Combined effects of fluid–solid interfacial slip and fluid inertia on the hydrodynamic performance of square shape textured parallel sliding contacts

  • Ismail Syed
  • M. Sarangi
Technical Paper


Lubrication performances of square shape textured parallel sliding contacts are examined under the combined influence of both fluid inertia and fluid slippage at the fluid–solid interface. A two-component slip length model and first-order perturbation method are adopted to formulate pressure governing equation consisting of fluid-slip and fluid inertia terms. The effect of texture size (aspect ratio), texture height ratio, reduced Reynolds number, slip length coefficient and critical threshold shear stress on the performance parameters like load support, end flow and friction parameter of parallel sliding contacts is studied. The results indicate that effect of fluid-slip is more influential than fluid inertia; therefore, the result shows similar and closer trend to the fluid-slip results. However, the magnitude of performance parameters depends on the effect of fluid inertia. Moreover, aspect ratio of 0.3–0.5 and lower value of texture height ratios can be used to achieve better hydrodynamic lubrication performance in parallel sliding contacts.


Fluid inertia Fluid–solid interfacial slip Hydrodynamic lubrication Parallel sliding contacts Square shape positive textures 

List of symbols


Constant slip length


Maximum clearance between the surfaces


Friction force


Film thickness of the lubricant


Height of the protrusion


Base length of surface texture


Length of the unit cell in x-direction


Length of the unit cell in z-direction


Pressure in the lubricant film


End flow in z-direction

u, v, w

Velocity components in the x, y and z-directions, respectively


Maximum velocity in xz plane


Slip velocity in x-direction


Load support


Slip velocity in z-direction


Dynamic viscosity of the lubricant


Density of the lubricant


Critical threshold shear stress of fluid


Critical shear stress of fluid in x-direction


Critical shear stress of fluid in z-direction

Non-dimensional parameters


Aspect ratio (area of textured surface area of unit cell)


Slip length coefficient \(\left( {{b \mathord{\left/ {\vphantom {b C}} \right. \kern-0pt} C}} \right)\)


Friction force \(\left( {{{FC} \mathord{\left/ {\vphantom {{FC} {\eta UL_{X} L_{Z} }}} \right. \kern-0pt} {\eta UL_{X} L_{Z} }}} \right)\)


Film thickness \(\left( {{h \mathord{\left/ {\vphantom {h C}} \right. \kern-0pt} C}} \right)\)


Texture height ratio \(\left( {{{h_{g} } \mathord{\left/ {\vphantom {{h_{g} } C}} \right. \kern-0pt} C}} \right)\)


Ratio of the imaginary cell lengths (\({{L_{X} } \mathord{\left/ {\vphantom {{L_{X} } {L_{Z} }}} \right. \kern-0pt} {L_{Z} }}\))


Pressure \(\left( {{{pC^{2} } \mathord{\left/ {\vphantom {{pC^{2} } {\eta UL_{X} }}} \right. \kern-0pt} {\eta UL_{X} }}} \right)\)


Steady-state non-dimensional pressure \(\left( {{{p_{0} C^{2} } \mathord{\left/ {\vphantom {{p_{0} C^{2} } {\eta UL_{X} }}} \right. \kern-0pt} {\eta UL_{X} }}} \right)\)


Non-dimensional first-order perturb pressure \(\left( {{{p_{1} C^{2} } \mathord{\left/ {\vphantom {{p_{1} C^{2} } {\eta UL_{X} }}} \right. \kern-0pt} {\eta UL_{X} }}} \right)\)


End flow \(\left( {{Q \mathord{\left/ {\vphantom {Q {UCL_{X} }}} \right. \kern-0pt} {UCL_{X} }}} \right)\)


Reduced Reynolds number \(\left( {\bar{R}e = \left( {{\raise0.7ex\hbox{$C$} \!\mathord{\left/ {\vphantom {C {L_{x} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${L_{x} }$}}} \right)\text{Re} } \right)\)


Velocity component in x-direction \(({u \mathord{\left/ {\vphantom {u U}} \right. \kern-0pt} U})\)


Velocity component in y-direction \({({vL_{X} } \mathord{\left/ {\vphantom {{vL_{X} } {UC}}} \right. \kern-0pt} {UC})}\)


Velocity component in z-direction \(({w \mathord{\left/ {\vphantom {w U}} \right. \kern-0pt} U})\)

\(\bar{u}_{0} ,\,\bar{v}_{0} ,\,\bar{w}_{0}\)

Steady-state velocity components


Slip velocity in x-direction \(\left( {{{U_{S} } \mathord{\left/ {\vphantom {{U_{S} } U}} \right. \kern-0pt} U}} \right)\)


Load support \(\left( {{{WC^{2} } \mathord{\left/ {\vphantom {{WC^{2} } {\eta UL^{2}_{X} L_{Z} }}} \right. \kern-0pt} {\eta UL^{2}_{X} L_{Z} }}} \right)\)


Slip velocity in z-direction \(\left( {{{W_{S} } \mathord{\left/ {\vphantom {{W_{S} } U}} \right. \kern-0pt} U}} \right)\)


x-coordinate \(\left( {{x \mathord{\left/ {\vphantom {x {L_{X} }}} \right. \kern-0pt} {L_{X} }}} \right)\)


y-coordinate \(\left( {{y \mathord{\left/ {\vphantom {y C}} \right. \kern-0pt} C}} \right)\)


z-coordinate \(\left( {{z \mathord{\left/ {\vphantom {z {L_{Z} }}} \right. \kern-0pt} {L_{Z} }}} \right)\)

\(\mu ({{L_{X} } \mathord{\left/ {\vphantom {{L_{X} } C}} \right. \kern-0pt} C})\)

Friction parameter

\(\bar{\tau }_{\text{Co}}\)

Critical shear stress \(\left( {{{\tau_{\text{Co}} C} \mathord{\left/ {\vphantom {{\tau_{\text{Co}} C} {\eta U}}} \right. \kern-0pt} {\eta U}}} \right)\)



This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.


  1. 1.
    Etsion I, Kligerman Y, Halperin G (1999) Analytical and experimental investigation of laser-textured mechanical seal faces. Tribol Trans 42:511–516CrossRefGoogle Scholar
  2. 2.
    Etsion I, Burstein L (1996) A model for mechanical seals with regular microsurface structure. Tribol Trans 39(3):677–683CrossRefGoogle Scholar
  3. 3.
    Yu H, Deng H, Huang W, Wang X (2013) The effect of dimple shapes on friction of parallel surfaces. Proc Inst Mech Eng Part J: J Eng Tribol 225:693–703CrossRefGoogle Scholar
  4. 4.
    Ronen A, Etsion I, Kligerman Y (2001) Friction reducing surface texturing in reciprocating automotive components. Tribol Trans 44(3):359–366CrossRefGoogle Scholar
  5. 5.
    Kligerman Y, Shinkarenko A (2015) Analysis of friction in surface textured components of reciprocating mechanism. Proc Inst Mech Eng Part J: J Eng Tribol 229(4):336–349CrossRefGoogle Scholar
  6. 6.
    Kligerman Y, Etsion I, Shinkarenko A (2005) Improving tribological performance of piston rings by partial surface texturing. ASME Trans J Tribol 127:632–638CrossRefGoogle Scholar
  7. 7.
    Miki N, Atsuko K, Atsushi K, Koji M, Takashi M, Yasuhisa A, Hatsuhiko U, Shinya S (2007) Applying micro-texture to cast iron surfaces to reduce the friction coefficient under lubricated conditions. Tribology Letters 28:131–137CrossRefGoogle Scholar
  8. 8.
    Ryk G, Kligerman Y, Etsion I (2002) Experimental investigations of laser surface texturing for reciprocating automotive components. Tribol Trans 45(4):444–449CrossRefGoogle Scholar
  9. 9.
    Ryk G, Kligerman Y, Etsion I, Shinkarenko A (2005) Experimental investigation of laser surface texturing for piston-ring friction reduction. Tribol Trans 48:583–588CrossRefGoogle Scholar
  10. 10.
    Ryk G, Etsion I (2006) Testing piston rings with partial laser surface texturing for friction reduction. Wear 261:792–796CrossRefGoogle Scholar
  11. 11.
    Ghosh MK, Majumdar BC, Sarangi M (2012) Theory of lubrication. McGraw Hill Education, BengaluruGoogle Scholar
  12. 12.
    Stolarski TA, Chai W (2008) Inertia effect in squeeze film air contact. Tribol Int 41:716–723CrossRefGoogle Scholar
  13. 13.
    Meng FM, Cen SQ, Wan DP (2011) Study of effect of inertia forces of oil film on performance of journal—thrust floating ring bearing using a new method. Proc Inst Mech Eng Part J: J Eng Tribol 225:1139–1151CrossRefGoogle Scholar
  14. 14.
    Syed I, Sarangi M (2012) Study of fluid inertia on textured parallel sliding contacts: using perturbation and velocity profile methods. In: 8th International conference on industrial tribology, Pune, IndiaGoogle Scholar
  15. 15.
    Ismail Syed, Sarangi M (2014) Hydrodynamic lubrication with deterministic micro textures considering fluid inertia effect. Tribol Int 69:30–38CrossRefGoogle Scholar
  16. 16.
    Sahlin F, Glavatskih SB, Almqvist T, Larsson R (2005) Two-dimensional CFD-analysis of micro-patterned surfaces in hydrodynamic lubrication. Trans ASME 127:96–102CrossRefGoogle Scholar
  17. 17.
    Cupillard S, Glavatskih S, Cervantes MJ (2009) Inertia effects in textured hydrodynamic contacts. Proc Inst Mech Eng Part J: J Eng Tribol 224:751–756CrossRefGoogle Scholar
  18. 18.
    Dobrica MB, Fillon M (2009) About the validity of Reynolds equation and inertia effects in textured slider of infinite width. Inst Mech Eng Part J: J Eng Tribol 223:69–78CrossRefGoogle Scholar
  19. 19.
    Thompson PA, Troian SM (1997) A general boundary condition for liquid flow at solid surfaces. Nature 389:360–362CrossRefGoogle Scholar
  20. 20.
    Barrat J, Bocquet L (1999) Large slip effect at a non-wetting fluid-solid interface. Phy Rev Lett 82:4671–4674CrossRefGoogle Scholar
  21. 21.
    Pit R, Hervet H, Leger L (2000) Direct experimental evidence of slip in hexadecane: solid interfaces. Phy Rev Lett 85:980–983CrossRefGoogle Scholar
  22. 22.
    Baudry J, Charlaix E, Tonck A, Mazuyer D (2001) Experimental evidence for a large slip effect at a nonwetting fluid-solid interface. Langmuir 17:5232–5236CrossRefGoogle Scholar
  23. 23.
    Zhu Y, Garnick S (2001) Rate-dependent slip of Newtonian liquid at smooth surfaces. Phy Rev Lett 87:096105CrossRefGoogle Scholar
  24. 24.
    Zhu Y, Garnick S (2002) Limits of the hydrodynamic no-slip boundary condition. Phy Rev Lett 88:106102CrossRefGoogle Scholar
  25. 25.
    Spikes H, Granick S (2003) Equation for slip of simple liquids at smooth solid surface. Am Chem Soc Langmuir 19:5065–5071Google Scholar
  26. 26.
    Wang Li-Li, Chang-Hou Lu, Ge Pei-Qi, Chen Shu-Jiang (2012) Study on the influence of critical shear stress on wall slip of spiral oil wedge journal bearing. Proc Inst Mech Eng Part J: J Eng Tribol 226(5):362–376CrossRefGoogle Scholar
  27. 27.
    Fortier AE, Salant RF (2005) Numerical analysis of a journal bearing with heterogeneous slip/no-slip surface. Trans ASME J Tribol 127:820–825CrossRefGoogle Scholar
  28. 28.
    Salant RF, Fortier AE (2004) Numerical analysis of slider bearing with a heterogeneous slip/no-slip surface. Tribol Trans 47:328–334CrossRefGoogle Scholar
  29. 29.
    Aurelian F, Patrick M, Mohamed H (2011) Wall slip effects in (elasto) hydrodynamic journal bearings. Tribol Int 44:868–877CrossRefGoogle Scholar
  30. 30.
    Tauviqirrahman M, Ismail R, Jamari J, Schipper DJ (2013) A study of surface texturing and boundary slip on improving the load support of lubricated parallel sliding contacts. Acta Mech 224:365–381MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    Tauviqirrahman M, Ismail R, Jamari J, Schipper DJ (2013) Combined effect of texturing and boundary slippage in lubricated sliding contacts. Tribology International 66:274–281CrossRefzbMATHGoogle Scholar
  32. 32.
    Ismail Syed, Sarangi M (2014) Effects of texture shape and fluid-solid interfacial slip on the hydrodynamic lubrication performance of parallel sliding contacts. Proc Inst Mech Eng Part J: J Eng Tribol 228(4):382–396CrossRefGoogle Scholar
  33. 33.
    Kakoty SK, Majumdar BC (2000) Effect of fluid inertia on the dynamic coefficients and stability of journal bearings. Proc Inst Mech Eng Part J: J Eng Tribol 214:229–242CrossRefGoogle Scholar

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringNational Institute of TechnologyWarangalIndia
  2. 2.Department of Mechanical EngineeringIndian Institute of TechnologyKharagpurIndia

Personalised recommendations