The Quarterly Journal of Mechanics and Applied Mathematics Advance Access originally published online on March 10, 2006
The Quarterly Journal of Mechanics and Applied Mathematics 2006 59(2):277-300; doi:10.1093/qjmam/hbl002
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Transient elastohydrodynamic drag on a particle moving near a deformable wall
( School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD )
Corresponding author: Oliver.Jensen{at}nottingham.ac.uk
We examine the prescribed time-dependent motion of a rigid particle (a sphere or a cylinder) moving in a viscous fluid close to a deformable wall. The fluid motion is described by a nonlinear evolution equation, derived using lubrication theory, which is solved using numerical and asymptotic methods; a local linear pressure–displacement model describes the wall. When the particle moves from rest towards the wall, fluid trapping beneath the particle leads to an overshoot in the normal force on the particle; a similarity solution is used to describe trapping at early times and a multiregion asymptotic structure describes fluid draining at late times. When the particle is pulled from rest away from the wall, a peeling process (described by a quasisteady travelling wave) determines the rate at which fluid can enter the growing gap between the particle and the wall, leading to a transient adhesive normal force. When a cylinder moves from rest transversely over the wall, transient peeling motion is again observed (especially when the wall is initially indented), giving rise to an overshoot in the transverse drag. Simulations for a translating sphere show highly nonlinear wall deformations characterized by a localized crescent-shaped ridge. Despite generating sharp transient deformations, we found no numerical evidence of finite-time choking events.