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

Abstract

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 angleαto 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. Whenαis 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.