Open Access
Volume 56, Number 4, July-August 2022
Page(s) 1255 - 1305
Published online 27 June 2022
  1. G. Allaire, Homogenization and two-scale convergence. SIAM J. Math. Anal. 23 (1992) 1482–1518. [Google Scholar]
  2. T. Arbogast, J. Douglas and U. Hornung, Derivation of the double porosity model of single phase flow via homogenization theory. SIAM J. Math. Anal. 21 (1990) 823–836. Sér. I 332 (2001) 223–228. [CrossRef] [MathSciNet] [Google Scholar]
  3. J.M. Arrieta and M. Villanueva-Pesqueira, Unfolding operator method for thin domains with a locally periodic highly oscillatory boundary. SIAM J. Math. Anal. 48 (2016) 1634–1671. [CrossRef] [MathSciNet] [Google Scholar]
  4. S. Bair and W.O. Winer, Shear strength measurements of lubricants at high pressure. ASME Ser. F. J. Lubr. Technol. 101 (1979) 251–257. [CrossRef] [Google Scholar]
  5. G. Bayada and M. Chambat, The transition between the Stokes equations and the Reynolds equation: a mathematical proof. Appl. Math. Opt. 14 (1986) 73–93. [CrossRef] [Google Scholar]
  6. G. Bayada and M. Chambat, New models in the theory of the hydrodynamic lubrication of rough surfaces. J. Tribol. 110 (1988) 402–407. [CrossRef] [Google Scholar]
  7. G. Bayada and G. Lukaszewicz, On micropolar fluids in the theory of lubrication. Rigorous derivation of an analogue of the Reynolds equation. Int. J. Eng. Sci. 34 (1996) 1477–1490. [CrossRef] [Google Scholar]
  8. G. Bayada, M. Chambat and S.R. Gamouana, About thin film micropolar asymptotic equations. Quart. Appl. Math. 59 (2001) 413–439. [CrossRef] [MathSciNet] [Google Scholar]
  9. G. Bayada, N. Benhaboucha and M. Chambat, New models in micropolar fluid and their application to lubrication. Math. Mod. Meth. Appl. Sci. 15 (2005) 343–374. [CrossRef] [Google Scholar]
  10. G. Bayada, N. Benhaboucha and M. Chambat, Wall slip induced by a micropolar fluid. J. Eng. Math. 60 (2008) 89–100. [CrossRef] [Google Scholar]
  11. M. Beneš, I. Pažanin and F.J. Suárez-Grau, Heat flow through a thin cooled pipe filled with a micropolar fluid. J. Theor. Appl. Mech. 53 (2015) 569–579. [Google Scholar]
  12. N. Benhaboucha, M. Chambat and I. Ciuperca, Asymptotic behaviour of pressure and stresses in a thin film flow with a rough boundary. Q. Appl. Math. 63 (2005) 369–400. [CrossRef] [Google Scholar]
  13. N.M. Bessonov, Boundary Viscosity Conception in Hydrodynamical Theory of Lubrication. Russian Academy of Sicence, Institute of the Problems of Mechanical Engineering, St-Petersbourg, preprint Vol. 81 (1993) 105–108. [Google Scholar]
  14. N.M. Bessonov, A new generalization of the Reynolds equation for a micropolar fluid and its application to bearing theory. Tribol. Int. 27 (1994) 105–108. [CrossRef] [Google Scholar]
  15. E. Bonaccurso, H.J. Butt and V.S. Craig, Surface roughness and hydrodynamic boundary slip of a Newtonian fluid in a completely wetting system. Phys. Re. Lett. 90 (2003) 144–501. [CrossRef] [Google Scholar]
  16. M. Bonnivard and F.J. Suárez-Grau, Homogenization of a large eddy simulation model for turbulent fluid motion near a rough wall. J. Math. Fluid Mech. 20 (2018) 1771–1813. [CrossRef] [MathSciNet] [Google Scholar]
  17. M. Bonnivard, F.J. Suárez-Grau and G. Tierra, On the influence of wavy riblets on the slip behaviour of viscous fluids. Z. Angew. Math. Phys. 67 (2016) 1–23. [CrossRef] [Google Scholar]
  18. M. Bonnivard, I. Pažanin and F.J. Suárez-Grau, Effects of rough boundary and nonzero boundary conditions on the lubrication process with micropolar fluid. Eur. J. Mech. B/Fluids 72 (2018) 501–518. [CrossRef] [MathSciNet] [Google Scholar]
  19. M. Boukrouche and L. Paoli, Asymptotic analysis of a micropolar fluid flow in a thin domain with a free and rough boundary. SIAM J. Math. Anal. 44 (2012) 1211–1256. [CrossRef] [MathSciNet] [Google Scholar]
  20. F. Boyer and P. Fabrie, Mathematical Tools for the Study of the Incompressible Navier–Stokes Equations and Related Models. Springer, (2013). [Google Scholar]
  21. D. Bresch, C. Choquet, L. Chupin, T. Colin and M. Gisclon, Roughness-induced effect at main order on the Reynolds approximation. SIAM Multiscale Model. Simul. 8 (2010) 997–1017. [CrossRef] [MathSciNet] [Google Scholar]
  22. D. Bucur, E. Feireisl and S. Nečasová, On the asymptotic limit of flows past a ribbed boundary. J. Math. Fluid Mech. 10 (2008) 554–568. [CrossRef] [MathSciNet] [Google Scholar]
  23. J. Casado-Díaz, M. Luna-Laynez and F.J. Suárez-Grau, A viscous fluid in a thin domain satisfying the slip condition on a slightly rough boundary. C. R. Math. 348 (2010) 967–971. [CrossRef] [Google Scholar]
  24. J. Casado-Díaz, M. Luna-Laynez and F.J. Suárez-Grau, Asymptotic behavior of the Navier–Stokes system in a thin domain with Navier condition on a slightly rough boundary. SIAM J. Math. Anal. 45 (2013) 1641–1674. [CrossRef] [MathSciNet] [Google Scholar]
  25. L. Chupin and S. Martin, Rigorous derivation of the thin film approximation with roughness-induced correctors. SIAM J. Math. Anal. 44 (2012) 3041–3070. [CrossRef] [MathSciNet] [Google Scholar]
  26. D. Cioranescu, A. Damlamian and G. Griso, Periodic unfolding and homogenization. C. R. Acad. Sci. Paris Sér. I 335 (2002) 99–104. [CrossRef] [Google Scholar]
  27. D. Cioranescu, P. Donato and R. Zaki, The periodic unfolding method in perforated domains. Portugaliae Math. 63 (2006) 467–496. [MathSciNet] [Google Scholar]
  28. V.S.J. Craig, C. Neto and D.R.M. Williams, Shear-dependent boundary slip in a aqueous Newtonian liquid. Phys. Rev. Lett. 87 (2001) 054504. [CrossRef] [PubMed] [Google Scholar]
  29. D. Dupuy, G. Panasenko and R. Stavre, Asymptotic methods for micropolar fluids in a tube structure. Math. Mod. Meth. Appl. Sci. 14 (2004) 735–758. [CrossRef] [Google Scholar]
  30. D. Dupuy, G. Panasenko and R. Stavre, Asymptotic solution for a micropolar flow in a curvilinear channel. Z. Angew. Math. Mech. 88 (2008) 793–807. [CrossRef] [MathSciNet] [Google Scholar]
  31. A.C. Eringen, Simple microfluids. Int. J. Eng. Sci. 2 (1964) 205–217. [CrossRef] [Google Scholar]
  32. A.C. Eringen, Theory of micropolar fluids. J. Math. Mech. 16 (1966) 1–16. [MathSciNet] [Google Scholar]
  33. V. Girault and P.A. Raviart, Finite Element Approximation of the Navier-Stokes Equation. Springer-Verlag (1979). [CrossRef] [Google Scholar]
  34. S.G. Hatzikiriakos and J.M. Delay, Wall slip of molten high density polyethylene I – Sliding plate rheometer studies. J. Rheol. 35 (1991) 497–523. [CrossRef] [Google Scholar]
  35. F. Hecht, New Development in FreeFem++. J. Numer. Math. 20 (2012) 251–265. [Google Scholar]
  36. H. Hervet, R. Pit and L. Léger, Friction and slip of a simple liquid at a solid surface. Tribol. Lett. 7 (1999) 147–152. [CrossRef] [Google Scholar]
  37. B.O. Jacobson, At the boundary between lubrication and wear. In: First World Tribology Conference, edited by I.M. Hutchings. Mech. Eng. Pub. London (1997) 291–298. [Google Scholar]
  38. B.O. Jacobson and B.J. Hamrock, Non-Newtonian fluid model incorporated into elastohydrodynamic lubrication of rectangular contacts. ASME J. Lubr. Technol. 106 (1984) 275–282. [Google Scholar]
  39. G.J. Jonhnston, R. Wayte and H.A. Spikes, The measurement and study of very thin lubricant films in concentrated contacts. Tribol. Trans. 34 (1991) 187–194. [CrossRef] [Google Scholar]
  40. N. Kaneta, Observation of wall slip in elastohydrodynamic lubrication. ASME J. Tribol. 106 (1990) 275–282. [Google Scholar]
  41. L. Léger, H. Hervet and R. Pit, Friction and flow with slip at fluid-solid interfaceds. In: Interfacial Properties on the Submicrometer Scale. ACS Symposium Series. Vol. 781, ACS, Washington, DC (2001) 154–167. [Google Scholar]
  42. J.-L. Ligier, Lubrification des paliers moteurs. Technip (1997). [Google Scholar]
  43. G. Lukaszewicz, Micropolar Fluids: Theory and Applications. Birkhäuser, Boston (1999). [CrossRef] [Google Scholar]
  44. J.B. Luo, P. Huang and S.Z. Wen, Thin film lubrication part I: Study on the transition between EHL and thin film lubrication using relative optical interference intensity technique. Wear 194 (1996) 107–115. [CrossRef] [Google Scholar]
  45. J.B. Luo, P. Huang, S.Z. Wen and L. Lawrence, Characteristics of fluid lubricant films at nano-scale. J. Tribol. 121 (1999) 872–878. [CrossRef] [Google Scholar]
  46. E. Marušić-Paloka, I. Pažanin and S. Marušić, Second order model in fluid film lubrication. C. R. Mecanique 340 (2012) 596–601. [CrossRef] [Google Scholar]
  47. E. Marušić-Paloka, I. Pažanin and S. Marušić, An effective model for the lubrication with micropolar fluid. Mech. Res. Commun. 52 (2013) 69–73. [CrossRef] [Google Scholar]
  48. Y.G. Meng and J. Zheng, A rheological model for lithinium lubricating grease. Tribol. Int. 31 (1999) 619–682. [Google Scholar]
  49. N.P. Migun, On hydrodynamic boundary conditions for microstructural fluids. Rheol. Acta 23 (1984) 575–581. [CrossRef] [Google Scholar]
  50. G. Nguetseng, A general convergence result for a functional related to the theory of homogenization. SIAM J. Math. Anal. 20 (1989) 608–623. [Google Scholar]
  51. I. Pažanin, Asymptotic behavior of micropolar fluid flow through a curved pipe. Acta Appl. Math. 116 (2011) 1–25. [CrossRef] [MathSciNet] [Google Scholar]
  52. I. Pažanin, On the micropolar flow in a circular pipe: the effects of the viscosity coefficients. Theor. Appl. Mech. Lett. 1 (2011) 062004. [CrossRef] [Google Scholar]
  53. I. Pažanin, Modeling of solute dispersion in a circular pipe filled with micropolar fluid. Math. Comput. Model. 57 (2012) 2366–2373. [Google Scholar]
  54. I. Pažanin, Asymptotic analysis of the lubrication problem with nonstandard boundary conditions for microrotation, to appear in FILOMAT (2016). [Google Scholar]
  55. I. Pažanin and F.J. Suárez-Grau, Effects of rough boundary on the heat transfer in a thin-film flow. C. R. Mécanique 341 (2013) 646–652. [CrossRef] [Google Scholar]
  56. I. Pažanin and F.J. Suárez-Grau, Analysis of the thin film flow in a rough thin domain filled with micropolar fluid. Comput. Math. Appl. 68 (2014) 1915–1932. [CrossRef] [MathSciNet] [Google Scholar]
  57. I. Pažanin and F.J. Suárez-Grau, Homogenization of the Darcy–Lapwood–Brinkman flow in a thin domain with highly oscillating boundaries. Bull. Malays. Math. Sci. Soc. 42 (2019) 3073–3109. [CrossRef] [MathSciNet] [Google Scholar]
  58. J. Prakash and P. Sinha, Lubrication theory for micropolar fluids and its application to a journal bearing. Int. J. Eng. Sci. 13 (1975) 217–232. [CrossRef] [Google Scholar]
  59. P.P. Prokhorenko, N.P. Migun and S.V. Grebenshchicov, Experimental studies of polar indicator liquids used in capillary penetrant testing. Int. J. Eng. Sci. 25 (1947) 482–489. [Google Scholar]
  60. O. Reynolds, On the theory of lubrication and its applications to Mr. Beauchamp Tower’s experiments, including an experimental determination of the viscosity of olive oil. Philos. Trans. R. Soc. London 177 (1886) 157–234. [CrossRef] [Google Scholar]
  61. P. Sinha and C. Singh, Micropolar squeeze films between rough rectangular plates. Appl. Sci. Res. 39 (1982) 167–179. [CrossRef] [Google Scholar]
  62. P. Sinha and C. Singh, The three-dimensional Reynolds equation for micropolar-fluid-lubricated bearings. Wear 76 (1982) 199–209. [CrossRef] [Google Scholar]
  63. H.A. Spikes, The hanlf-wetted bearing. Part 1: extended Reynolds equation. J. Eng. Tribol. 217 (2003) 1–14. [Google Scholar]
  64. F.J. Suárez-Grau, Effective boundary condition for a quasi-newtonian fluid at a slightly rough boundary starting from a Navier condition. ZAMM – J. Appl. Math. Mech. 95 (2015) 527–548. [CrossRef] [Google Scholar]
  65. F.J. Suárez-Grau, Asymptotic behavior of a non-Newtonian flow in a thin domain with Navier law on a rough boundary. Nonlinear Anal. 117 (2015) 99–123. [CrossRef] [MathSciNet] [Google Scholar]
  66. F.J. Suárez-Grau, Analysis of the roughness regimes for micropolar fluids via homogenization. Bull. Malays. Math. Sci. Soc. 44 (2021) 1613–1652. [CrossRef] [MathSciNet] [Google Scholar]
  67. A.Z. Szeri, Fluid Film Lubrication: Theory and Design. Cambridge University Press (1998). [CrossRef] [Google Scholar]
  68. J. Wilkening, Practical error estimates for Reynolds’ lubrication approximation and its higher order corrections. SIAM J. Math. Anal. 41 (2009) 588–630. [CrossRef] [MathSciNet] [Google Scholar]
  69. W.D. Wilson and X.B. Huang, Viscoplastic behavior of silicone oil in a metalforming inlet zone. ASME. J. Tribol. 111 (1989) 585–590. [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you