Heterogeneous flame propagation in the self-propagating high-temperature synthesis (SHS) process: Theory and experimental comparisons

A theory for the heterogeneous flame propagation in the Self-propagating High-temperature Synthesis process is formulated, describing a premixed-mode of propagation for the bulk flame supported by the nonpremixed reaction of dispersed non-metal particles in the liquid metal. Reaction at the particle surface assumes a finite rate while a temperature-sensitive Arrhenius-type liquid-phase mass diffusivity is incorporated. Ranges of flammability in terms of the mixture ratio and the extent of dilution are also identified. The problem is reduced to solving for the burning rate eigenvalue from two first-order differential equations in the same manner as that for flame propagation in fuel sprays. Solutions were obtained for the reaction between titamium and carbon leading to the formation of titanium carbide. By using a consistent set of physico-chemical parameters for this system, satisfactory quantitative agreement for the burning velocity is demonstrated between calculated results and experimental data in the literature. Furthermore, it is shown that the flame burning rate increases with decreasing particle size, that for most reported experimental results the particles react in the diffusion-controlled limit, that the flammable limits of the theory describe well the corresponding experimental limits, and that the Arrhenius mass diffusion expression provides a closer description of the flame response than the constant mass diffusivity.