Stability analysis of the unsaturated water flow equation: 2. Experimental verification

Abstract

Abstract. In this study, we verify the stability analysis of the unsaturated flow equation presented in paper 1. We compare finger sizes measured in laboratory experiments with predictions by the stability model. Using measured unsaturated hydraulic properties which are fitted and extrapolated over the entire water content range, the model enables us to predict finger sizes over a wide range of nonponding infiltration rates. The model predicts an increase of finger diameter at high and low infiltration rates for all soils. Such increases were also observed in our experiments. The model yields reliable predictions of finger diameters at high and intermediate infiltration rates but does not perform as well at infiltration rates <1 cm/h. This is caused by experimental limitations in accurately measuring hydraulic conductivities at low infiltration rates. A sensitivity analysis for initial water content and the shape parameter of the hydraulic conductivity curve showed that a small change of the parameters resulted in a relatively small change of finger size at high and intermediate infiltration rates but at low infiltration rates the finger size change was large, i.e., several orders of magnitude. We conclude that the stability model presented in paper 1 can be used for the assessment of wetting front instabilities in homogeneous soils over a wide range of nonponding infiltration rates.

Wetting front instabilities: a three-dimensional experimental investigation

“…The finger diameter might have been expected to increase in finer soils, due to the increase in capillarity as observed by Yao and Hendrickx (2001). Yao and Hendrickx (2001) reported that for sands with sieve sizes of 14-20, 20-30, 30-40, and 40-60, the finger diameters increased with decreasing particle size consistent with Eq. (3).…”

“…The fingering data, although displaying a certain random element, suggest that finger velocities are a function of intrinsic permeability, while finger diameters remain relatively constant, over the range of intrinsic permeabilities tested. The finger diameter might have been expected to increase in finer soils, due to the increase in capillarity as observed by Yao and Hendrickx (2001). Yao and Hendrickx (2001) reported that for sands with sieve sizes of 14-20, 20-30, 30-40, and 40-60, the finger diameters increased with decreasing particle size consistent with Eq.…”

Preferential flow and transport in soil: progress and prognosis

“…Unlike the surface phenomena discussed above, these instabilities occur under unsaturated conditions. Theory (Raats, 1973), plus observations in Hele–Shaw cells (White et al , 1976), lysimeters (Yao & Hendrickx, 2001), and the field (Glass et al , 1988), have led to a good understanding of the conditions that initiate fingering, and a determination of the conditions that determine the size, spatial separation and persistence of the fingers. New light‐transmission technologies have enhanced the utility of Hele–Shaw cell experiments (Roth, 2008), and the application of classical scaling models of capillary, gravity and viscous forces has resulted in new knowledge and understanding about fingering and unstable flows.…”

Unstable finger-like flow in water-repellent soils during wetting and redistribution – The case of a point water source

“…Fingered wetting fronts formed by unstable flow have been observed in many studies performed on water infiltration into initially dry wettable soils (Glass et al, 1989;Selker et al, 1992;Yao and Hendrickx, 2001). A theory for unstable fingered flow was developed inter alia by Raats (1973) and Parlange and Hill (1976).…”