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The drag on a microcantilever oscillating near a wall

Published online by Cambridge University Press:  02 December 2005

R. J. CLARKE
Affiliation:
Division of Applied Mathematics, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK
S. M. COX
Affiliation:
School of Mathematical Sciences, University of Adelaide, Adelaide 5005, Australia
P. M. WILLIAMS
Affiliation:
Laboratory of Biophysics and Surface Analysis, School of Pharmacy, University of Nottingham, University Park, Nottingham NG7 2RD, UK
O. E. JENSEN
Affiliation:
Division of Applied Mathematics, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK

Abstract

Motivated by devices such as the atomic force microscope, we compute the drag experienced by a cylindrical body of circular or rectangular cross-section oscillating at small amplitude near a plane wall. The body lies parallel to the wall and oscillates normally to it; the body is assumed to be long enough for the dominant flow to be two-dimensional. The flow is parameterized by a frequency parameter $\gamma^2$ (a Strouhal number) and the wall–body separation $\Delta$ (scaled on body radius). Numerical solutions of the unsteady Stokes equations obtained using finite-difference computations in bipolar coordinates (for circular cross-sections) and boundary-element computations (for rectangular cross-sections) are used to determine the drag on the body. Numerical results are validated and extended using asymptotic predictions (for circular cylinders) obtained at all extremes of $(\gamma,\Delta)$-parameter space. Regions in parameter space for which the wall has a significant effect on drag are identified.

Type
Papers
Copyright
© 2005 Cambridge University Press

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