Unexpected water content profiles under flux‐limited one‐dimensional downward infiltration in initially dry granular media

Abstract

[1] Distinct water-content profiles, having saturated q-bumps at and immediately behind wetting fronts, were observed in narrow columns (9 mm ID) of homogeneous air-dried glass beads under downward one-dimensional infiltration with applied water fluxes at lower than the saturated hydraulic conductivity. The infiltrating water content profiles and the position of the wetting front as a function of time were also calculated based on Richards' equation using an independently measured hydraulic conductivity function K(q), and water retention characteristic q(h), of the drainage process, and by applying a pressure boundary condition, h we , which is almost atmospheric pressure, at the moving wetting front. The good agreement between the calculated profiles and the observed confirms that the dynamic water entry pressure h we (where q(h we ) is the saturated water content), does exist for air-dried glass beads, although it is in contradiction to the modern theory of unsaturated water flow in porous media. This physical property of dry media creates an upward negative pressure profile behind the wetting front that would inevitably produce finger flow if the column diameter were larger. At the wetting front, the water content and pressure should be completely discontinuous at the level of pore size, and hence Darcy's equation cannot be applied across the interface between the air-dried and saturated media.

Non-monotonic Travelling Wave Fronts in a System of Fractional Flow Equations from Porous Media

“…B R. Hilfer hilfer@icp.uni-stuttgart.de 1 Much attention has recently been focussed on so-called saturation overshoot (see Hilfer and Steinle 2014;Xiong 2014 for recent reviews), a term that refers to the phenomenon of non-monotonic saturation profiles developing during wetting phase infiltration into a porous medium (Youngs 1958;Briggs and Katz 1966;Glass et al 1989;Shiozawa and Fujimaki 2004;DiCarlo 2004). A strong motivation for these studies were mathematical results excluding the existence of overshoot profiles for the traditional Richards equation from hydrology (Nieber 1996;Otto 1996Otto , 1997Geiger and Durnford 2000;Glass 2001, 2002;Egorov et al 2003;DiCarlo 2005DiCarlo , 2013Duijn et al 2007;Juanes 2008, 2009).…”

Adaptive rational spectral methods for the linear stability analysis of nonlinear fourth-order problems

“…The free energy is nonlocal (it is a function of water saturation and its gradient), and it leads to an additional term that is formally equivalent to an apparent surface tension at the wetting front: a nonlinear, fourth order term. The model predicts a saturation overshoot at the tips of the fingers, a feature that is believed to be essential for the instability of the infiltration front [70,42,30,71,31]. The mathemat-ical structure of the model is analogous to that describing the flow of thin films and driven contact lines [50,77,49,18,86,52,27,26,75,44,53], and to phase-field models of epitaxial growth of surfaces, binary transitions and solidification [21,22,19,40].…”

Ensemble phase averaged equations for multiphase flows in porous media. Part 1: The bundle-of-tubes model

“…In these systems, capillary action plays a crucial role in driving the motion of fluids within the porous media (Washburn, 1921;Richards, 1931;Scheidegger, 1974;Ianson and Hoff, 1986;Hall et al, 1984;Gray and Hassanizadeh, 1991;Liu, 1991;Hassanizadeh and Gray, 1993;Alava et al, 2004;Faybishenko, 2004). Extensive theoretical investigations and advanced experimental techniques, such as neutron radiography, have been applied to study the motion of the fluids (Gummerson et al, 1979;Hassanizadeh and Gray, 1993;Moseley and Dhir, 1996;Beliaev and Hassanizadeh, 2001;Gray et al, 2002;Lockington and Parlange, 2003;Tsakiroglou et al, 2003;Culligan et al, 2004;Shiozawa and Fujimaki, 2004;El Abd et al, 2005;Manthey et al, 2005;Le Guen and Kovscek, 2006;Hilfer, 2006;Czachor, 2007;Hall, 2007). Despite intensive interrogation, models for such flows are still largely empirical.…”

“…Later, experimental observations found that the pressure difference exhibits more complicated characters. The validity of both the diffusion approach and extensions of Darcy's law have been questioned (Gummerson et al, 1979;Hillel, 1980;Hassanizadeh and Gray, 1993;Prat, 1995;Lockington and Parlange, 2003;Tsakiroglou et al, 2003;Shiozawa and Fujimaki, 2004;Hilfer, 2006;Le Guen and Kovscek, 2006;Czachor, 2007;DiCarlo, 2007;Hall, 2007).…”