S. Basak, A. Raman and S. V. Garimella, “Hydrodynamic Loading of Microcantilevers Vibrating in Viscous Fluids,” Journal of Applied Physics Vol. 99, 114906, 2006.
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
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