization rate enhancement at which the reaction regime must change from homogeneous to heterogeneous, leads to predicted critical (transition) oxidizer pressures valid even approaching the practically important limit of pure gaseous ozidizer. On the assumption that this transition will occur when the metal vaporization rate approaches that expected in a vacuum (as has been experimentally observed by Turkdogan, Grieveson, and Darken), illustrative calculations are presented for the metals Na, Mg, Ca, Al, Be, Fe, and Zr vaporizing into oxygen-inert gas mixtures, and conclusions are drawn concerning the impossibility of the vapor phase reaction mode at surface temperatures too far below the metal boiling (or sublimation) point. It is also shown that the formalism can be extended to incorporate an alternative critical condition, perhaps more realistic under some experimental conditions, viz., oxygen penetration to the surface due to the finite thickness of the reaction zone. In either event, the model can be readily used to predict the homogeneous-heterogeneous transition locus and its dependence on the occurrence or nonoccurrence of product condensation, and physical, chemical, and aerodynamic parameters.