
Water and contaminant migration in the vadose, or unsaturated, zone have become critical to water resource development, agriculture, site restoration and waste disposal strategies. Because liquid transport is much slower in an unsaturated zone, transport through the vadose zone is usually the limiting factor for contaminant release, nutrient loss and groundwater recharge. Proposed regulations from the United States Environmental Protection Agency will soon require measurement of the unsaturated transport parameters for each geologic unit, soil horizon and engineered component for modelling and performance assessment needs.
The single most important transport property is hydraulic conductivity, K, which is a strong, non-linear function of the volumetric water content,
. Traditional methods of investigating unsaturated systems require very long times because normal gravity does not provide a large enough driving force relative to the low hydraulic conductivities that characterize unsaturated conditions. Pressure techniques often bypass portions of the sample because pressure is not a whole body force like gravity and will seek the path of least resistance, e.g., fractures, sandy areas and macropores, and can affect the stabilities of common minerals like calcite, clays and gypsum. To solve these problems, an unsaturated flow apparatus (UFA) was developed based on open-flow centrifugation. Hydraulic steady-state is achieved in hours in any porous media, even at very low water contents, by using an adjustable, whole-body driving force in combination with precision fluid flow ( Conca, J. L. and J. V. Wright. 1992. Applied Hydrogeology , 1: 5-24.). The UFA is actually a Darcy's Law machine in that the operator adjusts both the flux and the driving force, and attains any desired hydraulic steady-state. The normal operating range is from saturated down to 10-11 cm/s (10-8 darcy; 10-16 cm), or 10-14 cm/s for only saturated conditions. Temperature can be controlled from -20 degrees C to 150 degrees C. Sample sizes can range from less than 40 cm3 cores to Shelby-tube sized samples (280 cm3). Samples can be directly subcored in the field from trenches, outcrops and split-spoon drill cores, or recomposited back to field densities if obtained disaggregated. Whole rock cores and other solids are potted in a resin sleeve. The UFA can isolate and separate advection from other processes, e.g., diffusion or vapor flow, allowing precise measurement of the residual water content. The UFA instrument consists of an open-flow ultracentrifuge with constant, ultralow flow pumps that provide fluid to the sample surface through a rotating seal assembly and microdispersal system (Figure 1). The UFA can control accelerations up to 20,000 g, temperatures from -20 degrees C to 150 degrees C, and flow rates down to 0.001 ml/h. Effluent is collected in a transparent, volumetrically-calibrated chamber, which is observed during operation using a strobe light. The UFA Method is effective because it allows the operator to set the variables in Darcy's Law under which the fluid flux equals the hydraulic conductivity times the fluid driving force. Under a centripetal acceleration in which water is driven by both the matric potential gradient, and the centrifugal force per unit volume, Darcy's Law is

where q is the flux density into the sample, K is the hydraulic conductivity,
is the matric potential, d
/dr is the matric gradient, 
2r is the centrifugal force per unit volume, r is the radius from the axis of rotation,
is the fluid density, and
is the rotation speed in radians per second ( Nimmo, J. R., D. A. Stonestrom, and K. C. Akstin. 1994. Soil Science Society of America Jour. 58:49-56.). Above speeds of about 300 rpm, provided that sufficient flux density exists, d
/dr << 
2r. Rearranging the equation
and expressing hydraulic conductivity as a function of volumetric water content,
, Darcy's Law becomes

As an example, a silt from the Hanford formation accelerated to 2500 rpm with a flow rate of 0.01 ml/h reached hydraulic steady state in 10 hours at a target volumetric water content of 16.4% and an unsaturated hydraulic conductivity of 4 x 10-10 cm/s. Because of the ability to control the flow rate (±1% non-pulsating), rotation speed (±5 rpm) and weight measurement (±0.001 g), hydraulic conductivity is known to within ±8% at a volumetric water content known to within ±2%.2 Figure 2 shows hydraulic conductivity vs. moisture content data obtained in three weeks for six borehole samples using a single UFA.
Comparisons between the UFA Method, soil columns, van Genuchten/Mualem estimations and lysimeter measurements on the same materials show excellent agreement. Figure 3 shows results from a rock core of volcanic tuff using the UFA Method and a van Genuchten/Mualem estimation. Compaction from acceleration is negligible for subsurface soils at or near their field densities. Three dimensional deviations of the driving force with position in the sample are less than a factor of two, and water distribution is uniform in homogeneous samples. In heterogene-ous samples each component reaches its own steady-state condition as occurs in the field, conditions which cannot be reproduced with alternative methods, only with a UFA.
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