Abstract
At the microscale level, the vibrational characteristics of microstructures have been widely applied on biochemical microchips, especially for bio-molecules detection. The vibrational mechanics and mechanism of microcantilever beams immersed in the fluids for detecting target bio-molecules carried in the fluids have been widely studied and realized in recent years. However, it is not the case for microcantilever beams containing fluids inside (called suspended microchannel resonators, SMR). In this paper, an 1-D beam model for SMR is proposed and the formula for prediction of resonant frequency and resonant frequency shift are derived. For verification of validity of the 1-D beam model, three dimensional finite element simulations using ANSYS are performed. The effects of relevant parameters, such as density and viscosity of the fluids, on the frequency response are investigated. A link between numerical simulations and mathematical modeling is established through an equivalence relation. Subsequently, a useful formula of the resonant frequency shift as a function of the mass variation and the viscosity of the contained fluid is derived. Good agreement between the numerical simulations and the experimental data is obtained and the physical mechanism is elucidated.
Highlights
In recent years, the study of biosensors has been one of the most significant research fields in biotechnology
It is shown that the 1-D beam model is accurate and effective enough to predict the resonant frequency shift for a net added mass suspended in the flow channel
A master equation with regard to the position index α and the normalized position η is found through curve fitting. With this relation of α and η, we present a simple but sufficiently accurate formula for predicting the resonant frequency shift for the suspended microchannel resonator (SMR) containing a suspended net added mass
Summary
The study of biosensors has been one of the most significant research fields in biotechnology. Of the resonant frequency of the microcantilever induced by the molecular adhesion, and changes of adsorbed molecular mass are acquired on account of the resonant frequency alternation This is similar to the principle of the QCM sensor except for detecting the flexural vibration mode as the objective, rather than the thickwise shear vibration mode. Compared with conventional mass sensors, sensitivity of SMR (suspended microchannel resonator) is apparently elevated through diminishing high damping and friction drag induced by the viscosity of fluids. Burg et al.[16] and Sader et al.[17] presented their interesting experimental measurements and modeling revealing that the non-monotonic energy dissipation in this SMR device was observed over a large range of fluid viscosity. Resonant frequency shifts induced by mass variations within the suspended microchannel resonator will be predicted by this mathematical model. This paper is to analyze the frequency response of the suspended microchannel resonators to the loading mass, which is the main measurable signal relevant to biological applications
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