The fluid-coupled motion of micro and nanoscale cantilevers

Abstract

An understanding of the fluid coupled dynamics of micro and nanotechnology has the potential to yield significant advances yet many open and interesting questions remain. As an important example we consider the coupling of two closely spaced cantilevers immersed in a viscous fluid subject to an external driving. While one cantilever is driven to oscillate, the adjacent cantilever is passive. This system is modeled as two simple harmonic oscillators in an array whose motion is coupled through the fluid. Using simplified geometries and the unsteady Stokes equations, an analytical expression is developed that describes the dynamics of the passive cantilever. Full numerical simulations of the fluid-solid interactions that include the precise geometries of interest are performed. The analytical expressions are compared with the numerical simulations to develop insight into the fluid-coupled dynamics over a range of experimentally relevant parameters including the cantilever separation and frequency based Reynolds number. In addition, a shaker-based actuation device is investigated in order to demonstrate its feasibility for use with micro and nanoscale systems.