Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB T6G 2R3, Canada.
Fourien Inc., Edmonton, AB T6B 2N2, Canada.
Sensors (Basel). 2020 Nov 12;20(22):6459. doi: 10.3390/s20226459.
The bending resonance of micro-sized resonators has been utilized to study adsorption of analyte molecules in complex fluids of picogram quantity. Traditionally, the analysis to characterize the resonance frequency has focused solely on the mass change, whereas the effect of interfacial tension of the fluid has been largely neglected. By observing forced vibrations of a microfluidic cantilever filled with a series of alkanes using a laser Doppler vibrometer (LDV), we studied the effect of surface and interfacial tension on the resonance frequency. Here, we incorporated the Young-Laplace equation into the Euler-Bernoulli beam theory to consider extra stress that surface and interface tension exerts on the vibration of the cantilever. Based on the hypothesis that the near-surface region of a continuum is subject to the extra stress, thin surface and interface layers are introduced to our model. The thin layer is subject to an axial force exerted by the extra stress, which in turn affects the transverse vibration of the cantilever. We tested the analytical model by varying the interfacial tension between the silicon nitride microchannel cantilever and the filled alkanes, whose interfacial tension varies with chain length. Compared with the conventional Euler-Bernoulli model, our enhanced model provides a better agreement to the experimental results, shedding light on precision measurements using micro-sized cantilever resonators.
微尺寸谐振器的弯曲共振已被用于研究纳克数量级的复杂流体中分析物分子的吸附。传统上，用于表征共振频率的分析主要集中在质量变化上，而流体的界面张力的影响则被大大忽略。通过使用激光多普勒测振仪（LDV）观察填充有一系列烷烃的微流悬臂的强制振动，我们研究了表面和界面张力对共振频率的影响。在这里，我们将杨氏拉普拉斯方程纳入到欧拉-伯努利梁理论中，以考虑表面和界面张力对悬臂振动施加的额外应力。基于连续体的近表面区域受额外应力作用的假设，我们的模型引入了薄的表面和界面层。薄层受到额外应力施加的轴向力的作用，这反过来又影响了悬臂的横向振动。我们通过改变氮化硅微通道悬臂和填充烷烃之间的界面张力来测试分析模型，其界面张力随链长而变化。与传统的欧拉-伯努利模型相比，我们增强的模型与实验结果更吻合，为使用微尺寸悬臂谐振器进行精密测量提供了启示。
