  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.

Fluid Dynamics;Soft Condensed Matter