The Effect of Glycerol-Based Suspensions on the Characteristics of Resonators Excited by a Longitudinal Electric Field

At a Glance

Metadata	Details
Publication Date	2023-01-05
Journal	Sensors
Authors	A. P. Semyonov, Б. Д. Зайцев, A. A. Teplykh, И. А. Бородина
Institutions	Institute of Radio-Engineering and Electronics
Citations	5
Analysis	Full AI Review Included

Executive Summary

This research details a robust acoustoelectric method for accurately characterizing the mechanical properties of glycerol-based suspensions using bulk acoustic wave (BAW) piezoelectric resonators.

Core Achievement: Successfully determined the shear modulus of elasticity (C₆₆^s) and the shear viscosity coefficient (η₆₆^s) of glycerol-diamond suspensions by analyzing the electrical impedance of immersed AT-cut quartz resonators.
Methodology: The technique relies on fitting experimental frequency dependencies of electrical impedance to a theoretical model derived from Mason’s electromechanical equivalent circuit.
Sensor Performance: AT-cut quartz resonators (shear wave mode) provided reliable data, showing that changes in resonant frequency and quality factor directly correlate with changes in the suspension’s mechanical constants.
Suspension Behavior: The study revealed a non-monotonic relationship between diamond particle volume concentration and the suspension’s mechanical properties, specifically noting a minimum in both C₆₆^s and η₆₆^s around 0.147% concentration.
Validation: The shear viscosity coefficients derived from the resonator measurements showed good agreement with independent measurements obtained using a standard SV-10 liquid viscometer.
Limitation Noted: X-cut langasite resonators (longitudinal wave mode) were found unsuitable for accurate material constant determination due to high acoustic radiation loss into the liquid, severely reducing the quality factor (Q-factor ~16).

Technical Specifications

Parameter	Value	Unit	Context
Resonator 1 Material/Cut	AT-cut Quartz	N/A	Shear acoustic wave mode
Resonator 1 Thickness	370	µm	Piezoelectric plate
Resonator 1 Electrode Diameter	5.8	mm	Circular electrodes
Resonator 1 Resonant Frequency (Approx.)	4.4	MHz	Shear mode operation
Resonator 2 Material/Cut	X-cut Langasite	N/A	Longitudinal acoustic wave mode
Resonator 2 Thickness	706	µm	Piezoelectric plate
Resonator 2 Electrode Diameter	7.5	mm	Circular electrodes
Resonator 2 Resonant Frequency (Approx.)	4.1	MHz	Longitudinal mode operation
Experimental Temperature	27.3 ± 0.05	°C	Thermostatted environment
Diamond Particle Size	1-2	µm	Synthetic diamond powder
Maximum Diamond Volume Concentration Tested	2.857	%	Highest concentration sample
Suspension Base Density (Glycerol, 0.0%)	1230.3	kg/m³	Measured density
Suspension Base Shear Modulus (Glycerol, 0.0%)	2.7 x 10⁶	Pa	C₆₆^s derived from resonator
Suspension Base Shear Viscosity (Glycerol, 0.0%)	0.6	Pa·s	η₆₆^s derived from resonator
Minimum Viscosity Concentration Point	0.147	%	Concentration where η₆₆^s minimum was observed
Maximum Suspension Conductivity	0.1	µS/cm	Measured for all samples

Key Methodologies

Suspension Preparation: Six samples of glycerol-diamond suspensions were prepared with volume concentrations ranging from 0.098% to 2.86%. Diamond powder (1-2 µm) was added to 30 mL of glycerol and stirred magnetically for 5 hours.
Density Measurement: Sample densities were determined by weighing a fixed volume (1 mL) using an analytical balance, confirming theoretical density calculations.
Resonator Setup and Control: Quartz and langasite resonators were mounted in separate 30 mL plastic containers. The setup was maintained in a thermostat at 27.3 ± 0.05 °C, with temperature verified using a chromel-alumel thermocouple.
Free Resonator Calibration: The electrical impedance (real R and imaginary X parts) of the unloaded quartz resonator was measured across a frequency range using an E4990A impedance analyzer.
Quartz Material Constant Determination: The measured R and X data for the free resonator were fitted to the theoretical frequency dependencies calculated using Mason’s equivalent circuit. This process determined the intrinsic quartz constants (C₆₆, η₆₆, e₁₆, ε₁₁) via the least squares method.
Suspension Measurement: Each suspension sample was introduced to fully immerse the resonator. The R and X frequency dependencies of the loaded resonator were measured.
Suspension Material Constant Determination: Using the previously determined quartz constants, the measured loaded impedance data were fitted to the loaded Mason equivalent circuit model. This yielded the suspension’s shear modulus (C₆₆^s) and shear viscosity coefficient (η₆₆^s).
Viscosity Validation: The derived shear viscosity coefficients were cross-validated against direct measurements performed on the same samples using an SV-10 liquid viscometer.

Commercial Applications

This technology is highly relevant for industries requiring precise, real-time monitoring of fluid mechanical properties, especially in complex mixtures and colloidal systems.

Acoustic Metrology: High-accuracy determination of fundamental material constants (shear modulus, viscosity, density) for liquids and solid-liquid suspensions.
Liquid Sensors: Development of compact, reliable sensors for monitoring viscosity and elasticity in industrial processes.
Food and Beverage Industry: Quality control and process monitoring for complex fluids (e.g., emulsions, thickeners, gels).
Pharmaceutical and Biomedical: Characterization of drug suspensions, biological fluids, and highly viscous media.
Environmental Monitoring: Monitoring the state and composition of wastewater, groundwater, and reservoirs containing suspended solids.
Oil and Gas Production: Characterization of drilling muds, slurries, and high-viscosity reservoir fluids.

View Original Abstract

This study examines the effect of suspensions based on pure glycerol and diamond powder with different concentrations on the characteristics of resonators with a longitudinal electric field. We used two disk resonators made of the quartz and langasite plates with round electrodes on both sides of the plate and resonant frequencies of 4.4 and 4.1 MHz, operating in shear and longitudinal acoustic modes, respectively. Each resonator was mounted on the bottom of a 30 mL liquid container. During the experiments, the container was filled with the suspension under study in such a way that the resonator was completely immersed in the suspension, and the frequency dependences of the real and imaginary parts of the electrical impedance of the resonator were measured. As a result, the shear modulus of the elasticity and shear coefficient of the viscosity of the studied suspensions were determined. The material constants of the suspensions were found by fitting the theoretical frequency dependences of the real and imaginary parts of the electrical impedance of the resonator to the experimentally measured ones, which was calculated using Mason’s equivalent circuit. As a result, the dependencies of the density, shear modulus of elasticity, shear viscosity coefficient, and velocity of the shear acoustic wave on the volume concentration of the diamond particles were constructed.

Tech Support

Original Source

DOI: https://doi.org/10.3390/s23020608

References

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2022 - Compact liquid analyzer based on a resonator with a lateral excitation electric field [Crossref]
2015 - Liquid Sensor Based on a Piezoelectric Lateral Electric Field -Excited Resonator [Crossref]
2022 - A new liquid sensor based on a piezoelectric resonator with a radial electric field [Crossref]
2022 - Sensor System Based on a Piezoelectric Resonator with a Lateral Electric Field for Virus Diagnostics [Crossref]