Sensitivity of compositional measurement of high-pressure fluid mixtures using microcantilever frequency response
Introduction
Compact sensors based on cantilevers fabricated from different solid materials have received steadily growing attention for the characterization of pure fluids and fluid mixtures [[1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14]]. When an oscillating cantilever is immersed in a fluid, the fluid surrounding the cantilever is set in motion. This moving fluid then applies hydrodynamic forces on the cantilever, resulting in a decrease in the resonant frequency and the quality factor (Q-factor) of the cantilever oscillations compared to their values in vacuum [3,[15], [16], [17]]. The change in the resonant frequency and the Q-factor can be subsequently used to measure various thermophysical properties of the fluid such as its density and viscosity [1,2,9,13,[18], [19], [20]] and also to determine the composition of a fluid mixture [4,5,7,14,[21], [22], [23]].
For practical applications of detection techniques that exploit oscillating microcantilevers, it is of utmost importance to quantify their sensitivity and Limit of Detection (LOD), as these parameters directly determine the domain of usability of microcantilever-based analytical devices. There have been a limited number of experimental and theoretical studies in the literature on the sensitivity of microcantilever-based detection systems. For example, Zhao et al. [24] studied the effect of the geometry of a microcantilever on the sensitivity of density measurements and formulated an analytical expression for the sensitivity defined as the derivative of the cantilever resonant frequency with respect to the density of the fluid. They showed that the sensitivity could be improved by decreasing the length and the width of the microcantilever and also by using a higher-order resonant mode. They measured the resonant frequency of microcantilevers immersed in n-pentane, n-hexane, n-heptane, n-octane, and cyclohexane with densities ranging from 621 to 774 kg/m3 and calculated the best resolution of their density measurements as 0.057 kg/m3 for a 1.9 mm long rectangular cantilever. Boudjiet et al. [7] also showed that the sensitivity of fluid-density sensors based on uncoated microcantilevers can be improved by optimizing the device geometry. They fabricated microcantilevers of different shapes (in particular, rectangular, U-shaped and T-shaped) and dimensions and measured the concentration of H2 in mixtures of H2 and N2 using cantilever resonant frequencies. They found that shorter and wider rectangular cantilevers exhibited better sensitivity to density changes and cantilever thickness did not affect the sensitivity. For 1% H2 in the mixture, the relative difference between the model and the measured resonant frequency was 0.3 to 25% for the studied cantilevers. Tetin et al. [5] studied the shift in the resonant frequency of uncoated microcantilevers due to the changes in the density and viscosity of the surrounding fluid. They measured the relative shift in the resonant frequency of an immersed microcantilever due to the addition of CO2 or He to N2 and compared the experimentally obtained value of the shift with a theoretical model. They neglected the relatively small effect of viscosity on the observed shift of the resonant frequency and reported the sensitivity and LOD of their microcantilever system. Cox et al. [25] studied laterally vibrating microcantilevers immersed in water and aqueous glycerol solutions and measured the resonant frequency, the Q-factor, and the mass sensitivity of the resonant frequency. The mass sensitivities and the Q-factors of microcantilevers excited laterally were found to be higher than those of transversely excited microcantilevers, thus rendering laterally vibrating microcantilevers more suitable for operation in high-viscosity media. Beardslee et al. [26] studied the resonant frequency and the Q-factor of a cantilever immersed in water. They demonstrated that using the in-plane flexural mode reduces damping and mass loading due to the surrounding fluid and showed that shorter, wider, and thinner cantilevers operated with in-plane flexural modes give the best sensing characteristics. Furthermore, Loui et al. [27], Narducci et al. [28], Beardslee et al. [26] and Hocheng et al.[29] also suggested to optimize the cantilever geometry in order to increase the sensitivity of density measurements. All of the above-discussed experimental and computational studies of sensitivity of cantilever-based detection systems were carried out at a low pressure of the fluid surrounding the cantilever (typically at the atmospheric pressure). In addition, in analyzing measurement sensitivity, these studies largely neglected the effects of the changing fluid viscosity and they did not attempt to use the measured thermophysical properties of the fluid to determine fluid’s composition.
In this article, we present a systematic study of the sensitivity of measurement of binary fluid mixtures’ composition based on the measurement of frequency response of a microcantilever immersed in the fluid. To this end, we use a model system of ethanol−CO2 mixtures containing 0 – 0.04 wt fraction of ethanol at a pressure range between 10 MPa and 21 MPa and at 318 K. Such mixtures are frequently encountered in many technological processes such as supercritical drying of aerogels or fabrication of Micro-Electro-Mechanical Systems [[30], [31], [32], [33]]. We define the sensitivities of the compositional measurement as the derivatives of the cantilever resonant frequency or the Q-factor with respect to the weight fraction of ethanol in the mixture, , and derive analytical expressions for the sensitivity from Sader’s model [16] that includes the effects of viscous forces. Using the model sensitivity and the standard deviations of the resonant frequency and the Q-factor measured at given constant experimental conditions, we estimate LOD of ethanol in ethanol−CO2 mixtures. To the best of our knowledge, this work represents the first systematic study on the change in the resonant frequency or the Q-factor of immersed cantilevers with the mixture composition that also includes the effect of viscous forces in the sensitivity analysis.
Section snippets
Materials
CO2 used in the experiments was supplied by Aligaz Messer with a purity of 99.9%. Ethanol was supplied by Sigma-Aldrich with a purity of 99.8%. Both CO2 and ethanol were used as received.
Experimental procedure
Ferromagnetic cantilevers of different lengths made of nickel were produced using standard fabrication methods. The design and fabrication process of the cantilevers were explained in detail in our previous study [3]. The cantilevers used in the present study had nominal lengths of 150 μm and 200 μm, a nominal
Results and discussions
As stated in the introduction, sensitivity of the cantilever resonant frequency to changes in the weight fraction of ethanol in the mixture can be defined as the derivative of with respect to w. Similarly, sensitivity of the cantilever Q-factor to changes in is given by the derivative of with respect to w. Below, we derive analytical expressions for and on the basis of Sader’s model of hydrodynamic interactions [16]. The starting equations of Sader’s model for
Conclusion
We have studied the sensitivity of cantilever-based measurement of composition of ethanol−CO2 mixtures at 318 K and pressure range between 10 MPa to 21 MPa. To this end, we have derived analytical expressions quantifying the change in the resonant frequency and the Q-factor of an immersed cantilever with the ethanol weight fraction in the mixture. We have calculated the effect of viscous term on the sensitivity of compositional measurements and shown that its contribution is significant and
Acknowledgments
This project has received funding from the European Union´s Horizon 2020 research and innovation programme under grant agreement No 685648. We gratefully acknowledge Ummu Koc and Mahmut Bicer for the fabrication of the microcantilevers.
Shadi Khan Baloch received his Bachelor’s degree in 2008 in Electronics Engineering from Mehran UET Jamshoro in Sindh, Pakistan and worked as Assistant Manager Transmission from 2009 to 2013 in PTCL, the leading telecom company of Pakistan. In 2013, he joined Koç University in Istanbul, Turkey as a PhD student in the Electrical and Electronics Engineering Department. His research interests include using micrcocantilevers in chemical/bio sensing applications.
References (50)
- et al.
Determination of viscosity and density of fluids using frequency response of microcantilevers
J. Supercrit. Fluids
(2015) - et al.
Characterization of fluid mixtures at high pressures using frequency response of microcantilevers
Sensor Actuat. A: Phys.
(2017) - et al.
Frequency response of microcantilevers immersed in gaseous, liquid, and supercritical carbon dioxide
J. Supercrit. Fluids
(2013) - et al.
New characterization methods for monitoring small resonant frequency variation: experimental tests in the case of hydrogen detection with uncoated silicon microcantilever-based sensors
Sens. Actuat. B: Chem.
(2014) - et al.
Modeling and performance of uncoated microcantilever-based chemical sensors
Sens. Actuat. B: Chem.
(2010) - et al.
Preliminary results of the feasibility of hydrogen detection by the use of uncoated silicon microcantilever-based sensors
Int. J. Hydrogen Energy
(2014) - et al.
Geometry optimization of uncoated silicon microcantilever-based gas density sensors
Sens. Actuat.B: Chem.
(2015) - et al.
Precision density and viscosity measurement using two cantilevers with different widths
Sens. Actuat. A: Phys.
(2015) - et al.
A straightforward determination of fluid viscosity and density using microcantilevers: from experimental data to analytical expressions
Sensor Actuat. A: Phys.
(2011) - et al.
Effect of hydrodynamic force on microcantilever vibrations: applications to liquid-phase chemical sensing
Sens. Actuators B: Chem.
(2014)
Piezoelectric MEMS resonator-based oscillator for density and viscosity sensing
Sensor Actuat. A: Phys.
High-frequency viscoelastic measurements of fluids based on microcantilever sensing: New modeling and experimental issues
Sensor Actuat. A: Phys.
Determination of composition of ethanol-CO2 mixtures at high pressures using frequency response of microcantilevers
The J. Supercrit. Fluids
Viscosity and density values from excitation level response of piezoelectric-excited cantilever sensors
Sensor Actuat. A: Phys.
Detection and discrimination of pure gases and binary mixtures using a dual-modality microcantilever sensor
Sensor Actuat. A: Phys.
Unconventional uses of microcantilevers as chemical sensors in gas and liquid media
Sens. Actuators B: Chem.
A MEMS-based low pressure, light gas density and binary concentration sensor
Sensor Actuat. A: Phys.
Density measurement sensitivity of micro-cantilevers influenced by shape dimensions and operation modes
Sens. Actuators B: Chem.
Geometrical considerations for the design of liquid-phase biochemical sensors using a cantilever’s fundamental in-plane mode
Sens. Actuators B: Chem.
The effect of piezoresistive microcantilever geometry on cantilever sensitivity during surface stress chemical sensing
Sensor Actuat. A: Phys.
Sensitivity improvement of a microcantilever based mass sensor
Microelectron. Eng.
Shape effects of micromechanical cantilever sensor
Measurement
Experimental and theoretical investigation of supercritical drying of silica alcogels
J. Supercrit. Fluids
Supercritical drying of aerogels using CO 2: effect of extraction time on the end material textural properties
J. Supercrit. Fluids
Continuous extraction rate measurements during supercritical CO 2 drying of silica alcogel
J. Supercrit. Fluids
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Shadi Khan Baloch received his Bachelor’s degree in 2008 in Electronics Engineering from Mehran UET Jamshoro in Sindh, Pakistan and worked as Assistant Manager Transmission from 2009 to 2013 in PTCL, the leading telecom company of Pakistan. In 2013, he joined Koç University in Istanbul, Turkey as a PhD student in the Electrical and Electronics Engineering Department. His research interests include using micrcocantilevers in chemical/bio sensing applications.
Alexandr Jonáš received his M.S. degree in Biophysics from Masaryk University in the Czech Republic in 1996 and Ph.D. degree in Physical and Materials Engineering from the Brno University of Technology in the Czech Republic in 2001. He is currently working as a Research Scientist in the Department of Microphotonics at the Institute of Scientific Instruments of the Czech Academy of Sciences in Brno, Czech Republic. His research interests include the development and applications of optical micromanipulation, microscopy, and spectroscopy techniques for characterization of complex systems and environments.
Alper Kiraz is a professor of Physics and Electrical-Electronics Engineering at Koç University. He received his B.S. degree in Electrical-Electronics Engineering from Bilkent University in 1998, M.S. and Ph.D. degrees in Electrical and Computer Engineering from the University of California, Santa Barbara in 2000 and 2002, respectively. He worked as a post-doctoral researcher at the Chemistry Department of the Ludwig-Maximilians University, Munich and as a visiting professor at the Biomedical Engineering Department of the University of Michigan, Ann Arbor. His current research interests include optofluidics, energy photonics, optical manipulation, and biomedical instrumentation.
B. Erdem Alaca Department of Mechanical Engineering, Koc University, Istanbul, 34450, Turkey. B. Erdem Alaca received the B.S. degree in mechanical engineering from Boğaziçi University, Istanbul, Turkey, in 1997, and the M.S. and Ph.D. degrees in mechanical engineering from the University of Illinois at Urbana–Champaign in 1999 and 2003, respectively. He is currently an Associate Professor in the Department of Mechanical Engineering at Koç University, where he manages Mechanical Characterization and Microfabrication facilities. His research interests include mechanical behavior at the small-scale, fabrication technologies and precision instruments based on nanoelectromechanical devices. Prof. Alaca is a member of the Turkish National Committee on Theoretical and Applied Mechanics and the Institute of Electrical and Electronics Engineers (IEEE). He was a recipient of the 2009 Distinguished Young Scientist Award from the Turkish Academy of Sciences.
Can Erkey received his B.S. degree in Chemical Engineering in 1984 from Boğaziçi University in Istanbul, Turkey and his Ph.D. degree in 1989 in Chemical Engineering from Texas A&M University in College Station, USA. He served as an assistant professor, associate professor and professor in the Department of Chemical Engineering at the University of Connecticut. He has been a professor in the Chemical and Biological Department at Koc University in Istanbul, Turkey since 2006. He is serving as the Director of the Koc University Tüpraş Energy Center. His research interests are nanostructured materials, energy and supercritical fluids.