Open Access
Issue
Math. Model. Nat. Phenom.
Volume 20, 2025
Article Number 21
Number of page(s) 37
Section Mathematical methods
DOI https://doi.org/10.1051/mmnp/2025020
Published online 22 September 2025
  1. J.E. Cloud and P.E. Clark, Alternatives to the power-law fluid model for crosslinked fluids. Soc. Pet. Eng. J. 25 (1985) 935-942. [Google Scholar]
  2. S.N. Shah, Propant settling correlations for non-Newtonian fluids under static and dynamic conditions. Soc. Pet. Eng. J. 22 (1982) 164–170. [Google Scholar]
  3. G. Allaire, Homogenization of the Stokes flow in a connected porous medium. Asymp. Anal. 2 (1989) 203–222. [Google Scholar]
  4. E. Sanchez-Palencia, Nonhomogeneous media and vibration theory. Lecture Notes in Physics 127, Springer-Verlag (1980). [Google Scholar]
  5. L. Tartar, Incompressible fluid flow in a porous medium convergence of the homogenization process. Appendix to Lecture Notes in Physics, vol. 127 (1980). [Google Scholar]
  6. A. Bourgeat, O. Gipouloux and E. Marušić-Paloka, Filtration law for polymer ow through porous media. Multiscale Model. Simul. 1 (2003) 432–457. [Google Scholar]
  7. A. Bourgeat and A. Mikelić, Homogenization of a polymer flow through a porous medium. Nonlin. Anal. 26 (1996) 1221–1253. [Google Scholar]
  8. A. Bourgeat, E. Marušić-Paloka and A. Mikelić, Effective fluid flow in a porous medium containing a thin fissure. Asymp. Anal. 11 (1995) 241–262. [Google Scholar]
  9. A. Bourgeat, H. ElAmri and R. Tapiéro, Existence d’une taille critique pour une fissure dans un milieu poreux, Second Colloque Franco Chilien de Mathematiques Appliquées, Cepadués Edts, Tolouse (1991). [Google Scholar]
  10. H. Zhao and Z. Yao, Homogenization of a non-stationary Stokes flow in porous medium including a layer. J. Math. Anal. Appl. 342 (2008) 108–124. [Google Scholar]
  11. H. Zhao and Z. Yao, Effective models of the Navier–Stokes flow in porous media with a thin fissure. J. Math. Anal. Appl. 387 (2012) 542–555. [Google Scholar]
  12. A. Bourgeat, E. Marušić-Paloka and A. Mikelić, Effective behavior of porous medium containing a thin fissure, Proceedings of the Colloquium Calculus of Variations, Homogenization and Continuum Mechanics, Marseille, Series on Advances in Mathematics for Applied Sciences. World Scientific (1993). [Google Scholar]
  13. A. Bourgeat and R. Tapiéro, Homogenization in a perforated domain including a thin full interlayer, Proceedings of the Oberwolfach conference Porous Medium, in Int. Series in Numerical Mathematics, vol. 114, edited by J. Douglas Jr and U. Hornung. Birkhäuser (1993) 25-36. [Google Scholar]
  14. M. Anguiano and F.J. Suárez-Grau, Analysis of the effects of a fissure for a non-Newtonian fluid flow in a porous medium. Commun. Math. Sci. 16 (2018) 273–292. [Google Scholar]
  15. M. Anguiano, Homogenization of a non-stationary non-Newtonian flow in a porous medium containing a thin fissure. Eur. J. Appl. Math. 30 (2019) 248–277. [Google Scholar]
  16. A. Almqvist, J. Fabricius, T.S. Lundstraöm and Peter Wall, Flow in thin domains with a microstructure: lubrication and thin porous media, in AIP Conference Proceedings. AIP Publishing LLC 020172 (2017). [Google Scholar]
  17. M. Anguiano and F.J. Suárez-Grau, Derivation of a coupled Darcy–Reynolds equation for a fluid flow in a thin porous medium including a fissure. Z. Angew. Math. Phys. 68 (2017) Paper No. 52. [Google Scholar]
  18. M. Anguiano and R. Bunoiu, Homogenization of Bingham flow in thin porous media. Netw. Heterog. Media 15 (2020) 87–110. [Google Scholar]
  19. M. Anguiano, M. Bonnivard and F.J. Suárez-Grau, Carreau law for non-Newtonian fluid flow through a thin porous media. Q. J. Mech. Appl. Math. 75 (2022) 1–27. [Google Scholar]
  20. M. Anguiano, M. Bonnivard and F.J. Suárez-Grau, Effective models for generalized Newtonian fluids through a thin porous medium following the Carreau law. ZAMM Z. Angew. Math. Mech. 105 (2025) e202300920. [Google Scholar]
  21. M. Anguiano and F.J. Suárez-Grau, Homogenization of an incompressible non-Newtonian flow through a thin porous medium. Z. Angew. Math. Phys. 68 (2017) Paper No. 45. [Google Scholar]
  22. M. Anguiano and F.J. Suárez-Grau, The transition between the Navier–Stokes equations to the Darcy equation in a thin porous medium. Mediterr. J. Math. 15 (2018) Paper No. 45. [Google Scholar]
  23. M. Anguiano and F.J. Suárez-Grau, Newtonian fluid flow in a thin porous medium with non-homogeneous slip boundary conditions. Netw. Heterog. Media 14 (2019) 289–316. [Google Scholar]
  24. M. Anguiano and F.J. Suárez-Grau, Lower-dimensional nonlinear Brinkman’s law for non-newtonian flows in a thin porous medium. Mediterr. J. Math. 18 (2021) Paper No. 175. [Google Scholar]
  25. M. Anguiano and F.J. Suárez-Grau, Sharp pressure estimates for the Navier–Stokes system in thin porous media. Bull. Malay. Math. Sci. Soc. 46 (2023) Paper No. 117. [Google Scholar]
  26. J. Fabricius, J.G.I. Hellströom, T.S. Lundstraöm, E. Miroshnikova and P. Wall, Darcy’s law for flow in a periodic thin porous medium confined between two parallel plates. Transp. Porous Med. 115 (2016) 473–493. [Google Scholar]
  27. J. Fabricius, S. Manjate and P. Wall, On pressure-driven Hele–Shaw flow of power–law fluids. Appl. Anal. 101 (2022) 5107–5137. [Google Scholar]
  28. J. Fabricius and M. Gahn, Homogenization and Dimension Reduction of the Stokes problem with Navier-slip condition in thin perforated layers. Multiscale Model. Simul. 21 (2023) 1502–1533. [Google Scholar]
  29. T.O.M. Forslund, I.A.S. Larsson, H. Lycksam, et al., Non-Stokesian flow through ordered thin porous media imaged by tomographic-PIV. Exp. Fluids 62 (2021) Paper No. 46. [Google Scholar]
  30. N.F. Jouybari and T.S. Lundström, Investigation of post-Darcy flow in thin porous media. Transp. Porous Media 138 (2021) 157–184. [Google Scholar]
  31. C.C. Mei and B. Vernescu, Homogenization Methods for Multiscale Mechanics. World Scientific Publishing Co. Pte. Ltd., Singapore (2010). [Google Scholar]
  32. F.J. Suárez-Grau, Theoretical derivation of Darcy’s law for fluid flow in thin porous media. Math. Nachr. 295 (2022) 1–17. [Google Scholar]
  33. F.J. Suárez-Grau, Mathematical modeling of micropolar fluid flows through a thin porous medium. J. Eng. Math. 126 (2021) Paper No. 7. [Google Scholar]
  34. Y. Zhengan and Z. Hongxing, Homogenization of a stationary Navier–Stokes flow in porous medium with thin film. Acta Math. Sci. 28 (2008) 963–974. [Google Scholar]
  35. G. Bayada, N. Benhaboucha, and M. Chambat, Modeling of a thin film passing a thin porous medium. Asymp. Anal. 37 (2004) 227–256. [Google Scholar]
  36. M. Anguiano, Derivation of a quasi-stationary coupled Darcy–Reynolds equation for incompressible viscous fluid flow through a thin porous medium with a fissure. Math. Method Appl. Sci. 40 (2017) 4738–4757. [Google Scholar]
  37. D. Cioranescu, A. Damlamian and G. Griso, The periodic unfolding method in homogenization. SIAM J. Math. Anal. 40 (2008) 1585–1620. [Google Scholar]
  38. D. Cioranescu, A. Damlamian and G. Griso, The periodic unfolding method: theory and applications to partial differential problems, Series in Contemporary Mathematics, vol. 3. Springer, Singapore (2018). [Google Scholar]
  39. R. Temam, Navier–Stokes Equations. North Holland (1984). [Google Scholar]
  40. F. Boyer and P. Fabrie, Mathematical Tools for the Study of the Incompressible Navier–Stokes Equations and Related Models. Springer (2013). [Google Scholar]
  41. A. Mikelić and R. Tapiéro, Mathematical derivation of the power law describing polymer flow through a thin slab. RAIRO-Model. Math. Anal. Num. 29 (1995) 3–21. [Google Scholar]
  42. Y.S. Wu, K. Pruess and A. Witherspoon, Displacement of a Newtonian fluid by a non-Newtonian fluid in a porous medium. Transp. Porous Med. 6 (1991) 115–142. [Google Scholar]
  43. J. Baranger and K. Najib, Analyse numérique des écoulements quasi-Newtoniens dont la viscosité obeit a la loi puissance ou la loide Carreau. Numer. Math. 58 (1990) 35–49. [Google Scholar]
  44. A. Duvnjak, Derivation of non-linear Reynolds-type problem for lubrication of a rotating shaft. Z. Angew. Math. Mech. 82 (2002) 317–333. [Google Scholar]
  45. A. Mikelić, Non-Newtonian flow, in Homogenization and Porous Media, Interdisciplinary Applied Mathematics Series, vol. 6. Springer-Verlag, New York (1997) 45-68. [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.