04 Jan 2024
 | 04 Jan 2024

Modeling stable and unstable flow in unsaturated porous media for different infiltration rates

Jakub Kmec and Miloslav Šír

Abstract. The gravity-driven flow in unsaturated porous medium is still one of the biggest unsolved problems in multiphase flow. Sometimes a stable flow with an uniform wetting front is observed, but at other times it is unstable with distinct preferential pathways even if the porous material is homogeneous. The formation of an unstable wetting front in a porous medium depends on many factors such as the type of the porous medium, the initial saturation or the applied infiltration rate. As the infiltration rate increases, the wetting front first transitions from stable to unstable for low infiltration rates, and then from unstable to stable for 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. We also present that the instability of the wetting front is closely related to the saturation overshoot in 1D. Finally, we demonstrate that the flow can be still preferential even when the porous medium is completely wetted.

Jakub Kmec and Miloslav Šír

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on egusphere-2023-2785', Anonymous Referee #1, 25 Jan 2024
    • AC1: 'Reply on RC1', Jakub Kmec, 29 Jan 2024
  • RC2: 'Comment on egusphere-2023-2785', Anonymous Referee #2, 01 Feb 2024
    • AC2: 'Reply on RC2', Jakub Kmec, 29 Feb 2024
Jakub Kmec and Miloslav Šír
Jakub Kmec and Miloslav Šír


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Short summary
The most mysterious part of the hydrological cycle is the infiltration of water into porous soil. In this process, water enters the soil, some of it is retained in the soil or evaporates, and the remaining water continues to move below and through the rock environment. The physical description of infiltration, specifically the dependence of the infiltration rate on the flow, shows very unusual features that are beyond the normal human experience. Our paper is devoted to their elucidation.