Traveling Waves in Natural Counterflow Filtration Combustion and Their Stability

We consider two-dimensional filtration combustion in a porous medium in which an exothermic reaction takes place between the solid and a pure gaseous oxidant which is delivered to the reaction zone by filtration through the pores of the medium. As a result of the reaction, oxidant is consumed and a solid product is formed. The consumption of gas in the reaction causes a pressure gradient which drives filtration. Since no external forcing is required, this arrangement is termed natural filtration combustion. The samples are assumed to be open to gas permeation at one end with ignition at the other end so that gas flow is opposite to the direction of reaction propagation. This configuration is termed counterflow, so we study natural counterflow filtration combustion. This reaction scheme and configuration describe conditions of self-propagating high-temperature synthesis (SHS), in which combustion waves are employed to synthesize advanced materials. Asymptotic solutions describing traveling waves are determ...

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