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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 the 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
are 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 the physically relevant limits of soft
lubrication.