Effect of hydrodynamic force on microcantilever vibrations: Applications to liquid-phase chemical sensing

Abstract

Abstract: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 inplane 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 insitu 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.

Analytical Modeling of a Novel High- $Q$ Disk Resonator for Liquid-Phase Applications

“…Note that the actuation strain driving the system appears in the BVP only on the right-hand side of the second boundary condition, Eq. (14). Also note that the terms in Eq.…”

“…Also note that the terms in Eq. (14) that are proportional to ̈(L,t) and ̇(L,t) are frequency-dependent and correspond, respectively, to the portions of the end force due to (a) the rotational inertia of the disk and that of the fluid dragged by the disk and (b) the viscous torque exerted by the fluid on the disk. (See Fig.…”

“…Resonant devices based on micro/nanoelectromechanical systems (MEMS/NEMS) span a broad spectrum of important applications, including chemical detection [1][2][3][4][5][6][7], biosensing [2][3][4][6][7][8][9][10], rheological measurement [11][12][13][14], and energy harvesting [15][16][17]. However, many of these applications require liquid-phase operation, which poses significant challenges due to the drastic reduction in resonant frequency ( res ) and quality factor (Q) that is typically caused by the liquid's inertia and viscous energy dissipation [18][19][20][21].…”

Microcantilever: An Efficient Tool for Biosensing Applications

“…While analyzing the cantilever operating in the viscous medium, our first task is to study the effect of hydrodynamic force on the microcantilever vibrations [41] [42]. Hydrodynamic forces are the forces that the fluid exerts onto the body of the structure e.g.…”

Comparison of in-plane and out-of-plane piezoelectric microresonators for real-time monitoring of engine oil contamination with diesel

“…The determination of the density and the viscosity of liquids, through the measurement of the natural frequency and the quality factor of a mechanical resonator, has already been reported (Jakoby et al 2011;Dufour et al 2014). This approach presents several advantages with respect to traditional methods of rheological analysis: real-time measurements, on-line configuration, low liquid volumes, etc.…”