Permittivity measurement of thin liquid layers using open-ended coaxial probes

Abstract

The composition of a thin emulsion layer backed by air can be determined from permittivity measurements with an open-ended coaxial probe. In this work, techniques for probe design and determination of liquid permittivity are studied. Measurements on thin liquid layers backed by a low-permittivity material show that the measured apparent permittivity varies exponentially with the layer thickness, with a probe constant that is independent of measurement frequency and liquid permittivity. It is found that an electrostatic model is applicable for design of probes with regard to the probe's sensitivity depth. Models of different complexity for determination of permittivity are compared and it is shown that a bilinear model in combination with an empirical exponential model estimates the permittivity of thin liquid layers with high sensitivity provided that the thickness of the layer is known. The bilinear model uses calibration measurements on three samples with known permittivities. A somewhat lower precision is obtained with a full-wave model of the probe, but this model has the advantage that no calibration except a simple reference plane rotation is needed. However, the computation time of the full-wave model is high.