The characteristics of microcantilevers vibrating laterally in viscous liquid media are investigated and compared to those of similar microcantilevers vibrating in the out-of-plane direction. The hydrodynamic loading on the vibrating beam is first determined using a numerical model. A semi-analytical expression for the hydrodynamic forces in terms of the Reynolds number and the aspect ratio (beam thickness over beam width) is obtained by introducing a correction factor to Stokes’ solution for a vibrating plate of infinite area to account for the effects of the thickness. The results enable the effects of fluid damping and effective fluid mass on the resonant frequency and the quality factor (Q) to be investigated as a function of both the beam’s geometry and liquid medium’s properties and compared to experimentally determined values given in the literature. The resonant frequency and Q are found to be higher for laterally vibrating microcantilevers compared to those of similar geometry experiencing transverse (out-of-plane) vibration. Compared to transversely vibrating beams, the resonant frequency of laterally vibrating beams is shown to decrease at a slower rate (with respect to changes in viscosity) in media having higher viscosities than water. The theoretical results are compared to experimental data obtained for cantilevers completely immersed in solutions of varying aqueous percent glycerol. The increases in resonant frequency and Q are expected to yield much lower limits of detection in liquid-phase chemical sensing applications.
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1 January 2012
Research Article|
January 10 2012
Characteristics of laterally vibrating resonant microcantilevers in viscous liquid media
Russell Cox;
Russell Cox
1Department of Electrical and Computer Engineering,
Marquette University
, Milwaukee, Wisconsin 53233, USA
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Fabien Josse;
Fabien Josse
a)
1Department of Electrical and Computer Engineering,
Marquette University
, Milwaukee, Wisconsin 53233, USA
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Stephen M. Heinrich;
Stephen M. Heinrich
2Department of Civil and Environmental Engineering,
Marquette University
, Milwaukee, Wisconsin 53233, USA
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Oliver Brand;
Oliver Brand
3
School of Electrical and Computer Engineering, Georgia Institute of Technology
, Atlanta, Georgia 30332, USA
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Isabelle Dufour
Isabelle Dufour
4
Université de Bordeaux, CNRS, IMS Laboratory
, Talence, France
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a)
Author to whom correspondence should be addressed. Electronic mail: fabien.josse@marquette.edu.
J. Appl. Phys. 111, 014907 (2012)
Article history
Received:
November 02 2011
Accepted:
December 05 2011
Citation
Russell Cox, Fabien Josse, Stephen M. Heinrich, Oliver Brand, Isabelle Dufour; Characteristics of laterally vibrating resonant microcantilevers in viscous liquid media. J. Appl. Phys. 1 January 2012; 111 (1): 014907. https://doi.org/10.1063/1.3674278
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