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Lubrication of soft viscoelastic solids

Published online by Cambridge University Press:  23 June 2016

Anupam Pandey ,
Stefan Karpitschka ,
Cornelis H. Venner  and
Jacco H. Snoeijer
Anupam Pandey*
Affiliation:
Physics of Fluids Group, Faculty of Science and Technology, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
Stefan Karpitschka
Affiliation:
Physics of Fluids Group, Faculty of Science and Technology, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
Cornelis H. Venner
Affiliation:
Faculty of Engineering Technology, Engineering Fluid Dynamics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
Jacco H. Snoeijer
Affiliation:
Physics of Fluids Group, Faculty of Science and Technology, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
*
†Email address for correspondence: [email protected]
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Abstract

Lubrication flows appear in many applications in engineering, biophysics and nature. Separation of surfaces and minimisation of friction and wear is achieved when the lubricating fluid builds up a lift force. In this paper we analyse soft lubricated contacts by treating the solid walls as viscoelastic: soft materials are typically not purely elastic, but dissipate energy under dynamical loading conditions. We present a method for viscoelastic lubrication and focus on three canonical examples, namely Kelvin–Voigt, standard linear and power law rheology. It is shown how the solid viscoelasticity affects the lubrication process when the time scale of loading becomes comparable to the rheological time scale. We derive asymptotic relations between the lift force and the sliding velocity, which give scaling laws that inherit a signature of the rheology. In all cases the lift is found to decrease with respect to purely elastic systems.

JFM classification

Low-Reynolds-number flows: Lubrication theory Non-Newtonian Flows: Viscoelasticity
Type
Papers
Information
Journal of Fluid Mechanics , Volume 799 , 25 July 2016 , pp. 433 - 447
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Copyright
© 2016 Cambridge University Press 

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