Vibration response of microcantilevers bounded by a confined fluid.

Hydrodynamic predictions of fluid velocity and pressure distribution are made for fluid in a confined space bounded by a vibrating microcantilever and a fixed surface. The results are used to quantify damping factors and predict frequency response amplitudes of a microcantilever vibrating near a fixed surface. The theoretical predictions of vibration response compare favorably with experimental data.

Effective mass and flow patterns of fluids surrounding microcantilevers.

An analytical approach to determine the streamlines of fluid flow adjacent to the surfaces of vibrating cantilevers is presented. Fluid flow over the top and bottom surfaces of a microcantilever is established by solving two-dimensional Navier-Stokes equations for viscous flow. The x and y velocity components are used to establish streamlines for absolute fluid motion. These streamlines show a central stagnation core perpendicular and central to the cantilever surface extending along the full length of cantilevers, which most likely accounts for the added mass effect (induced mass) of fluid media around vibrating microcantilevers.