Regimes of Soft Lubrication

TL;DR

This paper reviews the different regimes of soft lubrication involving deformable objects near boundaries, focusing on elastic deformations, lubricant layer thickness, and establishing new scaling laws for thick elastic coatings.

Contribution

It provides a comprehensive overview of soft lubrication regimes and derives analytical scaling laws for large deformations in thin elastic coatings.

Findings

Analysis of small and large entrainment velocity regimes

Derivation of scaling laws for thick elastic layers

Establishment of boundary layer behaviors at contact edges

Abstract

Elastohydrodynamic lubrication, or simply soft lubrication, refers to the motion of deformable objects near a boundary lubricated by a fluid, and is one of the key physical mechanisms to minimise friction and wear in natural and engineered systems. Hence it is of particular interest to relate the thickness of the lubricant layer to the entrainment (sliding/rolling) velocity, the mechanical loading exerted onto the contacting elements, and properties of the elastic boundary. In this work we provide an overview of the various regimes of soft lubrication for two-dimensional cylinders in lubricated contact with compliant walls. We discuss the limits of small and large entrainment velocity, which is equivalent to large and small elastic deformations, as the cylinder moves near thick or thin elastic layers. The analysis focusses on thin elastic coatings, both compressible and incompressible, for which analytical scaling laws are not yet available in the regime of large deformations. By analysing the elastohydrodynamic boundary layers that appear at the edge of the contact, we establish the missing scaling laws - including prefactors. As such, we offer a rather complete overview of physically relevant limits of soft lubrication.