Analytical Modeling of Microfluidic Cantilever Sensor with Evaporating Ethanol

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Resonating microcantilevers are widely used for myriad biochemical sensing applications. Small samples can be characterized for their physical [1], chemical [2], and thermal [3] properties. An example of such a sensor is shown in Fig. 1, wherein microcantilevers with embedded microfluidic channels have been fabricated using low stress silicon rich SiN. The resonant frequency of these microstructures is very sensitive to mass of the liquid in the microchannel. We measure the evaporation of small volumes of ethanol within the channel and relate the evaporation rate to observed changes in the resonance frequency. Specifically, the microchannel is filled with ethanol and the outlet is then sealed while the inlet is open to ambient air. Due to changing mass density of ethanol as it evaporates, the resonance frequency of the cantilever shifts to a higher value. Understanding the relationship of the resonant modes and frequencies with the changing mass is essential for improving sensitivity and selectivity. During the experiment, the cantilever is sequentially excited at the resonance frequencies of its four vibrational modes (3 times for each mode), as demonstrated in Fig. 2. The nodal points of each mode are sequentially marked from N1 to N14, along the length of the channel. While the cantilever vibrates in its first mode, f1 increases during evaporation from 25.7 kHz to 31.5 kHz, as shown in Fig. 2(a). As the ethanol evaporates, its meniscus travels from the inlet to the outlet and encounters nodal regions, where the cantilever does not sense a change in the mass. This is evident by the flat regions of the curves in Fig. 2. Because the experiment is performed in an uncontrolled ambient environment, the evaporation profiles of the three measurements do not match. Similar experiments are performed to investigate f2, f3 and f4. The higher resonant frequencies f2, f3 and f4 contain more nodes as shown in Fig. 2. We developed numerical and analytical models to predict and understand the resonant behavior of this system. The numerical model employed a 3D elastic finite element based analysis to verify the experimental data for resonant frequencies f1 to f4 and the corresponding mode displacements. The ethanol in the channel is modeled as an elastic material with a very low Young’s modulus, relative to the cantilever material. The predicted increase in the resonant frequencies due to the removal of ethanol in the channel correlates well with experimental data. For the analytical model, we developed a one dimensional beam element model and the predicted resonant frequencies compared to with 95% of the numerical model. These models are useful for rational design and will be discussed in our presentation.

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Journal: TechConnect Briefs
Volume: 4, Informatics, Electronics and Microsystems: TechConnect Briefs 2018
Published: May 13, 2018
Pages: 165 - 168
Industry sector: Sensors, MEMS, Electronics
Topics: MEMS & NEMS Devices, Modeling & Applications
ISBN: 978-0-9988782-1-8