Rotation of an immersed cylinder sliding near a thin elastic coating

TL;DR

This paper develops a theoretical model showing that a cylinder sliding near a soft elastic wall in a viscous fluid must rotate to avoid torque, with rotation speed depending on sliding speed and wall softness, aligning with experimental findings.

Contribution

The study provides an analytical and numerical framework explaining the steady rotation of cylinders near soft walls, linking deformation, lubrication forces, and rotation.

Findings

Cylinder rotation scales with the cube of sliding speed.

Softer elastic layers lead to higher rotation speeds.

The model agrees qualitatively with experimental observations.

Abstract

It is known that an object translating parallel to a soft wall in a viscous fluid produces hydro- dynamic stresses that deform the wall, which, in turn, results in a lift force on the object. Recent experiments with cylinders sliding under gravity near a soft incline, which confirmed theoretical arguments for the lift force, also reported an unexplained steady-state rotation of the cylinders [Saintyves et al. PNAS 113(21), 2016]. Motivated by these observations, we show, in the lubrication limit, that an infinite cylinder that translates in a viscous fluid parallel to a soft wall at constant speed and separation distance must also rotate in order to remain free of torque. Using the Lorentz reciprocal theorem, we show analytically that for small deformations of the elastic layer, the angular velocity of the cylinder scales with the cube of the sliding speed. These predictions are confirmed numerically. We then apply the theory to the gravity-driven motion of a cylinder near a soft incline and find qualitative agreement with the experimental observations, namely that a softer elastic layer results in a greater angular speed of the cylinder.