3 results for Jensen, OE

  • Three-dimensional flow due to a microcantilever oscillating near a wall: an unsteady slender-body analysis.

    Clarke, Richard; Jensen, OE; Billingham, J; Williams, PW (2006)

    Journal article
    The University of Auckland Library

    We compute the drag on a slender rigid cylinder, of uniform circular cross-section, oscillating in a viscous fluid at small amplitude near a horizontal wall. The cylinder???s axis lies at an angle a to the horizontal and the cylinder oscillates in a vertical plane normal to either the wall or its own axis. The flow is described using an unsteady slender-body approximation, which we treat both numerically and using an iterative scheme that extends resistive-force theory to account for the leading-order effects of unsteady inertia and the wall. When a is small, two independent screening mechanisms are identified which suppress end-effects and produce approximately two-dimensional flow along the majority of the cylinder; however, three-dimensional effects influence the drag at larger tilt angles

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  • Stochastic elastohydrodynamics of a microcantilever oscillating near a wall

    Clarke, Richard; Jensen, OE; Billingham, J; Pearson, A; Williams, P (2006)

    Journal article
    The University of Auckland Library

    We consider the thermally driven motion of a microcantilever in a fluid environment near a wall, a configuration characteristic of the atomic force microscope. A theoretical model is presented which accounts for hydrodynamic interactions between the cantilever and wall over a wide range of frequencies and which exploits the fluctuation-dissipation theorem to capture the Brownian dynamics of the coupled fluid-cantilever system. Model predictions are tested against experimental thermal spectra for a cantilever in air and water. The model shows how, in a liquid environment, the effects of non- -correlated Brownian forcing appear in the power spectrum, particularly at low frequencies. The model also predicts accurately changes in the spectrum in liquid arising through hydrodynamic wall effects, which we show are strongly mediated by the angle at which the cantilever is tilted relative to the wall.

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  • Three-dimensional elastohydrodynamics of a thin plate oscillating above a wall

    Clarke, Richard; Jensen, OE; Billingham, J (2008)

    Journal article
    The University of Auckland Library

    We consider deflections of a thin rectangular elastic plate that is submerged within a Newtonian fluid. The plate is clamped along one edge and supported horizontally over a plane horizontal wall. We consider both external driving, where the clamped edge is vibrated vertically at high frequencies, and thermal driving, where the plate fluctuates under Brownian motion. In both cases, the amplitude of oscillation is assumed sufficiently small that the resulting flow has little convective inertia, although the oscillation frequency is sufficiently high to generate substantial unsteady inertia in the flow, a common scenario in many nano- and microdevices. We exploit the plate???s thinness to develop an integral-equation representation for the three-dimensional flow a so-called thin-plate theory which offers considerable computational savings over a full boundary-integral formulation. Limiting cases of high oscillation frequencies and small wall-plate separation distances are studied separately, leading to further simplified descriptions for the hydrodynamics. We validate these reduced integral representations against full boundary-integral computations, and identify the parameter ranges over which these simplified formulations are valid. Addressing the full flow-structure interaction, we also examine the limits of simpler two-dimensional hydrodynamic models. We compare the responses of a narrow plate under two- and three-dimensional hydrodynamic loading, and report differences in the frequency response curves that occur when the plate operates in water, in contrast to the excellent agreement observed in air.

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