Three‐Dimensional Numerical Modeling of a Capacitance Probe

Abstract

In this study, a three‐dimensional model represents a capacitance probe measurement. It is based on Laplace's equation, which is solved using the Finite Element Method. A three‐dimensional model can accurately represent both the probe geometry and nonaxisymmetric components of soil heterogeneity. As a result we have obtained a three‐dimensional‐cartography of electrical potential V(x, y, z) in the medium surrounding the electrodes and the effective dielectric constant of the media observed. The model was implemented to address such questions as the influence of the air/soil boundary when making measurements near the surface and the probe's volume of influence. It is shown that the volume of influence of the probe can be derived from a weighting function based on the density of electromagnetic energy and can be computed for a homogeneous medium. It is numerically observed that the probe's volume of influence is quite independent of the permittivity of the medium in which the probe is embedded. It is then verified that dielectric perturbations located outside the so defined volume of influence have little effect on the calculation of the effective dielectric constant seen by the capacitance probe.

Impact of Soil Structure on Microwave Volume Scattering Evaluated by a Two-Dimensional Numerical Model

“…In (6) and (7), the boundary conditions can be easily introduced in the integral term over (Γ). To solve (6) and (7), we used a C++ objectoriented programming for the finite-element code called fast adaptive finite-element modular object (FAFEMO) [22], [23].…”

A TDR Array Probe for Monitoring Near‐Surface Soil Moisture Distribution

“…Electrostatic analyses have commonly been used to simulate the sampling area for TDR probes (Knight, 1992; Ferré et al, 1998; Robinson et al, 2003a). The quasi‐static approximation is only valid for low‐frequency measurements (i.e., f < 100 MHz) since the wavelength of the EM signal (i.e., λ > 3 m in air) is much larger than the probe dimensions (Feynman et al, 1979; Bolvin et al, 2004), whereas this does not hold true for time‐domain measurements operated at high frequency. Thus, the relative EM field distribution of the TDR array (Fig.…”

Evaluation of Amount of Blood in Dry Blood Spots: Ring-Disk Electrode Conductometry

“…The RDE is used extensively in voltammetric applications (often in a rotating format); this geometry has been widely used for amperometric measurements in a wall-jet configuration. The RDE geometry has also been used in sensing capacitance of soils or liquids and electromigrative injection from a small loop in capillary electrophoresis, , etc. The use of the RDE geometry for conductivity measurement is scant; in a related geometry a cylindrical electrode (outer surface area active) with a small diameter wire (only tip active) protruding beyond the outer cylinder terminus was shown to be especially tolerant of suspended solids and floating debris .…”