FEA and Analytic Validation of Incremental Cell Constant for Four-Electrode Electrical Conductivity Measurement Suitable for Liquid Electrolyte

Determining the cell factor, which is required for measuring the electrical conductivity of a solution, is challenging, especially at elevated temperatures or under chemically aggressive conditions. Here we validate a practical, calibration-free method for measuring the electrical conductivity of aggressive solutions using a four-electrode probe and incremental immersion technique. The incremental cell factor (geometric factor) is determined from the change of conductance with respect to electrode immersion depth. An analytical expression for the geometric factor was developed and its range of validity determined through experiments with KCl( aq ) solutions and finite element analysis (FEA) using COMSOL. The experimental geometric factor was independent of solution conductivity across three orders of magnitude (varying by ±2 %), and the mean experimental value differed only 0.04 % from the FEA predictions. A parametric study of system dimensions was used to compare the analytic and simulated geometric factors. Further, we identify conditions where our analytic predictions give geometric factors within 2 % of the FEA. The technique is robust against solution wetting effects and total immersion uncertainties, making it suitable for high-temperature or corrosive environments, and does not require calibration with reference solutions.