The moving-boundary approach for modeling gravity-driven stable and unstable flow in soils

The Richards equation is unsuccessful at describing gravity-driven unstable flow with nonmonotonic water content distribution. This shortcoming is resolved in the current study by introducing the moving-boundary approach. Following this approach, the flow domain is divided into two subdomains with a sharp change in fluid saturation between them (moving boundary). The upper subdomain consists of water and air, whose relationship varies with space and time following the imposed boundary condition at the soil surface calculated by the Richards equation. The lower subdomain consists of an initially dry soil that remains constant. The location of the boundary between the two subdomains is part of the solution, rendering the problem nonlinear. The moving boundary solution was used after verification to demonstrate the effect of contact angle, soil characteristic curves and incoming flux on the dynamic water-entry pressure of the soil, which depends on the soil's wettability, incoming flux at the soil surface and the wetting front's propagation rate. Lower soil wettability hinders spontaneous invasion of the dry pores and, together with a higher input flux, induces water accumulation behind the wetting front (saturation overshoot). The wetting front starts to propagate once the pressure building up behind it exceeds the dynamic water-entry pressure. To conclude, the physically based novel moving-boundary approach for solving stable and gravity-driven unstable flow in soils was developed and verified. It supports the conjecture that saturation overshoot is a prerequisite for gravity-driven fingering.