We consider the problem of oscillation damping in air of a thermally actuated microlever as it is gradually approached towards an infinite wall in parallel geometry. As the gap is decreased from 20 nm down to 400 nm, we observe the increasing damping of the lever Brownian motion in the fluid laminar regime. This manifests itself as a linear decrease with distance of the lever quality factor accompanied by a dramatic softening of its resonance, and eventually leads to the freezing of the CL oscillation. We are able to quantitatively explain this behavior by analytically solving the Navier-Stokes equation with perfect slip boundary conditions. Our findings may have implications for microfluidics and micro- nano-electromechanical applications.
New estimations of the added mass and damping of two cylinders vibrating in a viscous fluid, from theoretical and numerical approaches
本文研究了两圆柱在粘性滞止流体中的小振动问题。基于亥姆霍兹展开和双极坐标系，提出了一种新的理论方法来估计作用在两个物体上的流体力。通过粘性流体附加系数，我们证明了这些力是{ \textcolor{black}{cylinder accelerations} }和速度的线性组合。{ \textcolor{black}{To assess the validity of this theory, we consider the case of two equal size cylinders, one of them being stationary while the other one is forced sinusoidally} }。自加质量和阻尼系数都随着Stokes数和分离距离的增加而减小。交叉附加质量和阻尼系数随Stokes数和间距的增大而增大。与无粘性结果相比，粘性的影响是增加了一个校正项，其标度为$Sk^{-1/2}$。当分离距离足够大时，两个圆柱的行为就好像它们是独立的，并且孤立圆柱的Stokes预测被恢复。与以前的工作相比，本理论提供了一个简单而灵活的替代容易确定的流体力和相关的附加系数。据我们所知，这也是第一次提出了一种数值方法的基础上的惩罚方法的流体-结构相互作用的背景下，相对较小的斯托克斯数，并成功地与理论预测。
