Characteristics of laterally vibrating resonant microcantilevers in viscous liquid media
Résumé
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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