Theoretical analysis of laterally vibrating microcantilever sensors in a viscous liquid medium

TLDR: In this article, the hydrodynamic forces on the microcantilever as a function of both Reynolds number and aspect ratio (thickness over width) were first calculated using a combination of numerical methods and Stokes' solution.

Abstract: THEORETICAL ANALYSIS OF LATERALLY VIBRATING MICROCANTILEVER SENSORS IN A VISCOUS LIQUID MEDIUM Russell Cox, B.S., M.S. Marquette University, 2011 Dynamically driven microcantilevers are normally excited into resonance in the out-of-plane flexural mode. The beam’s resonant frequency and quality factor are used to characterize the devices. The devices are well suited for operation in air, but are limited in viscous liquid media due to the increased viscous damping. In order to improve these characteristics, other vibration modes such as the in-plane (or lateral) flexural mode are investigated. In this work, microcantilevers vibrating in the in-plane flexural mode (or lateral direction) in a viscous liquid medium are investigated. The hydrodynamic forces on the microcantilever as a function of both Reynolds number and aspect ratio (thickness over width) are first calculated using a combination of numerical methods and Stokes’ solution. The results allowed for the resonant frequency, quality factor, and mass sensitivity to be investigated as a function of both beam geometry and medium properties. The predicted resonant frequency and quality factor for several different laterally vibrating beams in water are also found to match the trends given by experimentally determined values found in the literature. The results show a significant improvement over those of similar devices vibrating in the out-of-plane flexural mode. The resonant frequency increases by a factor proportional to the inverse of the beam’s aspect ratio. Moreover, the resonant frequency of a laterally vibrating beam shows a smaller decrease when immersed in water (5-10% compared to ~50% for transversely vibrating beams) and, as the viscosity increases, the resonant frequency decreases slower compared to beams excited transversely. The quality factor is found to increase by a factor of 2-4 or higher depending on the medium of operation and the beam geometry. Due to the increased resonant frequency and the decreased effective mass of the beam (compared to beams excited transversely), the estimated mass sensitivity of a laterally excited microcantilever is found to be much larger (up to two orders of magnitude). The improvement in these characteristics is expected to yield much lower limits of detection in liquid-phase bio-chemical sensing applications.