Wetting fronts in unsaturated porous media: The combined case of hysteresis and dynamic capillary pressure

Abstract

This paper extends the work of van Duijn et al. (2018) where travelling wave solutions for wetting fronts were considered under the presence of only capillary hysteresis effect and only dynamic capillary effect. In this work, we investigate how the gravity driven wetting fronts behave while moving through long vertical homogeneous porous columns, under the combined effect of capillary hysteresis and dynamic capillarity. It is shown that the developed saturation profiles will exhibit non-monotone behaviour if certain parametric conditions are satisfied. The characteristics of the profiles are explained in detail for all the cases. Moreover, parametric conditions that inhibit the fronts from reaching full saturation are laid out. The analysis agrees well with experimental observations. Finally, numerical results are shown that confirm all the theoretical predictions.