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Numerical Modeling of a Capacitance Probe Response

^a Laboratoire Environnement et Développement, Université Paris 7, 2 place Jussieu, F-75251 Paris Cedex 05, France
^b INRA, Unité de Science du Sol, Domaine St Paul, F-84914 Avignon Cedex 09, France
^c Laboratoire d'étude des Transferts en Hydrologie et Environnement, BP53, F-38041 Grenoble Cedex 09, France

View larger version (21K): [in a new window]   Fig. 1. Geometrical layout of the elements used in the simulations. For the polyvinyl chloride material, is used. db and Yb are the radial and horizontal bottom coordinates, respectively, of the boundaries. The figures between brackets correspond with coordinate nominal values that have possibly been modified in particular simulation conditions

View larger version (20K): [in a new window]   Fig. 2. Experimental setup used to calibrate the probe in liquids of various dielectric constants and to investigate the effects of various perturbations on the measurements

View larger version (28K): [in a new window]   Fig. 3. Effective dielectric constant as a function of dipping depth in ethanol, the depth origin corresponds with the probe tip at the ethanol surface. Black and white circles correspond with two sets of measurements. For Neuman boundary condition, the curves corresponding with and 1, respectively, outside of the vessel are practically superimposed

View larger version (11K): [in a new window]   Fig. 4. Effective dielectric constant in ethanol, as a function of sheath thickness of thermo-retractable material around the central electrode. Circles correspond with measurements. The line corresponds with a simulation assuming in the sheath

View larger version (13K): [in a new window]   Fig. 5. Effective dielectric constant in ethanol where a torus is dangling, as a function of the distance between the central electrode tip and the top surface of the torus. Negative values correspond with the tip above the torus. The torus section is a square of 9 mm2. Torus outside diameters of (a) 20, (b) 26, and (c) 32 mm, respectively. For the 32-mm torus diameter, the probe annular electrode may be inserted inside the torus. Circles correspond with measured values. Lines correspond with simulations assuming for the torus material (polyvinyl chloride)