Analysis of Coaxial Soil Cell in Reflection and Transmission

Accurate measurement of moisture content is a prime requirement in hydrological, geophysical and biogeochemical research as well as for material characterization and process control. Within these areas, accurate measurements of the surface area and bound water content is becoming increasingly important for providing answers to many fundamental questions ranging from characterization of cotton fiber maturity, to accurate characterization of soil water content in soil water conservation research to bio-plant water utilization to chemical reactions and diffusions of ionic species across membranes in cells as well as in the dense suspensions that occur in surface films. In these bound water materials, the errors in the traditional time-domain-reflectometer, “TDR”, exceed the range of the full span of the material’s permittivity that is being measured. Thus, there is a critical need to re-examine the TDR system and identify where the errors are to direct future research. One promising technique to address the increasing demands for higher accuracy water content measurements is utilization of electrical permittivity characterization of materials. This technique has enjoyed a strong following in the soil-science and geological community through measurements of apparent permittivity via time-domain-reflectometery as well in many process control applications. Recent research however, is indicating a need to increase the accuracy beyond that available from traditional TDR. The most logical pathway then becomes a transition from TDR based measurements to network analyzer measurements of absolute permittivity that will remove the adverse effects that high surface area soils and conductivity impart onto the measurements of apparent permittivity in traditional TDR applications. This research examines the theoretical basis behind the coaxial probe, from which the modern TDR probe originated from, to provide a basis on which to perform absolute permittivity measurements. The research reveals currently utilized formulations in accepted techniques for permittivity measurements which violate the underlying assumptions inherent in the basic models due to the TDR acting as an antenna by radiating energy off the end of the probe, rather than returning it back to the source as is the current assumption. To remove the effects of radiation from the experimental results obtain herein, this research utilized custom designed coaxial probes of various diameters and probe lengths by which to test the coaxial cell measurement technique for accuracy in determination of absolute permittivity. In doing so, the research reveals that the basic models available in the literature all omitted a key correction factor that is hypothesized by this research as being most likely due to fringe capacitance. To test this theory, a Poisson model of a coaxial cell was formulated to calculate the effective extra length provided by the fringe capacitance which is then used to correct the experimental results such that experimental measurements utilizing differing coaxial cell diameters and probe lengths, upon correction with the Poisson model derived correction factor, all produce the same results thereby lending support for the use of an augmented measurement technique, described herein, for measurement of absolute permittivity, as opposed to the traditional TDR measurement of apparent permittivity.