Hydrodynamic damping of microcantilevers near solid walls

Ryan C Tung, Purdue University

Abstract

The vibrations of microcantilevers in Atomic Force Microscopes (AFM) or Radio Frequency (RF) switches are strongly influenced by the viscous hydrodynamics of the surrounding fluid in the vicinity of a rigid wall. While prior efforts to model this hydrodynamic loading have focused on squeeze film damping effects at high Knudsen and squeeze numbers, the regime of low Knudsen and squeeze numbers is also very important for which squeeze film models need to be discarded in favor of unsteady Stokes hydrodynamics. We extend the work of Green and Sader [1,2] and present compact semi-analytical formulas for the unsteady viscous hydrodynamic function of slender microcantilevers oscillating near rigid walls, in terms of key non-dimensional numbers. Using these closed-form expressions, it becomes possible to predict easily the wet natural frequencies and quality factors (Q-factors) of multiple eigenmodes of microcantilevers near rigid walls in diverse applications ranging from AFM in liquids to RF microswitches under ambient conditions. The semi-analytical formulas are extensively validated by comparing their predicted wet natural frequencies and Q-factors with those based on three-dimensional, transient flow-structure interaction simulations, as well as previous experiments performed in the field by other researchers. Additionally we formulate modifications to the theory obtained in order to account for AFM cantilever tilt and larger Knudsen number regimes. We provide validation of these modifications using computational and experimental data.

Degree

M.S.M.E.

Advisors

Raman, Purdue University.

Subject Area

Mechanical engineering

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