Real-Time Complex Dielectric Constant Measurement of Liquids Using Epsilon-Near-Zero Supercoupling Channels

This article proposes a device for real-time measurement of the complex dielectric constant of liquids at
$X$
-band. The device consists of a narrow waveguide channel operating at the cut-off frequency to achieve a large field enhancement based on epsilon-near-zero (ENZ) supercoupling theory. A micro-3-D-printed sample holder is placed inside the channel and connected to feeding tubes that are designed to prevent energy leakage from the channel. The field enhancement and confinement inside the channel create a strong interaction with the liquids under test, thereby providing very sensitive measurements over a wide range of permittivities (approximately 1–65). Two variations of the device are fabricated. One that provides a higher accuracy and another that provides a higher sensitivity. A full-wave simulation-based forward model is developed and optimized using a constrained Nelder-Mead simplex. An inversion is performed based on the optimized forward model to find the complex permittivity from the measured scattering parameters. Two sets of experiments are performed, one of the static liquid mixtures and another of time-varying liquid mixtures. The static measurements are done with binary mixtures of ethanol-water and methanol-water. The time-varying measurements are done with ethanol-water-sugar mixtures and ethanol-water mixtures. The measured results are consistent between the two devices and are in very good agreement with the published literature over the entire range of dielectric constants tested.