Resonant microcantilevers vibrating laterally in viscous liquid media

Abstract

The characteristics of microcantilevers vibrating in the in-plane flexural mode (also known as lateral vibration) in viscous liquid media are investigated. A numerical model was utilized to determine a correction to Stokes' solution for an infinite plate to obtain an analytical expression for the hydrodynamic forces acting on a laterally vibrating microcantilever as a function of both Reynolds number and aspect ratio (thickness over width). The results allowed for the resonant frequency and quality factor to be investigated as a function of both beam geometry and medium properties. Trends in these characteristics can be used to optimize device geometry and maximize the frequency stability. As the thickness of a microcantilever is increased, both its stiffness and the medium's viscous damping increase. This will lead to an optimum quality factor in terms of the thickness. The characteristics of laterally and transversely vibrating microcantilevers with similar geometries are also compared. It is found that the resonant frequency and quality factor are higher for laterally vibrating microcantilevers (at least by a factor of 2 to 3 or higher for the Q-factor depending on the geometry) compared to those of similar beams under transverse (or out-of-plane) vibration. The improvement in sensitivity (due to the increase in frequency) and in the quality factor (thus a reduced frequency noise) are expected to yield much lower limits of detection in liquid-phase chemical sensing applications.