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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: a.pandey@utwente.nl
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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

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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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References

Bissett, E. J. 1989 The line contact problem of elastohydrodynamic lubrication. I: asymptotic structure for low speeds. Proc. R. Soc. Lond. A 424 (1867), 393–407.Google Scholar
Bretherton, F. P. 1961 The motion of long bubbles in tubes. J. Fluid Mech. 10, 166–188.CrossRefGoogle Scholar
Chambon, F. & Winter, H. H. 1987 Linear viscoelasticity at the gel point of a crosslinking PDMS with imbalanced stoichiometry. J. Rheol. 31 (8), 683–697.Google Scholar
Desrochers, J., Amrein, M. W. & Matyas, J. R. 2012 Viscoelasticity of the articular cartilage surface in early osteoarthritis. Osteoarthr. Cartil. 20 (5), 413–421.Google Scholar
Dowson, D. 1998 History of Tribology, 2nd edn. Wiley.Google Scholar
Feng, J. & Weinbaum, S. 2000 Lubrication theory in highly compressible porous media: the mechanics of skiing, from red cells to humans. J. Fluid Mech. 422, 281–317.CrossRefGoogle Scholar
Ferry, J. D. 1961 Viscoelastic Properties of Polymers. Wiley.Google Scholar
Fitz-Gerald, J. M. 1969 Mechanics of red-cell motion through very narrow capillaries. Proc. R. Soc. Lond. B 174 (1035), 193–227.Google Scholar
Hooke, C. J. & Huang, P. 1997 Elastohydrodynamic lubrication of soft viscoelastic materials in line contact. Proc. Inst. Mech. Engrs 211 (3), 185–194.Google Scholar
Hooke, C. J. & O’Donoghue, J. P. 1972 Elastohydrodynamic lubrication of soft, highly deformed contacts. Proc. Inst. Mech. Engrs C 14 (1), 34–48.Google Scholar
Hou, J. S., Mow, V. C., Lai, W. M. & Holmes, M. H. 1992 An analysis of the squeeze-film lubrication mechanism for articular cartilage. J. Biomech. 25 (3), 247–259.CrossRefGoogle ScholarPubMed
Johnson, K. L. 1987 Contact Mechanics. Cambridge University Press.Google Scholar
Jones, M. B., Fulford, G. R., Please, C. P., McElwain, D. L. S. & Collins, M. J. 2008 Elastohydrodynamics of the eyelid wiper. Bull. Math. Biol. 70 (2), 323–343.CrossRefGoogle ScholarPubMed
Karpitschka, S., Das, S., van Gorcum, M., Perrin, H., Andreotti, B. & Snoeijer, J. H. 2015 Droplets move over viscoelastic substrates by surfing a ridge. Nat. Commun. 6, 7891.Google Scholar
Leroy, S. & Charlaix, E. 2011 Hydrodynamic interactions for the measurement of thin film elastic properties. J. Fluid Mech. 674, 389–407.CrossRefGoogle Scholar
Leroy, S., Steinberger, A., Cottin-Bizonne, C., Restagno, F., Léger, L. & Charlaix, É. 2012 Hydrodynamic interaction between a spherical particle and an elastic surface: a gentle probe for soft thin films. Phys. Rev. Lett. 108, 264501.Google Scholar
Mani, M., Gopinath, A. & Mahadevan, L. 2012 How things get stuck: kinetics, elastohydrodynamics, and soft adhesion. Phys. Rev. Lett. 108 (22), 226104.CrossRefGoogle ScholarPubMed
Martin, A., Clain, J., Buguin, A. & Brochard-Wyart, F. 2002 Wetting transitions at soft, sliding interfaces. Phys. Rev. E 65, 031605.Google Scholar
Mow, V. C., Ateshian, G. A. & Spilker, R. L. 1993 Biomechanics of diarthrodial joints: a review of twenty years of progress. Trans. ASME. J. Biomech. Engng 115 (4B), 460–467.Google Scholar
Ng, T. S. K. & McKinley, G. H. 2008 Power law gels at finite strains: the nonlinear rheology of gluten gels. J. Rheol. 52 (2).Google Scholar
Reynolds, O. 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.Google Scholar
Saintyves, B., Jules, T., Salez, T. & Mahadevan, L. 2016 Self-sustained lift and low friction via soft lubrication. Proc. Natl Acad. Sci. 113 (21), 5847–5849.Google Scholar
Salez, T. & Mahadevan, L. 2015 Elastohydrodynamics of a sliding, spinning and sedimenting cylinder near a soft wall. J. Fluid Mech. 779, 181–196.CrossRefGoogle Scholar
Scaraggi, M. & Persson, B. N. J. 2014 Theory of viscoelastic lubrication. Tribol. Intl 72, 118–130.Google Scholar
Secomb, T. W., Skalak, R., Özkaya, N. & Gross, J. F. 1986 Flow of axisymmetric red blood cells in narrow capillaries. J. Fluid Mech. 163, 405–423.Google Scholar
Sekimoto, K. & Leibler, L. 1993 A mechanism for shear thickening of polymer-bearing surfaces: elasto-hydrodynamic coupling. Europhys. Lett. 23 (2), 113–117.CrossRefGoogle Scholar
Skotheim, J. M. & Mahadevan, L. 2004 Soft lubrication. Phys. Rev. Lett. 92 (24), 245509.CrossRefGoogle ScholarPubMed
Skotheim, J. M. & Mahadevan, L. 2005 Soft lubrication: the elastohydrodynamics of nonconforming and conforming contacts. Phys. Fluids 17 (9), 1–23.Google Scholar
Snoeijer, J. H., Eggers, J. & Venner, C. H. 2013 Similarity theory of lubricated Hertzian contacts. Phys. Fluids 25 (10), 101705.Google Scholar
Snoeijer, J. H. & van der Weele, K. 2014 Physics of the granite sphere fountain. Am. J. Phys. 82 (11).Google Scholar
Trickey, W. R., Lee, G. M. & Guilak, F. 2000 Viscoelastic properties of chondrocytes from normal and osteoarthritic human cartilage. J. Orthop. Res. 18 (6), 891–898.Google Scholar
Urzay, J. 2010 Asymptotic theory of the elastohydrodynamic adhesion and gliding motion of a solid particle over soft and sticky substrates at low Reynolds numbers. J. Fluid Mech. 653, 391–429.Google Scholar
Urzay, J., Llewellyn Smith, S. G. & Glover, B. J. 2007 The elastohydrodynamic force on a sphere near a soft wall. Phys. Fluids 19 (10), 103106.Google Scholar
Venner, C. H. & Lubrecht, A. A. 2000 Multi-Level Methods in Lubrication. Elsevier Science.Google Scholar
Wang, Y., Dhong, C. & Frechette, J. 2015 Out-of-contact elastohydrodynamic deformation due to lubrication forces. Phys. Rev. Lett. 115, 248302.Google Scholar