Skip to main content
×
Home
    • Aa
    • Aa

Lubrication of soft viscoelastic solids

  • Anupam Pandey (a1), Stefan Karpitschka (a1), Cornelis H. Venner (a2) and Jacco H. Snoeijer (a1) (a3)
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.

Copyright
Corresponding author
Email address for correspondence: a.pandey@utwente.nl
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

E. J. Bissett 1989 The line contact problem of elastohydrodynamic lubrication. I: asymptotic structure for low speeds. Proc. R. Soc. Lond. A 424 (1867), 393407.

F. Chambon  & H. H. Winter 1987 Linear viscoelasticity at the gel point of a crosslinking PDMS with imbalanced stoichiometry. J. Rheol. 31 (8), 683697.

J. Desrochers , M. W. Amrein  & J. R. Matyas 2012 Viscoelasticity of the articular cartilage surface in early osteoarthritis. Osteoarthr. Cartil. 20 (5), 413421.

J. M. Fitz-Gerald 1969 Mechanics of red-cell motion through very narrow capillaries. Proc. R. Soc. Lond. B 174 (1035), 193227.

J. S. Hou , V. C. Mow , W. M. Lai  & M. H. Holmes 1992 An analysis of the squeeze-film lubrication mechanism for articular cartilage. J. Biomech. 25 (3), 247259.

M. B. Jones , G. R. Fulford , C. P. Please , D. L. S. McElwain  & M. J. Collins 2008 Elastohydrodynamics of the eyelid wiper. Bull. Math. Biol. 70 (2), 323343.

S. Karpitschka , S. Das , M. van Gorcum , H. Perrin , B. Andreotti  & J. H. Snoeijer 2015 Droplets move over viscoelastic substrates by surfing a ridge. Nat. Commun. 6, 7891.

S. Leroy , A. Steinberger , C. Cottin-Bizonne , F. Restagno , L. Léger  & É. Charlaix 2012 Hydrodynamic interaction between a spherical particle and an elastic surface: a gentle probe for soft thin films. Phys. Rev. Lett. 108, 264501.

M. Mani , A. Gopinath  & L. Mahadevan 2012 How things get stuck: kinetics, elastohydrodynamics, and soft adhesion. Phys. Rev. Lett. 108 (22), 226104.

V. C. Mow , G. A. Ateshian  & R. L. Spilker 1993 Biomechanics of diarthrodial joints: a review of twenty years of progress. Trans. ASME. J. Biomech. Engng 115 (4B), 460467.

T. S. K. Ng  & G. H. McKinley 2008 Power law gels at finite strains: the nonlinear rheology of gluten gels. J. Rheol. 52 (2).

O. Reynolds 1886 On the theory of lubrication and its application to Mr Beauchamp Tower’s experiments, including an experimental determination of the viscosity of olive oil. Phil. Trans. R. Soc. Lond. 177, 157.

B. Saintyves , T. Jules , T. Salez  & L. Mahadevan 2016 Self-sustained lift and low friction via soft lubrication. Proc. Natl Acad. Sci. 113 (21), 58475849.

M. Scaraggi  & B. N. J. Persson 2014 Theory of viscoelastic lubrication. Tribol. Intl 72, 118130.

K. Sekimoto  & L. Leibler 1993 A mechanism for shear thickening of polymer-bearing surfaces: elasto-hydrodynamic coupling. Europhys. Lett. 23 (2), 113117.

J. M. Skotheim  & L. Mahadevan 2004 Soft lubrication. Phys. Rev. Lett. 92 (24), 245509.

J. M. Skotheim  & L. Mahadevan 2005 Soft lubrication: the elastohydrodynamics of nonconforming and conforming contacts. Phys. Fluids 17 (9), 123.

J. H. Snoeijer , J. Eggers  & C. H. Venner 2013 Similarity theory of lubricated Hertzian contacts. Phys. Fluids 25 (10), 101705.

J. H. Snoeijer  & K. van der Weele 2014 Physics of the granite sphere fountain. Am. J. Phys. 82 (11).

W. R. Trickey , G. M. Lee  & F. Guilak 2000 Viscoelastic properties of chondrocytes from normal and osteoarthritic human cartilage. J. Orthop. Res. 18 (6), 891898.

J. Urzay , S. G. Llewellyn Smith  & B. J. Glover 2007 The elastohydrodynamic force on a sphere near a soft wall. Phys. Fluids 19 (10), 103106.

C. H. Venner  & A. A. Lubrecht 2000 Multi-Level Methods in Lubrication. Elsevier Science.

Y. Wang , C. Dhong  & J. Frechette 2015 Out-of-contact elastohydrodynamic deformation due to lubrication forces. Phys. Rev. Lett. 115, 248302.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Keywords:

Metrics

Full text views

Total number of HTML views: 2
Total number of PDF views: 117 *
Loading metrics...

Abstract views

Total abstract views: 218 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 27th March 2017. This data will be updated every 24 hours.