The hydrodynamic loading of elastic microcantilevers vibrating in viscous fluids is analyzed computationally using a three-dimensional, finite element fluid-structure interaction model. The quality factors and added mass coefficients of several modes are computed accurately from the transient oscillations of the microcantilever in the fluid. The effects of microcantilever geometry, operation in higher bending modes, and orientation and proximity to a surface are analyzed in detail. The results indicate that in an infinite medium, microcantilever damping arises from localized fluid shear near the edges of the microcantilever. Closer to the surface, however, the damping arises due to a combination of squeeze film effects and viscous shear near the edges. The dependence of these mechanisms on microcantilever geometry and orientation in the proximity of a surface are discussed. The results provide a comprehensive understanding of the hydrodynamic loading of microcantilevers in viscous fluids and are expected to be of immediate interest in atomic force microscopy and microcantilever biosensors.
A mathematical model is presented to predict the oscillating dynamics of atomic force microscope cantilevers with nanoscale tips tapping on elastic samples in liquid environments. Theoretical simulations and experiments performed in liquids using low stiffness probes on hard and soft samples reveal that, unlike in air, the second flexural mode of the probe is momentarily excited near times of tip-sample contact. The model also predicts closely the tip amplitude and phase of the tip at different set points.
We analyze the hydrodynamic coupling between long, slender micromechanical beams ͑microbeams͒ deployed in an array and oscillating in a viscous, incompressible fluid. The unsteady Stokes equations are solved using a boundary integral technique in a two-dimensional plane containing the microbeam cross sections. The oscillations of nearest neighbor and the next neighbor microbeams couple hydrodynamically in unanticipated ways depending on the gap, frequency, and the relative phase and amplitude of their oscillation. A rational basis is provided for choosing the gap between neighboring microbeams in an array in order to either decouple their hydrodynamics or to couple them strongly. The results clearly suggest that the dynamics of microbeams in an array can be tuned in a cooperative manner so as to minimize or maximize the hydrodynamic resistance on individual microbeams.
Abstract-Piezoelectric fans are gaining in popularity as lowpower-consumption and low-noise devices for the removal of heat in confined spaces. The performance of piezoelectric fans has been studied by several authors, although primarily at the fundamental resonance mode. In this article the performance of piezoelectric fans operating at the higher resonance modes is studied in detail. Experiments are performed on a number of commercially available piezoelectric fans of varying length. Both finite element modeling and experimental impedance measurements are used to demonstrate that the electromechanical energy conversion (electromechanical coupling factors) in certain modes can be greater than in the first bending mode; however, losses in the piezoceramic are also shown to be higher at those modes. The overall power consumption of the fans is also found to increase with increasing mode number.Detailed flow visualizations are also performed to understand both the transient and steady-state fluid motion around these fans. The results indicate that certain advantages of piezoelectric fan operation at higher resonance modes are offset by increased power consumption and decreased fluid flow.
Piezoelectric fans typically consist of one piezoelectric patch bonded on one side of a thin, flexible elastic beam. The fan is excited at resonance and used to drive unsteady flows to cool microelectronics components. Field equations of the coupled structure governing the coupled longitudinal and bending motions of the fan are derived using linear constitutive equations, slender beam approximations, and Hamilton’s principle. Analytical solutions are found to the coupled eigenvalue problem. Eigenvalues and eigenfunctions for closed and open circuited configurations are predicted analytically and are found to be in excellent agreement with three-dimensional finite element results. Electromechanical Coupling Factors (EMCF) are computed using the analytical and finite element models and optimal fan geometries are identified for maximal EMCF. The analytical solution provides a convenient tool for the optimal design of such fans.
Improving the force resolution of atomic force microscopy for soft samples in liquid requires soft cantilevers with reduced hydrodynamic cross section. Single and dual axis torsion levers ͓Beyder and Sachs, 2006͔ are an attractive technology. They have reduced area and reduced drift due to the symmetric support ͓Beyder et al., 2006͔ can add a second dimension using two independent axes. Here we investigate the hydrodynamics of these probes using three-dimensional transient fluid-structure interaction models with comparison to the experimental data. The computed Q factors and wet/dry resonance frequencies of different modes compare well with experimental measurements indicating that continuum viscous hydrodynamics can be used effectively to predict probe performance. The modeling further explores cross-axis hydrodynamic coupling and the influence of a nearby sample plane to provide guidance on approach algorithms and the possibilities of parametric detection.
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