Theoretical and experimental study on some aspects of resistivity measurement of conductive media using both the four and the two-electrode methods

Abstract

CHAPTER 3 -REVIEW OFTHE SOLUTIONS OFTHE LAPLACE'S EQUATION 31 3.1 Overview 31 3.2 The Laplace's Equation 31 3.3 The Relationship between the Cylindrical and the Spheroidal Coordinates Systems 34 3.4 Solutions of the Laplace's Equations 36 3.4.1 Cylindrical coordinates 36 3.4.2 Prolate spheroidal coordinates 39 3.4.3 Oblate spheroidal coordinates 44 3.5 Concluding Remarks 47 CHAPTER 4 -RESISTIVITY MEASUREMENT OF FINITE-VOLUME SAMPLES USING THE FOUR-ELECTRODE METHOD WITH CONSIDERATION OF THE FINITE DIMENSIONS OF THE ELECTRODES 48 4.1 Overview 48 4.2 The Theoretical Geometric Factor for Resistivity Measurement with Slender Cylindrical Electrodes Modelled using the Prolate Spheroidal Coordinates 53 4.2.1 Potential of a point 54 4.2.2 Potential of an electrode 55 4.2.3 Potential difference between electrodes B and C 57 4.2.4 Theoretical geometric factor for resistivity measurement using the fourelectrode method in the prolate spheroidal coordinates 57 4.3 Numerical Simulations of the Derived Geometric Factor 58 -iv -ATTENTION: The Singapore Copyright Act applies to the use of this document. Nanyang Technological University Library WM NANYANC :^tS I TTEHNQUXilCAL yip IMTVBOTY 4.4 Measurement System 60 4.4.1 Square wave generator 60 4.4.2 Current source unit 61 4.4.3 Voltage measurement unit 61 4.5 Experimental Set-Up 62 4.5.1 Saline solutions 63 4.5.2 Electrodes 65 4.6 Experimental Procedures 66 4.6.1 Effect of the frequency on the measured resistance 66 4.6.2 Effects of s, l c and h on the measured resistance and the calculated resistivity 66 4.7 Experimental Results and Discussions 67 4.7.1 Shape of typical waveforms of V and V R 67 4.7.2 Effect of the frequency on the measured resistance 68 4.7.3 Effects of s, l c and h on the measured resistance and the calculated resistivity 69 4.8 Concluding Remarks 75