On the Stability of Counter Flow Filtration Combustion

A model for time-dependent nonplanar propagation is derived in the limit of large activation energy, and is used to study the stability of a planar travelling wave in counter flow filtration combustion, i.e., where an exothermic reaction front passes through a porous solid medium that reacts with a forced inflow of gas to form a porous solid, and where the direction of propagation of the front is opposite to that of the incoming gas. The model admits two types of front propagation, (i) gas deficient propagation, for which the reaction ceases upon consumption of the gas. and (ii) solid deficient propagation, for which the reaction ceases upon complete conversion of the initial solid. Multiple steadily propagating solutions can occur. With a heterogeneous form of the reaction rate, it is found that gas deficient propagation is stable (unstable) when, for example, the activation energy is sufficiently low (high), and that solid deficient propagation is always unstable unless the reaction rate is independent of the concentration of the gas. In this limit, solid deficient propagation is also stable (unstable) when the activation energy is sufficiently low (high). Sufficiently large and small mass flux of the gas entering the system can also destabilize the steadily propagating front, as discussed in the text.