Damping and Mass Sensitivity of Laterally Vibrating Resonant Microcantilevers in Viscous Liquid Media

The effect of liquid viscosity and density on the characteristics of laterally excited microcantilevers is investigated and compared to transversely excited microcantilevers. When immersed into a viscous liquid medium such as water from air, the resonant frequency of laterally (in-plane) vibrating microcantilevers is shown to decrease by only 5-10% as compared to ~50% reduction for transversely (out-of-plane) vibrating microcantilevers. Furthermore, as the viscosity of the medium increases the resonant frequency of a laterally vibrating beam is shown to decrease at a slower rate than that of a transversely vibrating beam. The decreased viscous damping also leads to increases in the quality factor of the system by a factor of 4-5 compared to beams vibrating transversely. The mass sensitivities of laterally vibrating beams are also theoretically predicted to be roughly two orders of magnitude larger in water for some cantilever geometries. The increase in the quality factor and mass sensitivity indicate that operating in the in-plane flexural mode (lateral vibration) will decrease the limit of detection compared to operating in the more common out-of-plane flexural mode (transverse vibration). These improvements in device characteristics indicate that microcantilevers excited laterally are more suited for operating in media of high viscosities

Resonant Characteristics of Rectangular Microcantilevers Vibrating Torsionally in Viscous Liquid Media

The resonant characteristics of rectangular microcantilevers vibrating in the torsional mode in viscous liquid media are investigated. The hydrodynamic load (torque per unit length) on the vibrating beam due to the liquid was first determined using a finite element model. An analytical expression of the hydrodynamic function in terms of the Reynolds number and aspect ratio, h/b (with thickness, h, and width, b) was then obtained by fitting the numerical results. This allowed for the resonance frequency and quality factor to be investigated as functions of both beam geometry and medium properties. Moreover, the effects of the aspect ratio on the cross-section\u27s torsional constant, K, which affects the microcantilever\u27s torsional stiffness, and on its polar moment of inertia, Jp, which is associated with the beam\u27s rotational inertia, are also considered when obtaining the resonance frequency and quality factor. Compared with microcantilevers under out-of-plane (transverse) flexural vibration, the results show that microcantilevers that vibrate in their 1st torsional or 1st in-plane (lateral) flexural resonant modes have higher resonance frequency and quality factor. The increase in resonance frequency and quality factor results in higher mass sensitivity and reduced frequency noise, respectively. The improvement in the sensitivity and quality factor are expected to yield much lower limits of detection in liquid-phase chemical sensing applications

Unconventional Uses of Microcantilevers as Chemical Sensors in Gas and Liquid Media

The use of microcantilevers as (bio)chemical sensors usually involves the application of a chemically sensitive layer. The coated device operates either in a static bending regime or in a dynamic flexural mode. While some of these coated devices may be operated successfully in both the static and the dynamic modes, others may suffer from certain shortcomings depending on the type of coating, the medium of operation and the sensing application. Such shortcomings include lack of selectivity and reversibility of the sensitive coating and a reduced quality factor due to the surrounding medium. In particular, the performance of microcantilevers excited in their standard out-of-plane dynamic mode drastically decreases in viscous liquid media. Moreover, the responses of coated cantilevers operating in the static bending mode are often difficult to interpret. To resolve these performance issues, the following emerging unconventional uses of microcantilevers are reviewed in this paper: (1) dynamic-mode operation without using a sensitive coating, (2) the use of in-plane vibration modes (both flexural and longitudinal) in liquid media, and (3) incorporation of viscoelastic effects in the coatings in the static mode of operation. The advantages and drawbacks of these atypical uses of microcantilevers for chemical sensing in gas and liquid environments are discussed

Effect of Hydrodynamic Force on Microcantilever Vibrations: Applications to Liquid-Phase Chemical Sensing

At the microscale, cantilever vibrations depend not only on the microstructure’s properties and geometry but also on the properties of the surrounding medium. In fact, when a microcantilever vibrates in a fluid, the fluid offers resistance to the motion of the beam. The study of the influence of the hydrodynamic force on the microcantilever’s vibrational spectrum can be used to either (1) optimize the use of microcantilevers for chemical detection in liquid media or (2) extract the mechanical properties of the fluid. The classical method for application (1) in gas is to operate the microcantilever in the dynamic transverse bending mode for chemical detection. However, the performance of microcantilevers excited in this standard out-of-plane dynamic mode drastically decreases in viscous liquid media. When immersed in liquids, in order to limit the decrease of both the resonant frequency and the quality factor, and improve sensitivity in sensing applications, alternative vibration modes that primarily shear the fluid (rather than involving motion normal to the fluid/beam interface) have been studied and tested: these include in-plane vibration modes (lateral bending mode and elongation mode). For application (2), the classical method to measure the rheological properties of fluids is to use a rheometer. However, such systems require sampling (no in-situ measurements) and a relatively large sample volume (a few milliliters). Moreover, the frequency range is limited to low frequencies (less than 200Hz). To overcome the limitations of this classical method, an alternative method based on the use of silicon microcantilevers is presented. The method, which is based on the use of analytical equations for the hydrodynamic force, permits the measurement of the complex shear modulus of viscoelastic fluids over a wide frequency range

Sorption-induced Static Bending of Microcantilevers Coated with Viscoelastic Material

Absorption of a chemical analyte into a polymercoating results in an expansion governed by the concentration and type of analyte that has diffused into the bulk of the coating. When the coating is attached to a microcantilever, this expansion results in bending of the device. Assuming that absorption (i.e., diffusion across the surface barrier into the bulk of the coating) is Fickian, with a rate of absorption that is proportional to the difference between the absorbed concentration and the equilibrium concentration, and the coating is elastic, the bending response of the coated device should exhibit a first-order behavior. However, for polymercoatings, complex behaviors exhibiting an overshoot that slowly decays to the steady-state value have been observed. A theoretical model of absorption-induced static bending of a microcantilever coated with a viscoelastic material is presented, starting from the general stress/strain relationship for a viscoelastic material. The model accounts for viscoelasticstress relaxation and possible coating plasticization. Calculated responses show that the model is capable of reproducing the same transient behavior exhibited in the experimental data. The theory presented can also be used for extracting viscoelasticproperties of the coating from the measured bending data

Resonant Microcantilevers for the Determination of the Loss Modulus of Thin Polymer Films

The increasing interest in polymer materials creates the need for accurate tools to characterize their mechanical properties. Due to energy dissipation in polymers during deformation, these materials exhibit viscoelastic behavior. Accurate determination of these viscoelastic properties and, more specifically, viscous losses, remains challenging and mainly unknown for thin polymer films. In this paper, a straightforward method to determine the loss modulus of organic materials using resonating microcantilevers has been developed. The extracted results for polyisobutylene show the variation of viscous losses over a large range of frequencies (7-350 kHz)

Generalized Knudsen number for unsteady fluid flow

We explore the scaling behavior of an unsteady flow that is generated by an oscillating body of finite size in a gas. If the gas is gradually rarefied, the Navier-Stokes equations begin to fail and a kinetic description of the flow becomes more appropriate. The failure of the Navier-Stokes equations can be thought to take place via two different physical mechanisms: either the continuum hypothesis breaks down as a result of a finite size effect or local equilibrium is violated due to the high rate of strain. By independently tuning the relevant linear dimension and the frequency of the oscillating body, we can experimentally observe these two different physical mechanisms. All the experimental data, however, can be collapsed using a single dimensionless scaling parameter that combines the relevant linear dimension and the frequency of the body. This proposed Knudsen number for an unsteady flow is rooted in a fundamental symmetry principle, namely, Galilean invariance