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.

A clamped dual‐ridged waveguide measurement system for the broadband, nondestructive characterization of sheet materials

“…Their applications are numerous with nondestructive inspection/evaluation and material characterization applications being the most popular. The most common types of waveguide probes are coaxial [ Folgerø and Tjomsland , ; Wu et al , ; Boybay and Ramahi , ; Shin and Eom , ; Olmi et al , ; Li and Chen , ; De Langhe et al , ; Baker‐Jarvis and Janezic , ; Bird , ] and rectangular/circular waveguide [ Sanadiki and Mostafavi , ; Ganchev et al , ; Bois et al , ; Chang et al , ; Maode et al , ; Hyde et al , ; Hyde and Havrilla , ; Tantot et al , ] probe systems. Coaxial probe systems provide the potential for broadband measurements; however, utilizing them for this purpose can be difficult.…”

“…Both coaxial and rectangular/circular waveguide probe one‐port (single) and two‐port (dual or clamped) systems have been developed. A great majority of the published waveguide probe research involves one‐port probe devices [ Folgerø and Tjomsland , ; Wu et al , ; Boybay and Ramahi , ; Shin and Eom , ; Olmi et al , ; Li and Chen , ; De Langhe et al , , ; Sanadiki and Mostafavi , ; Ganchev et al , ; Bois et al , ; Chang et al , ; Maode et al , ; Tantot et al , ]. These systems are very well suited for determining the complex permittivity ϵ r of a MUT yet suffer when one desires to fully characterize a material, i.e., determine unambiguously the complex permeability μ r as well as ϵ r , because of the lack of a second independent measurement.…”

Nondestructive Complex Permittivity and Permeability Extraction Using a Two-Layer Dual-Waveguide Probe Measurement Geometry

“…Waveguide probes, whether they be coaxial, rectangular, or circular, have numerous applications including nondestructive evaluation of solids and liquids [1][2][3][4][5][6][7][8][9][10][11][12][13][14], surface and subsurface crack detection [15][16][17][18][19], and even in vivo characterization of biological tissues [20,21]. The majority of the published waveguide probe research deals with single probe geometries.…”

Application of microwave reflectometry to biphasic flow characterization

“…Various models are available to link the measured reflection coefficient (denoted in hereafter) of the probes to the complex relative permittivity of the sample under test and its dimensions [3] [4]. In this work we will use the analytical model presented by Bondet [5].…”