Measurement of a Micro-Scale Fluid Physical Properties Using Torsional Vibration of a Micro Shaft

Measurement of a Micro-Scale Fluid Physical Properties Using Torsional Vibration of a Micro Shaft

Mina Ghanbari* Siamak Hossainpour Ghader Rezazadeh

Mechanical Engineering Department, Engineering Faculty of Khoy, Urmia University, Urmia, Iran

Mechanical Engineering Department, Sahand University of Technology, Tabriz, Iran

Mechanical Engineering Department, Faculty of Engineering, Urmia University, Urmia, Iran

Corresponding Author Email: 
m.ghanbari@urmia.ac.ir
Page: 
257-265
|
DOI: 
https://doi.org/10.18280/mmc_b.870407
Received: 
14 July 2018
| |
Accepted: 
14 December 2018
| | Citation

OPEN ACCESS

Abstract: 

The purpose of this study is presenting a novel micro-electromechanical (MEM) sensor for measurement of a micro-scale fluid physical properties. A mathematical model is proposed for this study which consists of a micro-shaft with one end fixed and a sensing element in the form of a cylinder at its free end. The fluid is bounded between the micro-cylinder as sensing element and the outer fixed cylinder. As fluids behave differently in micro-scale than macro, the fluid in the gap is modeled based on micro-polar fluid theory. The sensor can be actuated torsionally via applying an AC voltage to the pair of capacitive plates situated around the micro-shaft and the outer fixed cylinder. After deriving the equations of motion of the micro-shaft and also micro-scale fluid media, these coupled partial differential equations have been solved simultaneously using Galerkin based reduced order model. The dynamic response of the micro-shaft for different exciting frequencies has been investigated. It has been shown that inertial and damping effects of fluid, causes resonance frequency and resonance amplitude of the shaft to decrease. By calculating resonance frequency and resonance amplitude changes, physical properties of a fluid can be measured. Effects of geometrical parameters of the sensing element on the force response of the sensor have also been studied.  Through this study it was found that a sensor with large surface area of sensing element and small fluid gap, could measure fluid properties with high accuracy.

Keywords: 

MEMS, micropolar theory, micro-scale fluid, torsional vibration

1. Introduction
2. Micropolar Theory
3. Model Description and Assumptions
4. Numerical Solutions
5. Numerical Results
6. Conclusion
Nomenclature
  References

[1] Ebadian MA, Dillon J, Moore J, Jones K. (1996). Sensors for viscosity and shear strength measurement. Technical Report. Florida International Univ., Miami, FL (United States). https://doi.org/10.2172/666055

[2] Stoyanov PG, Grimes CA. (2000). A remote grey magnetostrictive viscosity sensor. Sensor and Actuators A 80(1): 8-14. 

[3] Martin BA, Wenzel  SW, Richard MW. (1990). Viscosity and density sensing with ultrasonic plate waves. Sensor and Actuators A 22: 704-708. https://doi.org/10.1016/S0924-4247(99)00288-5

[4] Rezazadeh G, Khatami F, Tahmasebi A. (2007). Investigation of thetorsion and bending effects on static stability of electrostatictorsional micromirrors. Microsystem Technologies 13(7): 715–722. https://doi.org/10.1007/s00542-006-0362-1

[5] Saif MTA, Alaca BE, Sehitoglu H. (1999). Analytical modeling of electrostatic membrane actuator micro pumps. Journal of Microelectromechanical Systems 8(3): 335-345. https://doi.org/10.1109/84.788638

[6] Bao M, Wang W. (1996). Future of Microelectro mechanical systems (MEMS). Sensors and Actuators A 56(1): 135-141. https://doi.org/info:doi/10.1016/0924-4247(96)01274-5

[7] Rezazadeh G, Ghanbari M, Mirzaee I. (2010). On the modeling of piezoelectrically actuated microsensor for Simultaneous measurement of fluids viscosity and density. Measurement 43(10): 1516-1524. https://doi.org/10.1016/j.measurement.2010.08.022

[8] Ghanbari M, Hossainpour S, Rezazadeh G. (2015). Study of squeeze film damping in a microbeam resonator based on micropolar theory. Latin American Journal of Solids and Structures 12(1): 77-91.

[9] Ghanbari M, Hossainpour S, Rezazadeh G. (2015). Studing thin film damping in a micro-beam resonator based on non-classical theories. Acta Mechanica Sinica 32(3): 369-379. https://doi.org/10.1007/s10409-015-0482-x

[10] Rezazadeh G, Ghanbari M. (2018). On the mathematical modeling of a MEMS-based sensor for simultaneous measurement of fluids viscosity and density. Sensing and Imaging 19: 27. https://doi.org/10.1007/s11220-018-0213-z

[11]  Enoksson P, Stemme G, Stemme E. (1995). Fluid density sensors based on resonance vibration. Sensors and Actuators A 47(1-3): 327-331. https://doi.org/10.1016/0924-4247(94)00915-5

[12] Sader JE. (1998). Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscopy. Journal of Applied Physics 84(64): 64–76. https://doi.org/10.1063/1.368002

[13] Agoston A, Keplinger F, Jakopy B. (2005). Evaluation of a vibrating micromachined cantilever sensor for measuring g the viscosity of complex organic liquids. Sensors and Actuators A 123: 82-86. https://doi.org/10.1016/j.sna.2005.02.020

[14] Castille CH, Dufour I, Lucat IC. (2010). Longitudinal vibration mode of piezoelectric thick-film cantilever-based sensors in liquid media. Applied Physics Letters 96: 154102. https://doi.org/10.1063/1.3387753

[15] Heinisch M, Voglhuber-Brunnmaier T, Reichel EK, Dufour I, Jakoby B. (2015). Electromagnetically driven torsional resonators for viscosiry and mass density sensing applications. Sensora and Actuators A 229(15): 182-191. https://doi.org/10.1016/j.sna.2015.03.033

[16] Heinisch M, Voglhuber-Brunnmaier T, Reichel, EK, Dufour I, Jakobe B. (2015). Application of resonant tuning forks with circular and rectangular crosssections for precise mass density and viscosity measurements. Sensors and Actuators A 226(1): 163-174. https://doi.org/10.1016/j.sna.2015.02.007

[17] Heinisch M, Reichel EK, Dufour I, Jakoby B. (2014). Modeling and experimental investigation of resonant viscosity and mass density sensors considering their cross sensitivity to temperature. Procedia engineering 87: 472-475. https://doi.org/10.1016/j.proeng.2014.11.391

[18] Zhao L, Hu Y, Wang T, Ding J, Liu X, Zhao Y, Jiang Z. (2016). A MEMS resonant sensor to measure fluid density and viscosity under flexural and torsional vibrating modes. Sensors 16(6): 830. https://doi.org/10.3390/s16060830

[19] Payam AF, Trewby W, Voitchovsky K. (2017). Simultaneous viscosity and density measurement of small volumes of liquids using a vibrating microcantilever. Analyst 142(9): 1492-1498. https://doi.org/10.1039/C6AN02674E

[20] Clara S, Antlinger H, Abdallah A, Reichel E, Hilber W, Jakoby B. (2016). An advanced viscosity and density sensor based on diamagnetically stabilized levitation. Sensora and Actuators A 248: 46-53. https://doi.org/10.1016/j.sna.2016.07.021

[21] Gonzalez M, Seren  HR, Ham G, Buzi E,  Bernero G, Deffenbaugh M. (2018). Viscosity and density measurements using mechanical osillators in oil and gas applications. IEEE Transactions on Instrumentation and Measurement 67(4): 804-807. https://doi.org/10.1109/TIM.2017.2761218

[22] Bircher B, Krenger R, Braun T. (2016). Automated high-throughput viscosity and density sensor using nanomechanical resonators. Sensora and Actuators B 223: 784-790. https://doi.org/10.1016/j.snb.2015.09.084

[23] Ghanbari M, Hossainpour S, Rezazadeh G. (2015). On the modeling of a piezoelectrically actuated micro-sensor for measurement of microscale fluid physical properties. Applied Physics A 121(2): 651-663.

[24] Eringen AC. (1996). Theory of micro-polar fluids. Journal of Mathematics and Mechanics 16(1): 1-18. https://doi.org/10.1512/iumj.1967.16.16001

[25] Erigena AC. (1972). Theory of thermomicrofluids. Journal of Mathematical Analysis and Applications 38(2): 480-496. https://doi.org/10.1016/0022-247X(72)90106-0

[26] Kucaba-Pietal A. (2008). Applicability of the micropolar fluid theory in solving microfluidics problems. Proceedings of 1st European Conference on Microfluidics, Bologna.

[27] Chen J, Liang C, Lee JD. (2011). Theory and simulation of micropolar fluid dynamics. Journal of Nanoengineering and Nanosystems 224: 31-39. https://doi.org/10.1177/1740349911400132

[28] Ahmadi G. (1976). Self-similar solution of incompressible micro-polar boundary layer flow over a semi-infinite plate. International Journal of Engineering Science 14(7): 639-646. https://doi.org/10.1016/0020-7225(76)90006-9

[29] Song X, Fang JC, Sheng W. (2009). Circuit for close-loop capacitive micro accelerometers. Journal of Beijing University of Aeronautics and Astronautics 35(3): 384-388.