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Type: Journal article
Title: The drag on a microcantilever oscillating near a wall
Author: Clarke, Richard John
Cox, Stephen Michael
Williams, P. M.
Jensen, O. E.
Citation: Journal of Fluid Mechanics, 2005; 545 (December):397-426
Publisher: Cambridge University Press
Issue Date: 2005
ISSN: 0022-1120
School/Discipline: School of Mathematical Sciences
Statement of
R. J. Clarke, S. M. Cox, P. M. Williams and O. E. Jensen
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 γ² (a Strouhal number) and the wall–body separation Δ (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 (γ, Δ)-parameter space. Regions in parameter space for which the wall has a significant effect on drag are identified.
Rights: Copyright © 2005 Cambridge University Press
DOI: 10.1017/S0022112005006907
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Appears in Collections:Mathematical Sciences publications

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