Temperature- and Volume-Fraction-Dependent Debye Model for the Dielectric Properties of Binary Mixtures of Water and Methanol at Microwave Frequencies

The microwave-frequency dielectric properties of binary mixtures of water and methanol are a strong function of the temperature and water percentage. The resulting tunability of the dielectric properties via heating/cooling and/or changes in volume fraction makes these mixtures versatile, low-cost dielectric testbed environments for the development of new microwave sensing and heating technologies. We address a gap in the dielectric spectroscopy literature by characterizing the temperature-dependent dielectric properties of binary mixtures of deionized water and methanol. The dielectric properties of pure deionized water (100% water), pure methanol (0% water), and binary mixtures at 20%, 40%, 60%, and 80% water are measured at <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$5~^{\circ } $</tex-math> </inline-formula>C increments from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$20~^{\circ } $</tex-math> </inline-formula>C to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$60~^{\circ } $</tex-math> </inline-formula>C over the frequency range from 0.5 to 10 GHz using a commercial open-ended coaxial probe. We developed a dielectric-properties model for the binary mixtures based on a single-pole Debye equation with parameters that are second-order polynomial functions of both temperature and water percentage. We validated the optimized model parameters by comparing the model predictions with not only the measured dielectric properties of the mixtures at temperatures and percentages used in the model derivation but also the measured properties for intermediate mixtures not used in the derivation and those in previous studies. The low-level discrepancy in all cases was well within the reported uncertainty of open-ended coaxial probe measurements. The derived temperature- and volume-fraction-dependent Debye parameters yield a compact analytical model for a binary mixture that is useful for microwave-frequency testbeds.