Henrik H. Nissen

Modified half-cell method for measuring the solute diffusion coefficient in undisturbed, unsaturated soil.

Predictive models for the solute diffusion coefficient, D S , dependency on volumetric soil-water content, 0, are often applied in simulations of solute transport and fate in natural, undisturbed soils. However, all available D S (θ) models have been developed from measurements on sieved, repacked soil. In this study, D S for chloride was measured in both repacked and undisturbed loamy sands at different soil-water contents. The measurements on undisturbed soil were carried out using a modified half-cell method, where the source half-cell is a sieved and repacked soil core and the other half-cell is an undisturbed soil core. Thus, the problems of (i) incomplete contact area at the interface between undisturbed half-cells and (ii) potentially different diffusion properties in undisturbed half-cells can be avoided. The modified half-cell method requires that the diffusion coefficient in sieved, repacked soil is determined separately and that the experimental data is analyzed with a numerical solution to the diffusion equation. No significant difference in chloride D S (θ) between undisturbed and sieved, repacked soil was observed for a Danish (Foulum) loamy sand and a Japanese (Hiroshima) loamy sand. A recently presented soil type dependent D S (θ) model, derived from repacked soil data, shows it to be applicable also for predicting solute diffusion coefficients in natural, undisturbed soils.

Printed Circuit Board Time Domain Reflectometry Probe: Measurements of Soil Water Content

Time domain reflectometry (TDR) is a widely used, nondestructive measurement technique for determining soil-water content (θ) and bulk soil electrical conductivity. Until recently, small scale applications of TDR have been restricted because of the lack of small-scale, high-resolution TDR probes. As a result of the introduction of the TDR coil probe principle (Nissen et al. 1998b) and, in this study, the printed circuit board TDR probe (PCBP), the lower limit of the measurement scale for TDR is changing. The travel time of the electromagnetic waves in the PCBP was prolonged by forcing the electromagnetic waves to travel in a three-rod serpentine waveguide produced in the copper cladding of a circuit laminate (50 mm long, 10 mm width, 0.64 to 1.00 mm thickness). The apparent relative dielectric permittivity (K a ) measured by the PCBP (K a, PCBP ) was calibrated against K a measured by a standard two-rod TDR probe in air and six fluids of various K a . A two-phase dielectric mixing model was used to describe the contributions of the circuit laminate and the surrounding media to K a , PCBP . Eleven PCBPs were produced on four different types of circuit laminate with well known water absorption properties. Minor changes in K a attributable to water absorption could be observed for some of the circuit laminates. However, all four circuit laminates showed equal measurement performance during water infiltration in an initially air-dried soil. None of the circuit laminates was damaged by the soil environment during the water transport experiments. The waveguide of the PCBP is in direct contact with the soil, which should enable the PCBP to also measure electrical conductivity (EC). A calibration experiment was carried out where the load resistance (R 1 ) and the EC were measured in deionized water and six KC1 solutions by the PCBPs and a conductivity meter, respectively. A simple linear relationship was found between RL and EC. Therefore, in contrast to the TDR coil probe, the PCBP seems promising for obtaining simultaneous, small-scale and high-resolution TDR measurements of water and solute transport.

Time Domain Reflectometry Developments In Soil Science: I. Unbalanced Two-rod Probe Spatial Sensitivity And Sampling Volume

The use of parallel two-rod time domain reflectometry (TDR) probes is widespread because the two-rod probe is the least destructive of the conventional TDR probes and has a larger sample volume than a three-rod probe of equal dimensions. However, in order to transform the electromagnetic signal from unbalanced to balanced at the point of connection with the cable, two-rod probes have been thought to require a balun, making the probe construction both more expensive and more complicated. In this study, a two-rod probe without a balun (unbalanced) was exposed to a rising air-water interface, creating a sharp dielectric permittivity boundary within the sample volume of the probe. The probes were horizontal, but they were located within a vertical plane, i.e., one rod was placed above the other. A shorting diode technique was used to improve the location of the end reflection on the TDR traces. Two experiments were carried out differing only in the connection of the coaxial cable to the probe rods. In one experiment, the conductor was connected to the lower rod and the shield was connected to the upper rod. In the second experiment these connections were reversed. Using a numerical model, the relative dielectric permittivity (K) responses of two-rod balanced and unbalanced TDR probes were predicted as a function of the fluid interface height. The measured and modeled responses of the unbalanced two-rod probe matched perfectly, and there was no observed increase in the spatial sensitivity of the probe adjacent to either rod. Furthermore, the modeled probe responses as well as the sample areas for the balanced and unbalanced probe configurations were identical. Based on these results, we suggest that baluns be omitted from two-rod TDR probe designs.

Transverse sample area of two- and three-rod time domain reflectometry probes: Electrical conductivity

[1] Numerical models have been applied successfully to the analysis of the sensitivity and transverse spatial sample areas of time domain reflectometry (TDR) probes to lateral variations in dielectric permittivity (e). However, no similar treatment has been presented for the spatial sensitivity of TDR to lateral variations in electrical conductivity (s). The objective of this investigation was to examine the response of conventional two- and threerod probes to sharp changes in s within their sample areas. The spatial weighting, predicted numerically for probes of varying geometries with sharp e boundaries and two different s contrasts in the plane perpendicular to the direction of wave propagation, shows good agreement with the TDR-measured s. For low-loss conditions the sensitivity distribution of TDR is shown to be independent of the value of s. This demonstrates that the spatial sensitivities to dielectric permittivity and electrical conductivity are the same for these conditions and that TDR-measured water contents can be used to correct TDRmeasured s for water content effects. INDEX TERMS: 1832 Hydrology: Groundwater transport; 1831 Hydrology: Groundwater quality; 1894 Hydrology: Instruments and techniques; KEYWORDS: time domain reflectometry, electrical conductivity, sample area, monitoring Citation: Ferre ´, T. P. A., H. H. Nissen, J. H. Knight, and P. Moldrup, Transverse sample area of two- and three-rod time domain reflectometry probes: Electrical conductivity, Water Resour. Res., 39(9), 1261, doi:10.1029/2002WR001572, 2003.

Time domain reflectometry developments in soil science: II. Coaxial flow cell for measuring effluent electrical conductivity

Time Domain Reflectometry (TDR) is a recognized and widely used technique for measuring electrical conductivity (EC) and volumetric water content (&thgr;) in porous media. The ability of TDR to measure both EC and &thgr; is especially appealing in solute transport in variably saturated media. It is commonly assumed that TDR measurements are representative of the EC and &thgr; in the horizontal plane in which the probe is located. The problem is that it is difficult to recognize heterogeneous solute transport with TDR, especially if it occurs outside the sample volume or in regions where the solute is giving little weight to the TDR-measured EC. To determine the presence of heterogeneous solute transport effectively, there is a need for a device to monitor the EC boundary conditions. In this study, a simple and easy-to-make coaxial flow cell is designed and tested for this purpose. The flow cell is made primarily of cheap, prefabricated, and readily available components, and the construction requires only a hacksaw and some welding skills. The idea is to make the effluent from a solute transport experiment pass through the coaxial flow cell, thereby obtaining a measure of the effluent EC. In addition to providing detailed information on the solute transport through the entire sample of porous medium, it will also detect, for example, bypass flow. A solute transport experiment was carried out in a PVC pipe packed with coarse silica sand under saturated conditions to calibrate the flow cell and to demonstrate its potential use. Step input breakthrough and breakdown functions were created using tap water and a KCl solution. Highly detailed measurements of EC in the effluent were obtained, from which solute transport parameters can easily be inferred.

Time domain reflectometry developments in soil science: III. Small-scale probe for measuring bulk soil electrical conductivity

It is commonly believed that Time Domain Reflectometry (TDR) measures bulk soil electrical conductivity (EC) and volumetric water content within the same, well-defined sample volume. However, recent studies have shown that the sample volume is a function of the distribution of EC and dielectric permittivity near the probe. One result of this spatially distributed sensitivity is measurement-induced dispersion. That is, when TDR is used to measure a sharp advancing solute front, the measured EC is some average across the sharp front, leading to incorrect smoothing of the breakthrough curve. A reduction of the probe dimensions is the only solution to this artificial smoothing problem. In this study, a small scale TDR probe is presented and tested. The small probe dimensions produce a near point measurement of EC but make water content measurements unreliable. The small scale EC TDR (SEC-TDR) probe is simple, inexpensive, and made with readily available components. A solute transport experiment was carried out under saturated conditions in a plastic pipe packed with coarse silica sand. Five SEC-TDR probes were inserted, monitoring the EC at various positions along the column, and a coaxial flow cell was used to monitor the effluent EC. Step solute breakthrough and displacement breakthrough responses were created using tap water and a KCl solution. Highly detailed measurements of EC were obtained from which the dispersivity (λ) was inferred. The λ measured by the SEC-TDR probes was significantly lower than λ measured in the effluent by the coaxial flow cell, suggesting that the SEC-TDR probe can reduce the problem of TDR-induced dispersion under even the most challenging conditions.