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An analytical study of the squeezing flow of synovialfluid

Published online by Cambridge University Press:  07 March 2013

Mahdia Yousfi ,
Benyebka Bou-Saïd  and
John Tichy
Mahdia Yousfi
Affiliation:
Département de Génie Mécanique, Université 20 août 1955 de Skikda, BP 26, Skikda 21000, Algérie
Benyebka Bou-Saïd*
Affiliation:
Université de Lyon, CNRS INSA-Lyon, LaMCoS, UMR 5259, 69621 Villeurbanne Cedex, France
John Tichy
Affiliation:
Department of Mechanical, Aerospace, and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180-3590, USA
*
aCorresponding author: [email protected]
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Abstract

The problem of the squeezing of a fluid film with a complex rheology is studied. Thefluid is represented by the Phan-Tien and Tanner (PTT) constitutive equation. The goal ofthe paper is to develop an analytical approach which allows one to describe and quantifythis process, which is often present in classical lubrication problems, but particularlyin human joints. The present approach can potentially supplement time-consuming and costlypurely numerical methods which are also susceptible to misleading artifacts. A parametricstudy reveals the effect of fluid elasticity compared to viscous effects and someexplanation is suggested as to their possible links with joint diseases.

Keywords

Squeeze filmsynovial fluidPTT constitutive equationmodified Reynolds equation
Type
Research Article
Information
Mechanics & Industry , Volume 14 , Issue 1 , 2013 , pp. 59 - 69
Copyright
© AFM, EDP Sciences 2013

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References

J.H. Dumbleton, Tribology of natural and artificial joints, Elsevier Scientific Publishing Company, Amsterdam, 1981
Unsworth, A., Dowson, D., Wright, V., Analysis of boosted lubrication in human joints, J. Mech. Eng. Sci. 12 (1970) 364–369 Google Scholar
Unsworth, A., Dowson, D., Wright, V., some new evidence on human joint lubrication, Ann. Rheum. Dis. 34 (1975) 277–285 CrossRefGoogle Scholar
Hlavacek, M., The role of synovial fluid filtration by cartilage in lubrication of synovial joints. IV. Squeeze-film lubrication: the central film thickness for normal and inflammatory synovial fluids for axial symmetry under high loading conditions, J. Biomec. 28 (1995) 1199–1205 CrossRefGoogle ScholarPubMed
Liu, F., Jin, Z.M., Hirt, F., Rieker, C., Roberts, P., Grigoris, P., Transient elastohydrodynamic lubrication analysis of metal-on-metal hip implant under simulated walking conditions, J. Biomec. 39 (2006) 905–914 CrossRefGoogle ScholarPubMed
Mazzucco, D., McKinley, G., Scott, R.D., Spector, M., Rheology of joint fluid in total knee arthroplasty patients, J. Orthopaedic Res. 20 (2002) 1157–1163 CrossRefGoogle ScholarPubMed
Y.C. Fung, Biomechanics mechanical properties of living tissues, Springer-Verlag, New York, 1993
Ogston, A.G., Stainer, J.E., The physiological function of hyaluronic acid in synovial fluid: Viscous, elastic and lubricant properties, Phys. 119 (1953) 244–252 Google ScholarPubMed
King, R.G., A rheological measurement of three synovial fluids, Rheol. Acta. 5 (1966) 41–44 CrossRefGoogle Scholar
C.W. McCutchen, Lubrication of joints, In: The joints and synovial fluid, L. Sokoloff, (ed.), Academic Press, New York, USA, 1978, pp. 437–483
V.C. Mow, G.A. Ateshian, Friction, lubrication and wear of diarthrodial joints, In: V.C. Mow, W.C. Hayes, (ed.), Basic OrthopaedicBiomechanics, Raven Press, Philadelphia, USA, 1997, pp. 275–315
Oates, K.M.N., Krause, W.E., Colby, R.H., Using rheology to probe the mechanism of joint lubrication, Polyelectrolyte/protein interactions in synovial fluid, Mater. Res. Soc. Symp. Proc. 711 (2002) 53–58 Google Scholar
Szwajczak, E., Kucaba-Pietal, A., Telega, J.J., Liquid crystalline properties of synovial fluid, Eng. Trans. 49 (2001) 315–358 Google Scholar
Oda, Y., Sugishita, J., The spinnability effect under lubrication (part1): Lubrication system of natural joint, Jpn J. Tribol. 50 (2005) 261–270 Google Scholar
Ghosh, P., Guidolin, D., Potential mechanism of action of intra-articular hyaluronan therapy in osteoarthritis: Are the effects molecular weight dependent?, Seminars in Arthritis and Rheumatism 32 (2002) 10–37 CrossRefGoogle ScholarPubMed
Safari, M., Bjelle, A., Gudmundsson, M., Hõgfors, C., Granhed, H., Clinical assessment of rheumatic diseases using viscoelastic parameters for synovial fluid, Biorheology 27 (1990) 659–674 Google ScholarPubMed
Kobayashi, Y., Okamoto, A., Nishinari, K., Viscoelasticity of hyaluronic acid with different molecular weights Biorheology 31 (1994) 235–244 Google Scholar
Hills, B.A., Crawford, R.W., Normal and prosthetic synovial joints are lubricated by surface-active phospholipid: a hypothesis, J. Arthroplasty 18 (2003) 499–505 CrossRefGoogle ScholarPubMed
Bujurke, N.M., Jagadeeswar, M., Hiremath, P.S., Analysis of normal stress effects in a squeeze film porous bearing, Wear 116 (1987) 237–248 CrossRefGoogle Scholar
Pascovici, M.D., Cicone, T., Squeeze-film of unconformal, compliant and layered contacts, Tribol. Inter. 36 (2003) 791–799 CrossRefGoogle Scholar
Phan-Thien, N., Tanner, R.I., A new constitutive equation derived from network theory, J. Non-Newtonian Fluid Mech. 2 (1977) 353–365 CrossRefGoogle Scholar
Bou-Saïd, B., Ehret, P., Boundary element method for transient viscoelastic flow: the MPTT model, Tribol. Trans. 39 (1996) 314–321 CrossRefGoogle Scholar
Akyildiz, F.T., Bellout, H., Viscoelastic Lubrication with Phan-Thien-Tanner Fluid, J. Tribol. 126 (2004) 288–291 CrossRefGoogle Scholar
Meziane, A., Bou-Saïd, B., Tichy, J., Modelling human hip joint lubrication subject to walking cycle, Lubr. Sci. 20 (2008) 205–222 CrossRefGoogle Scholar
R.S.Fein, Are synovial joints squeeze-film lubricated? In: Proceedings of the institution of mechanical engineers 181 (1966) 125–128
P.A. Torzilli, The lubrication of Human joints in: D.G. Fleming, B.N. Feinberg, (ed.), Handbook of engineering in medicine and biology, CRC Press, Cleveland, Ohio, USA, 1976, pp. 225–251
Timothy, J.P., David, F.J., The viscous squeeze-film behaviour of shear-thinning fluids, J. Non-Newtonian Fluid Mech. 27 (1988) 27–46 Google Scholar
Sinha, P., Singh, C., Prasad, K.R., Lubrication of human joints- a microcontinuum approach, Wear 80 (1982) 159–181 CrossRefGoogle Scholar
Bujurke, N.M., Slider bearings lubricated by a second grade fluid with reference to synovial joints, Wear 78 (1982) 355–363 CrossRefGoogle Scholar
Nabhani, M., Khlifi, M.E., Bou-Saïd, B., A numerical simulation of viscous shear effects on porous squeeze-film using the Darcy-Brinkman model, Mécanique & industries 11 (2010) 327–337 CrossRefGoogle Scholar
R.B. Bird, R.C. Armstrong, O. Hassager, Dynamics of polymeric liquids, Vol. 1, John Wiley & Sons Inc., New York, 1987
P. Ehret, Contribution à l’étude du comportement de mécanismes lubrifiés sous chargements transitoires, Thèse, INSA de Lyon, 1993
Tichy, J., Bou-Saïd, B., The Phan-Thien and Tanner model applied to thin film, spherical coordinates: applications for lubrication of hip joint replacement, J. Biomech. Eng. 130 (2008) 021012:1-6 CrossRefGoogle ScholarPubMed
Lee, S.J., Denn, M.M., Crochet, M.J., Metzner, A.B., Compressive flow between parallel disks. I. Newtonian fluid with a transverse viscosity gradient, J. Non-Newtonian Fluid Mech. 10 (1982) 3–30 CrossRefGoogle Scholar