Elastohydrodynamics of a sliding, spinning and sedimenting cylinder near a soft wall

TL;DR

This paper develops an asymptotic theory for the motion of a fluid-immersed cylinder near a soft wall, revealing complex behaviors like oscillations, lift generation, and spin effects through nonlinear equations.

Contribution

It introduces a novel asymptotic framework for elastohydrodynamic interactions of a cylinder near a soft wall, including unexpected dynamic behaviors and a generalization to wall poroelasticity.

Findings

Particle can spontaneously oscillate during sliding

Lift can be generated via a Magnus-like effect

Sedimentation can exhibit a singularity

Abstract

We consider the motion of a fluid-immersed negatively buoyant particle in the vicinity of a thin compressible elastic wall, a situation that arises in a variety of technological and natural settings. We use scaling arguments to establish different regimes of sliding, and complement these estimates using thin-film lubrication dynamics to determine an asymptotic theory for the sedimentation, sliding, and spinning motions of a cylinder. The resulting theory takes the form of three coupled nonlinear singular-differential equations. Numerical integration of the resulting equations confirms our scaling relations and further yields a range of unexpected behaviours. Despite the low-Reynolds feature of the flow, we demonstrate that the particle can spontaneously oscillate when sliding, can generate lift via a Magnus-like effect, can undergo a spin-induced reversal effect, and also shows an unusual sedimentation singularity. Our description also allows us to address a sedimentation-sliding transition that can lead to the particle coasting over very long distances, similar to certain geophysical phenomena. Finally, we show that a small modification of our theory allows to generalize the results to account for additional effects such as wall poroelasticity.