Dynamic capillary pressure, hysteresis and gravity-driven fingering in porous media

Experimental data collected from the unstable, or fingered, flow of water through soils have shown that the traditional porous media equation is unable to explain the characteristic structure of the moisture distribution within these fingers. One and two-dimensional numerical solutions are presented for an alternative non-equilibrium porous medium equation as proposed by [1] which incorporates a dynamic hysteretic capillary pressure model. Computed profiles capture both the non-monotonic property of finger evolution as well as the limited lateral growth of the instabilities.