Theoretical models for the combustion of alloyable materials

Abstract

The purpose of this work is to extend a theoretical model of layered (laminar) media for SHS combustion presented in an earlier article [1] to explore possible mechanisms for after-burning in SHS (i.e., gasless) combustion. As before, our particular interest is how the microscopic geometry of the solid reactants is reflected in the combustion wave and in the reaction product. The model is constructed from alternating lamina of two pure reactants that interdiffuse exothermically to form a product. Here, the laminar model is extended to contain layers of differing thicknesses. Using asymptotic theory, it was found that under certain conditions, the combustion wave can become “detached,” and an initial thin flame propagates through the media, leaving a slower, thicker flame following behind (i.e., afterburning). Thin laminae are consumed in the initial flame and are thick in the secondary. The thin flame has a width determined by the inverse of the activation energy of diffusion, as found previously. The width of the afterburning zone, however, is determined by the absolute time of diffusion for the thicker laminae. Naturally, when the laminae are all the same thickness, there is only one thin flame. The condition for the appearance of afterburning is found to be contingent on the square of the ratio of smallestto-largest thicknesses being considerably less than unity.