1. Introduction
Real‐ time monitoring of liquid properties—particularly viscosity and density—is critical in
many industrial applications (e.g., process control, food and oil industries, and biomedical
diagnostics). Microfabricated devices based on piezoelectric resonators offer an attractive
approach thanks to their small size, rapid response, and low sample volumes. In this report,
we review two recent works on piezoelectric MEMS resonators and membranes for liquid
property measurements, then propose a design for an integrated MFC‐ based device that
can be embedded into a pipe system for inline measurement.
2. Literature Review
2.1. Piezoelectric MEMS Resonator Oscillator
In the 2014 work (Manzaneque et al.) , a piezoelectric MEMS resonator is immersed in liquid
and incorporated into an oscillator circuit. The device exploits the change in its natural
frequency and quality factor (Q) when interacting with different liquids. Key points include:
Resonator Model: The resonator is modeled as a damped second-order system:
Piezoelectric Coupling: The conversion of mechanical vibrations to electrical
signals is modeled by the piezoelectric admittance:
and
are the actuation and sensing coupling coefficients, respectively.
They represent how efficiently the piezoelectric material converts energy between its
electrical and mechanical forms
Interface Electronics: A compensation strategy (using a dummy device) minimizes
parasitic effects, allowing reliable determination of the resonant frequency even
under heavy liquid damping.
2.2. Piezoelectric-Excited Membrane
The 2017 paper (Liu et al.) presents a piezoelectric-excited membrane device designed for
rapid measurement of viscosity and mass density. Notable aspects include:
Membrane Dynamics: The resonant frequency under stress (e.g., induced by a
pressure difference) is given by:
where
accounts for the mass loading effect of the liquid.
Linear Relations: By rearrangement, the following simplified forms are derived: , .
Here, is the liquid density and its viscosity. These relationships allow
independent extraction of both parameters from the measured resonant frequency
and Q factor.
3. Device Design and Manufacturing Strategy
3.1. Conceptual Design
The proposed device integrates a piezoelectric resonator or membrane into a microfluidic
flow cell (MFC) mounted within a pipe. Key design features include:
Flow Integration: A microchannel is formed on or integrated with the sensor chip,
ensuring that the liquid flows over the resonator.
Sensing Element: A piezoelectric thin film (e.g., AlN or PVDF) is patterned onto a
silicon substrate. The resonator geometry (e.g., a cantilever or membrane) is chosen
to provide sufficient displacement and sensitivity.
Electrical Interface: An oscillator circuit is integrated with the sensor. In order to
track frequency and phase (and thereby Q factor), the circuit includes a dummy
device or compensation network to cancel parasitic capacitances.
4. Proposed Device Architecture
Sensor Chip: A piezoelectric resonator (or membrane) patterned on silicon.
Microfluidic Flow Cell: A microchannel is integrated onto the sensor chip so that the
liquid flows directly over the resonator.
Electronic Interface: An oscillator circuit with compensation for parasitic effects,
using a dummy sensor branch.
Signal Processing: A frequency counter and phase detection circuitry are used to
determine resonant frequency shifts and changes in Q factor.
Calibration Module: A calibration routine (possibly implemented in firmware) that
converts frequency and Q measurements into density and viscosity values using the
linear relationships derived above.
5. Expected Performance Range:
Density: 0.68–0.9 g/cm³ (Manzaneque et al., 2014).
Viscosity: 0.4–1733 cP (Lu et al., 2017).
Resolution: Δρ ≈ 4×10⁻⁶ g/mL, Δη ≈ 2×10⁻³ mPa·s (for high-viscosity liquids).
Stability: Allan deviation ~10⁻⁷ (comparable to MEMS oscillators).
Keywords and Explanations
Parasitic Effects:
Unintended electrical characteristics (such as stray capacitance or inductance) that arise
due to the physical layout and inherent properties of components and interconnects. These
effects can distort the signal by adding extra phase shifts or attenuating the amplitude,
making it harder to accurately measure the resonator's response.
Parasitic Capacitance:
Unwanted capacitance that exists between conductors (e.g., traces, electrodes) due to their
proximity. In sensor circuits, parasitic capacitance can lead to signal leakage (feedthrough)
and can mask the true signal generated by the sensor.
Feedthrough:
The phenomenon in which a signal bypasses the intended signal path, often due to parasitic
capacitance or coupling, resulting in an undesired background or baseline response that
interferes with the accurate measurement of the sensor’s output.
Dummy Device:
A replica or non-active version of the sensor structure designed to mimic the parasitic effects
of the active sensor. By measuring the response of the dummy device and subtracting it
from the active sensor’s output, one can cancel out unwanted parasitic signals, thereby
isolating the true sensor response.
Mass Loading:
The effect by which the addition of mass (such as a liquid contacting the sensor) shifts the
resonant frequency of the sensor. In the context of the device, mass loading is used to infer
the liquid’s density since a greater mass load typically results in a lower resonant frequency.
Quality Factor (Q Factor):
A dimensionless parameter that describes the damping of the resonator. A high Q factor
means the resonator oscillates with minimal energy loss, resulting in a sharper resonance
peak. Changes in the Q factor can indicate variations in the viscosity of the surrounding
liquid.
Resonant Frequency:
The natural frequency at which the sensor or resonator oscillates with the highest amplitude.
Shifts in resonant frequency due to changes in mass loading (from the liquid) are used to
deduce the density of the liquid.
Piezoelectric Effect:
The ability of certain materials to generate an electrical charge in response to mechanical
stress (and vice versa). This principle is used in the sensor to convert mechanical vibrations
into an electrical signal for measurement.
Microfluidic Flow Cell (MFC):
A miniaturized channel or chamber that directs the flow of liquid over the sensor. Integration
of the MFC allows for inline and real-time measurement of liquid properties in a controlled
environment.
6. Conclusion
The MFC-based sensor combines the advantages of MEMS resonators and
piezoelectric membranes, enabling real-time, non-invasive measurement of η and ρ
in flowing liquids. Future work includes optimizing MFC geometry and field testing
under industrial conditions.
7. References
1. Piezoelectric MEMS resonator-based oscillator for density and viscosity sensing.
Manzaneque, T., Ruiz-Díez, V., Hernando-García, J., Wistrea, E., Kucera, M., Schmid, U., &
Sánchez-Rojas, J. L. (2014). Published in Sensors and Actuators A: Physical, 220, 305–
315.
2. Piezoelectric-excited membrane for liquids viscosity and mass density
measurement. Lu, X., Hou, L., Zhang, L., Tong, Y., Zhao, G., & Cheng, Z.-Y. (2017).
Published in Sensors and Actuators A: Physical, 261, 196–201.
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