Modeling 2D gravity-driven flow in unsaturated porous media for different infiltration rates

Abstract. The gravity-driven flow in an unsaturated porous medium remains one of the most important unsolved problems in multiphase flow. Sometimes a diffusion-like flow with a uniform wetting front, known as stable flow, is observed, but, at other times, the flow is unstable with distinct preferential pathways. The formation of an unstable wetting front in a porous medium depends on many factors, including the type of porous medium, the initial saturation, and the applied infiltration rate. As the infiltration rate increases, the wetting front first transitions from stable to unstable at low infiltration rates and then from unstable to stable at high infiltration rates. We propose a governing equation and its discretized form, the semi-continuum model, to describe this significant non-monotonic transition. We show that the semi-continuum model is able to capture the influx dependence together with the correct finger width and spacing. Moreover, we demonstrate that the instability of the wetting front is closely related to the saturation overshoot in one dimension. Finally, we show that the flow can still be preferential even when the porous medium is completely wetted.