Some stability aspects of gas combustion in porous media

Some aspects of the stability of hot-spot and oblique gas-combustion fronts in porous media are considered using a thermal model. A general expression for the velocity of a curved wave front of filtration gas combustion is obtained taking into account the curvature and local slope of the front. It is shown that curvature always promotes stabilization of the front. The slope of the front, in principle, can have a destabilizing effect. However, because this effect is weaker than the curvature effect, it does not cause development of instability. The roles of convective heat and mass transfer between the hot spot and the ambient gas flow and selective diffusion in the development of local instability are analyzed. Criteria are found for the development of hot-spot instability, and the ranges of system parameters in which instability is possible are determined. The effect of variation in the length of the front during wave propagation on the development of instability of an oblique front is considered. Accounting for this factor gives a criterion for instability development that coincides with the experimental one.