Viscous cavity damping of a microlever in a simple fluid

TL;DR

This paper investigates how a microlever's oscillation damping increases as it approaches a wall in a fluid, revealing a linear damping trend and resonance softening explained by Navier-Stokes solutions, relevant for microfluidics.

Contribution

It provides a quantitative analytical model for viscous damping of a microlever near a wall, incorporating slip boundary conditions, advancing understanding in microfluidic damping mechanisms.

Findings

Damping increases linearly with decreasing gap size.

Resonance frequency softens significantly as the gap narrows.

Oscillation eventually freezes at very small gaps.

Abstract

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.