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a Radian International, Los Alamos, NM 87544 USA
b Dep. of Chemical and Bioresource Engineering, Colorado State Univ., Fort Collins, CO, 80523 USA
steve_geiger{at}radian.com
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMaterials and methodsResultsDiscussionSummaryREFERENCES |
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMaterials and methodsResultsDiscussionSummaryREFERENCES |
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Unstable infiltration of water resulting in flow fingering has been observed under varied conditions in laboratory studies. It has been shown that flow fingers form below the interface during ponded infiltration in layered systems where a fine soil is underlain by a coarser soil that is initially air-dry (Hill and Parlange, 1972; Glass et al., 1989a,b; Baker and Hillel, 1990). Infiltration has also been shown to become unstable at the cessation of ponding in homogeneous media (Diment and Watson, 1985; Tamai et al., 1987) and under non-ponding fluxes in media which are hydrophobic (Hendrickx et al., 1993). In addition, fingered flows have been noted to occur in air-dry, homogeneous sands under steady, non-ponding infiltration (Selker et al., 1992a; Babel et al., 1995; Yao and Hendrickx, 1996).
The conditions that lead to unstable flow in homogeneous media are not well understood. Mechanistic stability analyses (Hill, 1952; Saffman and Taylor, 1958; Chouke et al., 1959) predict that infiltration is unstable if the pressure of the invading fluid increases faster spatially than that of the displaced fluid in regions perturbed in the direction of flow. For water displacing air vertically downward, this criterion is equivalent to having a soil water pressure gradient which is positive downward—or opposing the direction of flow—as determined through rigorous hydrodynamic stability analysis (Philip, 1975). This criterion of instability has been substantiated with infiltration experiments (White et al., 1976). Soil water pressures will be positive in the downward direction during non-ponding infiltration if the wetting front is sharp and saturated. Theories on fingering in homogeneous soils under non-ponding infiltration assume unconditional instability resulting in flow fingers if the system geometry permits (Parlange and Hill, 1976; Glass et al., 1991). Others have postulated that stability is conditional on the basis of soil texture (Raats, 1973). According to the Richards' equation, under the conditions of steady, non-ponding infiltration, water flows with soil water pressure gradients that are either negative or zero in the direction of flow (Philip, 1957; Rubin, 1966). Consequently, Philip (1975) concluded that wetting fronts in homogeneous soils subject to non-ponding infiltration would be unconditionally stable if increases in air pressure ahead of the wetting front were negligible.
Various combinations of applied flux, grain size distribution, and initial soil water content can result in wetting profiles that have a sharp, saturated wetting front. Sharp, saturated wetting fronts have been noted to occur in air-dry media under fluxes less than the saturated hydraulic conductivity (Moore, 1939; Smith, 1967; Lu et al., 1994a). Accordingly, flow fingers formed in two and three-dimensional columns under non-ponding infiltration in air-dry media (Selker et al., 1992a; Babel et al., 1995; Yao and Hendrickx, 1996). The condition of air-dry initial soil water content alone, however, is not a sufficient predictor of instability. Stable wetting fronts were achieved in initially air-dry media during infiltration into layered soils by increasing the percentage of fines in the lower layer (Baker and Hillel, 1990) and in homogeneous soils by applying fluxes below a critical value (Yao and Hendrickx, 1996). Infiltration in the presence of initial soil water tends to make the wetting front diffuse (Lu et al., 1994a) and such conditions have produced stable wetting fronts (Diment and Watson, 1985; Lu et al., 1994b; Glass and Nicholl, 1996).
The objectives of this study are as follows: (i) measure soil water pressure over time at fixed depths following passage of the wetting front during steady, one-dimensional, non-ponding infiltration in homogenous sands, (ii) present a mechanistic model which explains soil water pressure gradients characteristic of stable and unstable infiltration in homogeneous media, and (iii) interpret the data in terms of flow stability and the proposed model.
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Materials and methods |
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TOPABSTRACTINTRODUCTIONMaterials and methodsResultsDiscussionSummaryREFERENCES |
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Water Application
Infiltration events were simulated by placing a single drip needle above the upper surface of the soil. The drip needles were connected to a syringe infusion pump (Harvard Apparatus Inc., South Natick, MA) which was calibrated for flow rates between 2.0 and 0.001 mL/min by means of 10.0- and 20.0-mL syringes. In some of the low flow rate experiments, the needle dripper was lowered near the surface of the media to minimize cycling of pressures due to low drip frequency. By having the drip needle closer to the media surface, a more continuous flow of water from the needle to the surface was observed, instead of large drops forming and then falling to the surface at discrete intervals. Deionized water, equilibrated at laboratory temperature (18.3–20.0°C) was used as the wetting fluid for all experiments. The columns were packed to approximately 15 mm below the top creating a headspace between the sand surface and the top of the column. The columns were covered with Parafilm (American National Can, Greenwich, CT) during infiltration to minimize evaporation from the media surface. At the beginning of an infiltration event, the surface of the soil was observed to become wetted over the entire area in the time it took for 4 to 7 drops to fall.
Data Measurements
Small diameter (4.0 mm) ceramic tensiometers in conjunction with fast responding pressure transducers (PX26-005DV, Omega Engineering, Inc., Stamford, CT) were inserted into column ports to measure soil water pressures during infiltration runs. Ceramic tensiometer tips were wrapped with Parafilm on all sides with the exception of the flat base of the tip which abuts to a small cloth contact sheet, to ensure hydraulic contact between tensiometer and media, during infiltration runs. Columns were packed with removable stoppers in the tensiometer ports. Tensiometers were placed in the ports just after arrival of the wetting front to preclude any flow of water from the tensiometer tip into the air-dry media. In experiments with initial soil water contents that were greater than air-dry, the tensiometers were placed in the ports prior to the wetting front arrival. A datalogger running on a PC was used to collect data. Tensiometer calibrations were checked for accuracy and linearity prior to each infiltration run. All pressures in subsequent figures and text are stated in units of head of water, hw.
Depth of wetting front penetration was monitored over time by a visualization system. Photos were taken with a video camera (4910 CCD series, Cohu Inc., San Diego) and digitized with a high-resolution analog-to-digital converter card operating on a PC. Each photo contains a measurement scale (accurate to 1.0 mm) and clock which measures the cumulative time (accurate to 0.1 s) from the beginning of infiltration. Under intense lighting, the advancing edge of the wetting front is clearly visible against the clean, white silica sand.
Experiments
A total of 56 infiltration experiments into air-dry media were completed. In the following text and figures, applied fluxes will be referred to as dimensionless fluxes (q*) that represent the ratio of specific flux to saturated hydraulic conductivity of the medium. Experiments with soil water pressure measured at a depth of 10 mm were run in duplicate for F-95 sand and the three sieved separates under steady applied dimensionless fluxes of 2, 5, 20, and 50% and for F-14 sand under dimensionless fluxes of 2, 5, and 20%. At least one infiltration test was run for each sand where soil water pressure was measured at a depth of 70 mm below the surface. Two infiltration tests were run with initial soil water contents corresponding to field capacity and pressure measurements were taken at 70 mm depth. Columns of F-14 sand and the 60–80 separate were saturated and allowed to drain with suctions of 100 and 150 cm respectively maintained at their base for a period of 48 hours before the infiltration tests. Initial soil water contents were 0.04 (F-14 sand) and 0.05 (60–80 separate). The depth of wetting front penetration over time was recorded in 11 experiments of infiltration into air-dry sands.
Additional infiltration experiments were conducted in which air pressures were measured at a fixed depth as the wetting front approached. All air access ports were stoppered during these measurements, and air was only allowed to escape at the base of the packed columns. Air pressure was measured with a pressure transducer inserted into an air-tight fitting in the side of the packed column.
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Results |
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TOPABSTRACTINTRODUCTIONMaterials and methodsResultsDiscussionSummaryREFERENCES |
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and the 100–140 separate
and asymptotically approached steady values. In both cases, the steady value of soil water pressure that was eventually reached was an increasing function of the applied flux. The value of the soil water pressure near the wetting front was found to be an increasing function of the applied flux and the mean grain size of the media. This value of soil water pressure corresponds to the beginning of Region II as illustrated in Fig. 3 and is believed to be very close to the soil water pressure at the wetting front, or water-entry pressure. Figure 5 is a plot of the soil water pressure measured at 10 mm, just after the wetting front passed, against the dimensionless applied flux for each of the samples with air-dry initial soil water content.
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Experiments with F-14 sand showed that soil water pressures measured at 10 and 70 mm approached the same steady value over time. This illustrates that 
approaches a value where the hydraulic conductivity equals the applied flux since there is a unit gradient of hydraulic head.
Effects of Initial Soil Water
Additional infiltration tests were performed in columns with initial soil water contents greater than air-dry. Dimensionless fluxes of 0.05 and 0.50, for the F-14 and 60–80 samples respectively, were applied to the pre-wet samples and pressures were recorded at a depth of 70 mm (Fig. 6)
. The presence of initial soil water affected observed pressure changes during infiltration. Soil water pressures increased following the passage of the wetting front in both experiments. In contrast, soil water pressures decreased over time for both of the samples subject to the same fluxes with air-dry initial soil water contents.
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Two general types of behavior were observed when measuring depth of the wetting front over time for one-dimensional, non-ponding infiltration in sands of air-dry initial soil water content. Figure 7
shows the difference (
Z) between the measured and saturated front depths over time for infiltration into the F-14 sand and 60–80 separate. For the F-14 sand, the wetting profile was saturated for the first 300 s. An increase in front velocity after 300 s indicates that the profile was no longer completely saturated.
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Z vs. time curves was found to increase with decreasing applied flux, indicating greater divergence from a saturated front for lower fluxes.
Air Pressure Measurements
Air pressure was measured over time during three infiltration experiments in the 100–140 sand separate (dimensionless flux of 0.50) and one experiment in the F-14 sand (dimensionless flux of 0.20). In the experiments with the 100–140 separate, maximum air pressures were recorded in the range of 0.1 to 0.3 cm of water. The maximum pressures were observed to occur approximately 10 seconds prior to the wetting front visibly reaching the air measurement port. No increase in air pressure was measured during the infiltration experiment in F-14 sand.
Mechanistic Model of Unstable Flow in Homogeneous Media
In this section, a model is presented that explains the soil water pressure trends found in the experiments. The model is based on the Darcy-Buckingham flux equation, hysteretic soil water retention functions, and dynamic water-entry pressures.
Water moves through initially air-dry, hydrophilic media with a discontinuity in soil water pressure at the wetting front. Following the onset of low rate infiltration, regions of high saturation occur locally at the surface. These regions are then drained as a result of the sorptivity of the dry media and the force of gravity (Youngs, 1960). The ability of air-dry, coarse sand to drain the locally high saturation regions at the wetting front is limited. This process is manifested in an apparent water-entry pressure (Hillel and Baker, 1988; Baker and Hillel, 1990; Glass et al., 1989a). The water-entry pressure, or soil water pressure at the leading edge of the wetting front, is an increasing function of the flux through the media under air-dry initial soil water conditions. This has been noted for the case of upward imbibition of water in air-dry sand and is likely attributable to contact angle dependence upon velocity of the three phase (water, air, solid) boundary (Iwata et al., 1988).
The dynamic water-entry pressure controls the soil water content and, ultimately, stability of the wetting front. Under conditions of higher relative fluxes, increased water-entry pressures result in high soil water contents near the invading wetting front. If the hydraulic conductivity related to the soil water content at the wetting front is in excess of the flux at the front, unstable flow results. Consider the Darcy-Buckingham flux equation:
 | (1) |
) the hydraulic conductivity, hw the soil water pressure (expressed as a head), t is time, and z the spatial coordinate measured positive in the direction of gravity. From Eq. [1], at any depth and time a condition of q < K() results in the following inequality:
 | (2) |
Thus, Eq. [2] describes a gradient in soil water pressure which is positive in the direction of flow and represents unstable flow (Philip, 1975).
An initial wetting curve, primary drainage curve, and primary wetting curve are shown to illustrate the relationship between soil water pressure and soil water content (Fig. 8a)
and soil water pressure and hydraulic conductivity (Fig. 8b) for a hypothetical coarse sand. The initial wetting curve is similar to that measured for water invading air-dry sand (Liu et al., 1994). During infiltration into air-dry sand, soil water pressure at the advancing edge of the wetting front must fall somewhere along the initial wetting curve where soil water content is greater than zero. A value of soil water content (q) is specified such that the hydraulic conductivity at that soil water content is equal to the applied flux. If F is the soil water content at the wetting front, then the difference between F and q will determine if soil water pressure increases or decreases at a given depth over time as the wetting front passes.
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F)A, corresponds to a hydraulic conductivity which is larger than the applied flux. The soil water content (F)A is controlled by the dynamic soil water entry pressure. By Eq. [1], the gradient in soil water pressure in the infiltration profile must be positive in the direction of flow since q < K(). Soil water pressures follow the Path A 
A* over time at a given depth as approaches q from (F)A. In this case, the maximum pressure is at the wetting front and pressures become more negative above the front. This condition represents unstable flow. Alternatively, depending upon the media and initial conditions, the pressure at the wetting front may correspond to a (F)B where K[(F)B] is less than the applied flux. In this case, soil water content at the wetting front increases from (F)B to q along the initial wetting curve and soil water pressures increase over time at a fixed depth (Path B B* in Fig. 8a). Soil water profiles for the two scenarios are illustrated in Fig. 9
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Discussion |
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TOPABSTRACTINTRODUCTIONMaterials and methodsResultsDiscussionSummaryREFERENCES |
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According to the mechanistic model, wetting fronts will be stable in initially air-dry soils when the applied flux is below some critical value. In the infiltration experiments conducted for this paper, soil water pressures measured near the wetting front were found to decrease with decreasing applied fluxes. In the two finer sands, a critical flux was found. Below this flux, stable flow occurred, but above this flux, flow was unstable. Accordingly, three-dimensional laboratory infiltration studies by Yao and Hendrickx (1996) performed with air-dry initial soil water content also showed that lowering applied fluxes below a critical value results in stabilization of wetting fronts.
Consistent with the conceptual model presented in this paper, our experiments show that soil water pressure approaches a higher value at steady state when initial soil water content is greater than air-dry. As depicted in Fig. 8a, the pressure relating to q is higher when approached on the primary wetting curve than if approached by drainage from the initial wetting curve (i.e., along Path A A*). This is consistent with the findings of others (Stonestrom and Akstin, 1994) when lower values of soil water pressure were measured at the surface during steady, non-ponding infiltration at a given rate than if the same rate was achieved by step increases in flux.
In the mechanistic model presented, higher initial soil water contents stabilized the front. Initial soil water affects infiltration in coarse sands by lowering the soil water pressure, resulting in a condition of q > K(F) at the wetting front. In the one-dimensional infiltration experiments conducted in our study, measured soil water pressures at the wetting front were lower with initial soil water contents than with initially air-dry media and stable flow resulted. Similarly, initial soil water contents that were greater than air-dry have been shown to produce wetting fronts that were diffuse compared to the sharp fronts which occurred under air-dry initial soil water contents in visualization studies (Lu et al., 1994a). Two-dimensional infiltration studies have also shown that addition of initial soil water produced stable wetting fronts (Diment and Watson, 1985; Lu et al., 1994b; Glass and Nicholl, 1996).
The increase in wetting front velocity after the wetting front has reached a certain depth, as observed in some of the experiments, is also explained by the model. During the initial stages of infiltration, the wetting profile is saturated and moves with a velocity equal to the completely saturated, plug flow velocity. Considering scenario A in Fig. 8a, drainage would begin to occur at the surface when soil water pressure, following Path A A* over time, was lowered beneath the air-entry pressure. Eventually, a condition is reached where there is a region of higher water content (possibly saturated) at the wetting front, transitioning above to a region of lower soil water content that extends to the surface of the column. This profile at the wetting front remains constant with respect to the moving frame-of-reference. This is similar to experimental observations (Selker et al., 1992b; Glass et al., 1989a) and modeling results (Nieber, 1996) of soil water profiles within flow fingers in two-dimensional studies where it has been shown that fingers have a region of high soil water content at the tip. The final, higher velocity of the wetting front is equal to the rate at which the transition zone—of lower soil water content—lengthens over time.
Previous findings that flow fingers in two-dimensional infiltration experiments (Selker et al., 1992c) and non-monotonic soil water pressure histories in one-dimensional infiltration experiments (Stonestrom and Akstin, 1994) were not caused by air-pressure buildup ahead of the wetting front were supported by experiments conducted for this study. Detectable increases in air pressure were only observed in experiments with the finer textured sand (100–140 separate). In the coarser sand that always produced soil water pressure gradients characteristic of unstable flow, increases in air pressure were not detected. This finding, coupled with the observation that presence of initial soil water in an amount greater than the air-dry condition produced soil water pressure gradients consistent with a stable flow field, indicates that air-pressure buildup is not requisite for unstable flow to occur in homogeneous media subject to steady, non-ponding infiltration.
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Summary |
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TOPABSTRACTINTRODUCTIONMaterials and methodsResultsDiscussionSummaryREFERENCES |
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A mechanistic model which explains soil water pressure trends during infiltration in homogeneous media has been presented. The model uses a dynamic soil water entry pressure, the Darcy-Buckingham flux equation and hysteretic soil water retention curves to explain pressure gradients characteristic of stable and unstable flow. In the model, if the soil water content at the wetting front has a hydraulic conductivity that is higher than the flux at the front, unstable flow will result.
In air-dry sands, it was shown that lower applied fluxes resulted in lower soil water pressures near the wetting front and more stable soil water pressure profiles. In the two finer sands, a critical flux was found, below which infiltration was stable. The presence of initial soil water also lowered water-entry pressures and produced stable wetting fronts in systems that were unstable with air-dry initial soil water content.Saffman Taylor 1958
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ACKNOWLEDGMENTS |
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REFERENCES |
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TOPABSTRACTINTRODUCTIONMaterials and methodsResultsDiscussionSummaryREFERENCES |
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