Saffman–Taylor problem in filtration combustion

Abstract

In the hydrodynamic approximation, postulating the combustion zone thickness to be much smaller than the channel width, the problem of filtration combustion (FC) has the same spectrum of solutions as the well-known Saffaman-Taylor (ST) problem of the displacement of a high-viscosity liquid by a low-viscosity one. In both cases, the spectrum of solutions includes families of symmetrical and asymmetrical fingers. In the ST problem, asymmetrical fingers are considered unrealizable because of the effect of surface tension at the interface between the liquids, which suppresses the formation of asymmetrical fingers. For FC, there is no exclusion of asymmetrical solutions, since the interphase boundary is a reaction front with zero surface tension. In the present work, it is experimentally demonstrated that an increase in the channel width above a critical value, a planar FC wave loses its stability and the combustion front propagates along one of the channel walls in the form of an asymmetrical finger.