Gravity-driven viscous infiltration - common to flow in unsaturated rocks and soils

From constant wetting front velocities in various unsaturated homogeneous porous and fissured media it is concluded that viscous forces balance gravity during infiltration. The velocity of the wetting front in a particular permeable medium thus results from the geometry of the interconnected water conduits, and the rate qS and the duration tS of water input. The basic parameters of gravity-driven viscous flow are the film thickness F and the specific contact length L of flow i.e., the contact length of mobile water with the stationary parts per unit area of the permeable medium. Mobile water content is w = F L; volume flux density is q = A F^3 L g u^(-1), and average velocity of flow is v = B F^2 g u^(-1), (g is gravity, u is kinematic viscosity; A, B depend on flow geometry). tS together with any two parameters of w, q, and v determine a water content wave (WCW) that moves through a homogeneous permeable medium. Capillary potential is due to the solid-water-gas interaction at the pore scale. Its spatial gradient abstracts water from a WCW. The volume of abstracted water, and its scales of time and length are estimated from the deviation of a measured WCW from the one expected during purely gravity-driven viscous flow. Vertical abstraction lengths, AL, were derived from 215 WCWs that were induced by sprinkler irrigation and measured with TDR-equipment. The majority is in the range of 0.5 ≤ AL ≤ 2 m which is the typical depth scale of soil horizons and profiles. The range suggests that capillarity is important to soil hydrology whereas its significance wanes when flow paths are considerably longer than AL.