Nanoflows Induced By Mems And Nems: Limits Of Two-Dimensional Models

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.