Electrostatic sensing mechanisms in core–shell semi-cylindrical capacitive sensors for liquid height detection

Semi-cylindrical capacitive sensors have emerged as a promising way of monitoring liquid height in cylindrical vessels and tubes, despite still presenting significant challenges for sensor design, since the established models cannot account for the dependence of the capacitance on varying dielectric media and electrode configuration in non-uniform structures. In particular, the behavior of capacitors where the electrodes are mounted outside the tube and not in direct contact with the analyte poses significant added challenges due to a core–shell structure with different permittivity values. In this article, we present an empirical design rule for core–shell semi-cylindrical capacitors that accounts for electrode positioning, vessel wall thickness, and dielectric media. We show that in core–shell structures, accepted models that treat the arched electrode plates as non-interacting parallel constituents fail due to the non-uniform electric field that develops within the cylinder. When considering the azimuthal separation of arched electrodes, the maximal sensitivity for the sensor is achieved when the electrodes cover symmetrical sectors of roughly 100° on opposite sides of the cylinder. This result is explained as an inverse correlation between the reduction of parasitic fringing fields within the shell material and the minimization of the electrode separation.