Published online 12 October 2005
Published in Vadose Zone J 4:977-982 (2005)
DOI: 10.2136/vzj2005.0048
© 2005 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
NOTES
A Time Domain Reflectometry Coaxial Cell for Manipulation and Monitoring of Water Content and Electrical Conductivity in Variably Saturated Porous Media
Scott B. Jonesa,*,
R. William Macea and
Dani Orb
a Dep. of Plant, Soils, and Biometeorology, Utah State Univ., Logan, UT 84322-4820
b Dep. of Civil and Environmental Engineering, Univ. of Connecticut, Storrs, CT 06269-2037
* Corresponding author (scott.jones{at}usu.edu)
Received 21 March 2005.
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ABSTRACT
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Time domain reflectometry (TDR) is an effective and accurate method for determination of porous media dielectric permittivity (i.e., for soil water content) and electrical conductivity (EC). Characterization of these properties using controlled wetting or drying of the porous media is of interest for studying and quantifying porous media physical and chemical properties. Our objectives were to develop a TDR measurement cell providing sample water content adjustment and solution exchange capability without repacking or disturbing the sample. A coaxial cell provides a well-defined sample packing volume in which radial distribution of the electromagnetic field averages the transmission line measurements over the entire sample. Using concentric porous stainless steel tubes as electrical conductors, complete or partial saturation of the porous medium (via matric potential control) was possible with the additional key advantage of soil solution exchange without changes in pore space or sample porosity. Solution exchange and suction adjustment were controlled through the center tube with influent solution (ECw) entering the sample through the outer wall and for unsaturated measurements an air inlet port facilitates air exchange. The cell was temperature controlled using an external PVC jacket connected to a circulating water bath. Both saturated and unsaturated measurements of electrical conductivity resulted in excellent agreement between measurements and model predictions. Permittivity measurements were dependent on cell orientation, likely due to differences in the water distribution within the cell. The utility of this new coaxial TDR pressure cell design for porous media research is the ability to simultaneously measure dielectric and ECb in a fixed pore space where water content and solution electrical conductivity are adjustable.
Abbreviations: EC, electrical conductivity • TDR, time domain reflectometry
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INTRODUCTION
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TIME DOMAIN REFLECTOMETRY (TDR) employs a fast rise signal propagating through a porous medium for permittivity determination from travel time and electrical conductivity determined from signal attenuation. Water content is inferred from the dielectric measurement due to the large contrast in the permittivity of water compared to other constituents of solid and air. In spite of the high dielectric measurement accuracy TDR provides, the dielectric-water content relationship is often a matter of uncertainty requiring soil-specific calibration. Common approaches for calibration are to vary water content by mixing air-dry soil and water maintaining a constant bulk density. A coaxial TDR probe geometry was used in the pioneering work of Topp et al. (1980) where cells were repacked at different water contents for incremental dielectric measurements. Even under the best circumstances the repacking and variation of water content of a sample generates unavoidable differences in the bulk density of the sample and more importantly, changes in the structural properties that are associated with electrical and dielectric properties (Jacobsen and Schjonning, 1993; Robinson et al., 2003a).
Investigators using TDR to provide information on water retention bring the soil sample to an equilibrium potential by applying a constant pressure gradient across the porous semi-permeable membrane, driving water movement while preventing air from entering a pressurized chamber. This facilitates adjustment of sample water content by removal of solution as in the pressure plate apparatus described by (Dane and Hopmans, 2002). (Wraith and Or, 2001) used a 15 bar pressure plate in combination with internally installed TDR probes to measure water retention in finer textured soils. (Wildenschild et al., 2001) incorporated tensiometers into a 1 bar pressure (Tempe) cell which served to provide single- and multi-step outflow experiments from water potential measurements at varying water contents. (Friedman and Jones, 2001) used two orthogonally oriented TDR probes to measure the anisotropy in permittivity and electrical conductivity measurements in mica under drying conditions. Some limitations in these systems are that they can't readily facilitate reintroducing water into the sample or cycling water for adjustment of the soil solution electrical conductivity for example.
Our objectives were to develop and test a TDR-based pressure cell (i) capable of continuous monitoring of water content and electrical conductivity, (ii) with the capacity to exchange soil solution with minor or no sample disturbance, and (iii) controlling sample water content via matric potential adjustment for unsaturated measurements (i.e., within the bubbling pressure range of the porous membrane walls).
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THEORETICAL CONSIDERATIONS
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The measured bulk permittivity, 
b, of agronomic soils and porous media of low surface area is well correlated to the volumetric water content. This relationship was described by (Topp et al., 1980) using the following widely used empirical equation
 | [1] |
The bulk permittivity can also be approximated using dielectric mixture theory coupled with the temperature dependence of the water-phase permittivity given by
 | [2] |
where this relation describes the free-water permittivity decrease with increasing temperature. Assuming the solid (s) and air phase permittivities (a) are temperature-independent, we can compute the bulk permittivity of a sample of known porosity, 
, according to Roth et al. (1990)
 | [3] |
where 
is an empirical parameter relating phase inclusion geometries with the applied electromagnetic field. In general is taken as 0.5 for isotropic conditions and ranges in layered systems from 1 to –1 for electric field-inclusion orientations that are parallel or perpendicular, respectively.
Modeled predictions of electrical conductivity in porous media are presented as a comparison for measurements in the TDR pressure cell. The measured ECb is modeled in terms of the constituent physical properties. The solution ECw and saturated volumetric water content, 
sat, serve as inputs to model ECb. An empirical relationship describing the unsaturated and saturated states of porous media as a function of is (Eq. [28] in (Mualem and Friedman, 1991)
 | [4] |
where is 0.5 for coarse and stable structured soils (Mualem, 1976). This model allows prediction of ECb for variations in ECw or . The temperature dependence of ECw(T) has been described in terms of an empirical relationship written as a function of the ECw at 25°C (Stogryn, 1971)
 | [5] |
The value of ECw is temperature corrected to 25°C using the empirical coefficients shown or alternatively using the simplified form assuming the typical 2% increase in EC for every 1°C rise in temperature {i.e., ECw(T) = ECw(25°C) [1 – 0.02(25 – T)]}.
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MATERIALS AND METHODS
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The TDR pressure cell was constructed of three concentric cylinders of stainless steel shown in Fig. 1
. The solid outer shell is separated from the outer conductor made of porous sintered stainless steel (45-µm pore size, Mott Metallurgical, Farmington, CT) by a 0.5-cm gap, which is sealed at each end. Fluids enter and exit through two ports marked ‘a’ in Fig. 1, which are tapped into the solid outer shell at opposite sides. These ports can be used to apply pressure or tension to the sample for fluid removal or addition. The inner diameter of the sintered stainless steel cylinder is six centimeters and forms the outer conductor of the TDR wave guide. The sintered porous stainless steel center conductor (0.5-µm pore size) has an inner diameter of 1 cm and outer diameter of 1.3 cm. This inner cylinder is used to control the tension applied to the sample. It is open at both ends to allow free movement of fluids to either end of the cell and application of pressure or tension. These two wave guides are threaded into a PVC cap and attached to a 50-ohm coaxial cable all of which is embedded in marine epoxy (System III, Portland, OR). There is a plastic (nonconducting) tube at the bottom end connected to the center wave guide cylinder (marked C in Fig. 1). The top end has another PVC cap adapted with o-rings to slip over a second plastic tube attached to the (nonconducting) center wave guide, which threads onto the outer wave guide thus sealing the sample at both ends and allowing a path to the sample through ports a and c in Fig. 1. The effective inner length of the TDR pressure cell is 19.6 cm giving a total sample volume of 528 cm3. Fringing effects occurring at the distal end of the transmission line may include part of the cap in the dielectric measurement where the inner and outer conductors are the same length and in contact with the flat epoxy-filled cap used here. Calibration was made in air and water (Robinson et al., 2003) for greater dielectric measurement accuracy and to minimize fringing effects.
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Fig. 1. Cutaway schematic of time domain reflectometry (TDR) pressure cell showing components: (a) input/output port for P.M. solution exchange (coarse membrane), (b) temperature control port (circulating water bath), (c) input/output port for P.M. solution exchange (fine membrane), (d) 50 ohm coaxial cable, (e) porous stainless steel inner tube (0.5 um pore size), (f) solid stainless steel sleeve, and (g) porous stainless steel outer tube (40 µm pore size). Inset picture shows actual cell with cap removed.
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Sand (0.189–0.295 mm) was packed to a bulk density of 1.46 g cm–3 into the water-filled cell to avoid air entrapment. The PVC cap (Fig. 1) was installed over the center wave guide port by screwing the cap onto the outer wave guide until it is firmly seated. An o-ring provided a seal around the center wave guide port. When temperature control was employed, a water jacket was slipped on after the outer wave guide ports were removed. Once the water jacket was in place the ports were re-threaded through the water jacket o-ring seals. The cap was then threaded back on, sealing both the cell and the water jacket simultaneously.
The cell was set up for either vertical or horizontal orientation using one of the 0.5-cm center tube ports as an outlet; all other ports were plugged. This port was attached through a hanging column to a burette to monitor the volume of outflow from the cell and was configured to minimize evaporation during the length of time the test was run. Air entry was provided to the media through a small hole drilled through the cap. The hanging water column exiting the center tube of the cell provided up to 1 m of suction within the sample. Water content was adjusted using step changes in suction, allowing the cell to reach an equilibrium water content at each step change in suction. Permittivity and electrical conductivity determinations were recorded every minute using a TDR (1502 Tektronix cable tester, Beaverton OR.) and WinTDR analysis software (Or et al., 2004).
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RESULTS
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There is a tradeoff between designing for larger sampling volumes and introducing gravity-dependent stratification of water content in the sample profile of coarser-textured media. This variation in water content (dielectric) within the coaxial cell influences the propagation of the TDR signal and therefore the averaged dielectric measurement. This effect depends on the porous medium water retention, the cell size, and its orientation with respect to the gravity field. Measurements of water retention in coarser materials require corrections to account for errors associated with non-uniform profile water content (Jalbert and Dane, 2001; Tokunaga et al., 2002).
Measurements of dielectric permittivity based on travel-time analysis are plotted in Fig. 2
showing the response with the cell oriented both horizontally and vertically. The empirical permittivity-water content relationship presented by Topp et al. (1980) is also plotted for comparison. Measurements made near saturation are in agreement with the expected results for both cell orientations. Measurements in the horizontal orientation diverge at about 75% saturation and the vertical cell measurements diverge at 50% saturation with both cell orientation measurements converging again at about 25% saturation above the Topp et al. prediction. Repeated draining experiments showed similar trends for both orientations. The signal propagating through the vertically oriented cell results in refractive index averaging of the bulk permittivity (Schaap et al., 2003). The divergence from predicted permittivity based on the Topp et al. (1980) model can in part be attributed to the change in signal propagation velocity caused by the stratified water content distribution in the horizontal cell. (Nissen et al., 2003) demonstrated this effect using three-rod TDR probes being gradually immersed in different dielectric liquids. As the liquid transitioned from the lower to the central rod, there was a sharp increase in permittivity and again another increase as the liquid contacted and enveloped the upper rod, highlighting the separation of the signal propagation thereby complicating the analysis of permittivity. Their Fig. 5 (case L) demonstrates the same enhancement in permittivity shown in our Fig. 2 (horizontal), where their permittivity determinations actually exceed ( = 27.5) the system permittivity when all three rods are completely immersed ( = 25). Using the same system, electrically conductive liquids were also evaluated using the signal attenuation to relate electrical conductivity. These measurements were in excellent agreement with model calculations for the case of electrical conductivity (Ferre et al., 2003). Apparent enhancement of the permittivity-water content relationship (i.e., above Topp et al., 1980) at water contents <0.25 is not explained by cell orientation and may be an unexplored artifact of this novel cell design.
Figure 3
shows the measured ECb determined by TDR as a function of volumetric water content where ECw was 3 ds m–1 and the sand porosity was 0.45. Measured ECb data were compared to modeled results from Eq. [2] assuming n = 0.5, showing excellent correlation. The cell was effective in controlling sample water content using an imposed suction on the inner tube, while providing travel-time measurements of bulk permittivity and electrical conductivity. Time to equilibrium for ECb increased with decreasing volumetric water content shown in Fig. 3 due to the proportionate reduction in unsaturated hydraulic conductivity. Equilibrium times varied from several hours to more than 10 d and are typically controlled by either the saturated hydraulic conductivity of the inner porous membrane (i.e., at higher water content) and eventually the reduced unsaturated hydraulic conductivity of the sample as water content is reduced. Considerations for optimal membrane physical properties should be related to candidate porous media properties for maximizing the matric potential range of operation (Jones and Or, 1998). These results and those following demonstrate the usefulness of the TDR pressure cell for continuous monitoring of permittivity and electrical conductivity having the capability to alter solution EC, water content, and temperature within a fixed sample pore space. We envision the cell providing a simple and useful tool to test new theoretical models looking at combined effects from changes in temperature, chemical constituents, and water content. Limitations apply to fine-textured samples such as clays which may swell, shrink, and reduce the membrane effectiveness by clogging.
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Fig. 3. Time domain reflectometry (TDR) measured bulk electrical conductivity (EC) (ECb) as a function of water content in sand for a solution ECw of 3 dS m–1. The Mualem and Friedman (1991) model (Eq. [2]) was plotted for comparison. The length of time allotted between changes in matric potential based on attainment of equilibrium conditions is also plotted as a function of water content.
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Electrical Conductivity Tests (Solution Exchange)
A significant advantage of the pressure cell is the ability to vary solution or concentration without changes in pore space or sample porosity for our samples. This is a significant benefit for studying the effects of varying solution EC on bulk EC measurements. This is done by starting with the saturated sand mixture in the pressure cell with the center tube connected to a peristaltic pump to facilitate exchange of different ECw solutions through the cell in series. Influent solution ECw was compared to the effluent ECe and with the TDR measured bulk ECb in the sample. In Fig. 4
, values of ECe were relatively unaltered by the sand when compared to influent ECw using a 1:1 line. The TDR measured bulk ECb includes the presence of the nonconducting sand matrix responsible for the reduced ECb relative to ECe. Measured ECb showed excellent agreement with modeled results from Eq. [2] using the calibration and measurement technique outlined by (Castiglione and Shouse, 2003) which is an option in the WinTDR analysis software (Or et al., 2004). The sand remained saturated during measurements with step changes in ECw illustrated by the inset graph of Fig. 4. Time to equilibrium after an increase in ECw was generally <20 min. Sample temperature can also be maintained or varied to observe effects on permittivity and EC measurements.
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Fig. 4. Time domain reflectometry (TDR) measured bulk electrical conductivity (EC) (ECb) as a function of solution ECw, measured independently with an EC meter. Effluent ECe was also measured using the same meter and is compared to ECw with a 1:1 line. The saturated sand (0.18–0.295 mm) porosity was 0.45 and model prediction is from Eq. [2]. Inset displays time to equilibrium with changes in ECb.
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Temperature Control
Temperature effects on measured and EC were observed with the outer PVC jacket (see Fig. 1) attached to the cell. The sample temperature was varied and maintained using a circulating water bath pump attached to the cell with tubing. Three different experimental volumetric water contents of 45, 39, and 21% were achieved by adjusting the tube suction head to 18, 20, and 25 cm, respectively. Electrical conductivity and permittivity were measured while the temperature of the sample was raised from 5 to 55°C (and back again for = 45%) at each of three water contents. Figure 5
shows the measured increasing ECb with increasing temperature on measured and modeled ECb at the three water contents. The temperature effects on electrical conductivity are much more pronounced at higher as increasing the soil water partition increases activity level of the salt molecules. The temperature dependent ECb response was predicted using Eq. [4] and Eq. [5], showing good agreement with the measured data.
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Fig. 5. Time domain reflectometry (TDR) ECb values for three different water contents (ECw = 3 dS m–1) as a function of temperature. Model predictions are given by combining Eq. [2] and [3].
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From the same set of measurements, the temperature dependence of permittivity measurements is shown and modeled in Fig. 6
, where measured b values show the expected reduction in free water permittivity with increasing temperature. To model this effect the dielectric mixture equation of Roth et al. (1990) (Eq. [3]) was used with assumed solid and air permittivities of 5 and 1. The temperature effect was modeled by the water-phase temperature-dependence from Eq. [2]. Model predictions obtained using a value of = 0.45 provided a reasonable fit to the data with a slight over prediction of permittivity at the highest water content. One source of potential error for this cell design arises from the fringing field that occurs at the end of the conductor where inner and outer conductors were of equal length. We measured a 2.5% error in permittivity (b 
80) when calibration was made with vs. without the cap in place. The fringing effect of the cap is reduced to <0.5% when calibration and measurements are made with the cap in place. A suggested improvement for future cell designs is to reduce the inner conductor length to maintain the fringing field within the sample (Bussey, 1980).
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Fig. 6. Measured and modeled bulk permittivity of sand as a function of temperature at three different volumetric water contents. Modeled results employed a three-phase mixing model (Roth et al., 1990) assuming temperature-dependent water permittivity with solid- and air-phase permittivity values of 5 and 1, respectively. The parameter was set to 0.45.
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Cell Design Considerations and Limitations
The pore-size of the porous membranes forming the inner and outer cell walls dictate the range of matric suctions that may be applied for water removal. Smaller pore size (limited to around 0.2 µm for sintered stainless steel) also requires longer time to equilibrium due to reduced saturated hydraulic conductivity. Consideration of porous medium particle size is also important relative to membrane pore size as fine-textured samples may result in membrane clogging when pore and particle sizes are similar. As illustrated in Fig. 2, cell orientation has an impact on water configuration and subsequent signal averaging of the bulk permittivity. Porous media with narrowly-distributed particle size result in greater water content difference in the profile at equilibrium and potentially larger deviation from the expected – relationship (i.e., as in Topp et al., 1980).
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SUMMARY
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A TDR coaxial cell was constructed using concentric porous stainless steel cylinders that act as both porous membranes and as wave-guides for TDR measurements of permittivity and electrical conductivity. The pore size of each membrane determines the respective membrane bubbling pressures and thereby sets limits on the matric potential operating range of the cell as well as hydraulic conductivities influencing solution exchange rates. Sample solution is easily exchanged via the porous membranes. We demonstrated the influence of cell orientation which showed diverging permittivity-water content relations resulting from different signal propagation velocities. Vertically oriented cells are recommended to avoid the complications of signal splitting that was suggested to occur in the horizontal orientation (Nissen et al., 2003). Continuous measurements of EC and water content enable direct assessment of the attainment of equilibrium for both water content and bulk electrical conductivity. The effect of degree-of-saturation on bulk electrical conductivity was studied in a fixed pore space; and various salt solutions were used within the same undisturbed porous medium. Results show excellent agreement with theoretical models for bulk EC as a function of solution EC, water content, and temperature. Temperature control was maintained using a circulating water jacket around the cell. The TDR pressure cell allows continuous monitoring of permittivity and electrical conductivity with the capability to adjust temperature, salt solution, and water content within the undisturbed pore space, thereby providing a simple and useful tool to test theoretical models using these coupled measurements.
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ACKNOWLEDGMENTS
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This project was supported by National Research Initiative Competitive Grant no. 2002-35107-12507 and 2001-01248 (John Wraith–PI) from the USDA Cooperative State Research, Education, and Extension Service and the Utah Agricultural Experiment Station under UAES paper no. 7623. We express appreciation to Seth Humphries and Jeff VanShaar for their assistance with measurements and Christopher Chaves for image generation.
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ABSTRACT
INTRODUCTION
