Modeling Gravity‐Driven Unstable Flow in Subcritical Water‐Repellent Soils With a Time‐Dependent Contact Angle

Abstract

AbstractUnstable flow in homogeneous dry soils, including saturation overshoot, is associated with a nonzero soil‐water contact angle (CA); 1D and 2D models for such flow, based on the moving‐boundary concept, were recently developed, solved, and verified for a constant high CA. However, in many natural soils rendered water‐repellent by natural organic matter, the CA decreases with time to a value that enables water infiltration. Thus, a mathematical model that includes the effect of time‐dependent CA on water‐content distribution and flow in the soil profile is developed in this study. This model, which also uses the moving‐boundary approach, simulates the effect of time‐dependent CA on unstable infiltration patterns. Comparison with a constant CA sheds light on the time‐dependent CA's influence on the aforementioned parameters. The 1D simulations indicate that a higher rate of CA decrease induces a higher wetting‐front velocity and shorter saturation‐overshoot length than a constant CA. However, due to flux imbalance at the wetting front for specific decreasing CA rates, the wetting‐front velocity first increases, and then decreases to an equilibrium value. The 2D simulations show that a time‐dependent CA significantly reduces water‐content accumulation at the finger tip. Moreover, a faster rate of decreasing CA results in a broader and longer plume shape, the latter being more pronounced. Effects of incoming flux at the soil surface and initial time‐dependent CA are also detailed for 1D and 2D flow. This theoretical study demonstrates that a time‐dependent CA significantly influences the formation of saturation overshoot and further impacts unstable flow generation.