“Inviscid finger” instability in regular models of a porous medium

Displacement of a fluid from a porous medium is considered. The flow is assumed to be fast enough, i.e., the Reynolds number based on the characteristic pore size is large. If he driving fluid is less dense (for example, a gas), the interface is unstable. This instability is similar to the well–known viscous finger instability but the governing parameter is density instead of viscosity. The instability is demonstrated experimentally using two–dimensional models. In square lattices of perpendicular channels, noticeable branching of fingers is not observed, which is attributed to the anisotropy of such an artificial porous medium. A more ordinary pattern with finger branching is obtained in a two–dimensional layer of spheres, which appears to be more isotropic. A simple model describing flow in a square lattice is proposed. The initial stage of growth is considered, and the instability increment is estimated. A qualitative analysis of the nonlinear stage is performed.