Regimes of Soft Lubrication

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.

arXiv comment21 pages, 8 figures

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• Regimes of Soft Lubrication
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• Lift at low Reynolds number
• Soft-lubrication interactions between a rigid sphere and an elastic wall
• Gradient-dynamics model for liquid drops on elastic substrates
• Reduced models of unidirectional flows in compliant rectangular ducts at finite Reynolds number
• Droplet settling on solids coated with a soft layer
• Capillary lubrication of a spherical particle near a fluid interface
• Modeling Leidenfrost levitation of soft elastic solids
• Hovering of an actively driven fluid-lubricated foil
• Theory and simulation of elastoinertial rectification of oscillatory flows in two-dimensional deformable rectangular channels