Here we study viscous oscillatory nanoflows generated in a fluid by mechanical oscillations of miniaturized resonators. In particular, we focus on the limits of two-dimensional cylinder theory, which approximates a slender nanoresonator, such as an atomic force microscopy microcantilever or a nanobeam resonator, as a cylinder oscillating in a fluid. The cylinder theory is the mainstay in the micro- and nanoelectromechanical systems literature, but is only accurate in certain regimes. We observe and explain two distinct routes to the breakdown of the cylinder theory. First, when a substrate is present, squeeze film effects become significant and the cylinder theory underpredicts the fluid force applied to the resonator. Second, the cylinder theory overpredicts the fluid force when axial flow becomes relatively large. This occurs at higher bending modes where the spatial gradients along the beam are larger. A dimensionless squeeze number and axial flow number are introduced to facilitate in-depth investigations into the limitations of the two-dimensional cylinder theory. Results from experiments and three-dimensional finite-element models are presented in order to illustrate where two-dimensional flow models break down.

中文翻译：

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MEMS和NEMS诱导的纳米流：二维模型的局限性

在这里，我们研究由小型谐振器的机械振荡在流体中产生的粘性振荡纳米流。特别地，我们关注二维圆柱理论的局限性，二维圆柱理论近似于细长的纳米谐振器，例如原子力显微镜微悬臂梁或纳米束谐振器，因为圆柱体在流体中振荡。圆柱理论是微机电系统文献的主要内容，但仅在某些情况下才是准确的。我们观察并解释了推论圆柱理论的两种不同途径。首先，当存在基板时，挤压膜效应变得明显，并且圆柱理论无法预测施加到谐振器的流体力。其次，当轴向流变得相对较大时，汽缸理论会过高地预测流体力。这发生在较高的弯曲模式下，其中沿梁的空间梯度较大。引入了无量纲的挤压数和轴向流数，以促进对二维圆柱理论的局限性的深入研究。给出了实验和三维有限元模型的结果，以说明二维流模型在哪里破裂。