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

Unstable 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.