Two-front traveling waves in filtration combustion

This paper considers a model of filtration combustion in a porous layer immersed in a bath of gaseous oxidizer at constant pressure p₀, which provides for exchange of the oxidizer between the pores, which have initial pressure p₀, and the bath. Such models describe the process of combustion synthesis of high-temperature materials. The case is considered when the exchange rate b₀ between the pores and the bath, and p₀ are both small, while the filtration coefficient b along the porous layer is large. Thus the model describes the process of combustion synthesis under low-pressure conditions. In this paper, uniformly propagating solutions having two thin reaction zones in which the reaction rate is appreciable, separated by an extended intermediate zone in which the reaction proceeds very slowly, are found. Approximate analytical methods are used to derive explicit analytical expressions for various quantities of interest, including the combustion temperature and the propagation velocity, and to describe the structure of the solution. Also, profiles for the reaction rate, temperature, pressure, density, and depth of conversion are numerically computed, and the two-front structure is shown to be stable for the parameter values considered.