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The four-electrode method is commonly used for in situ measurement of the electrical resistivity of biological tissues. In this paper, a new geometric factor between the resistivity and measured resistance using the four-electrode interface is derived in the prolate spheroidal coordinates and experimentally validated. Evaluation of the experimental results shows that the resistivities determined using both the derived geometric factor and a commercial conductivity meter are in close agreement even when the length of the immersed electrodes becomes long with respect to the inter-electrode spacing. The evaluation also shows the effect of the relative size of the sample volume when the limitation to semi-infinite volume begins to result in poor accuracy.

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In this work, we derive a new geometric factor in oblate spheroidal coordinates for conductivity or resistivity measurements using two planar disc electrodes based on the electromagnetic field theory and neglecting the electrode polarization effects. The experiments were conducted on saline solutions contained in a grounded metallic bath to validate the obtained values of the derived geometric factor. The effect of the polarization impedance at the electrodes is found to be negligible when using relatively nonpolarizable silver-silver chloride electrodes at a frequency of 3 kHz. Our experimental results also show that the resistivity values determined using both the new geometric factor and a commercial conductivity meter are in good agreement for small electrode radius, interelectrode spacing and depth of sample, therefore making it a promising technique for applications in microfluidics devices. The effects of current density and temperature on the measurement results are also presented.