Hydrodynamic loading of microcantilevers vibrating in viscous fluids

Sudipta Basak, Birck Nanotechnology Center and School of Mechanical Engineering, Purdue University
Arvind Raman, Birck Nanotechnology Center and School of Mechanical Engineering, Purdue University
Suresh Garimella, School of Mechanical Engineering

Abstract

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.