On the correspondence between the homogeneous and heterogeneous theories of SHS

A comparison was conducted on the correspondence, and differences between the conventional homogeneous theory of flame propagation in self-propagating high-temperature synthesis (SHS) and the heterogeneous theory that properly accounts for the role of the high melting point particles in the mixture compact and the associated diffusion-limited reaction at the particle surface. By reformulating the governing equations for the bulk flame propagation in the condensed medium for the heterogeneous theory, it is demonstrated that they are of the same form as those for the homogeneous theory, except for the fact that the "reaction" term for the homogeneous theory is that of the empirical law of mass action with the temperature-sensitive Arrhenius kinetics, while that of the heterogeneous theory is the diffusion-controlled surface reaction with the temperature-sensitive Arrhenius liquid-phase mass-diffusion and a specific functional form for the concentration dependence. As such, the Arrhenius diffusion of the physically appropriate heterogeneous propagation was mimicked well by the Arrhenius kinetics of the homogeneous propagation in previous formulations. It is further shown that the particle size dependence of the "frequency factor" for the heterogeneous reaction term is the same as that previously inserted in the homogeneous reaction term in an ad hoc manner. The reformulated heterogeneous theory was then applied to the steady propagation of the planar flame in the doubly-infinite domain in the adiabatic limit to illustrate its utility.