Open Access
Issue
ESAIM: M2AN
Volume 53, Number 4, July-August 2019
Page(s) 1083 - 1124
DOI https://doi.org/10.1051/m2an/2019013
Published online 04 July 2019
  1. J.C. Adams, mudpack: multigrid portable fortran software for the efficient solution of linear elliptic partial differential equations. Appl. Math. Comput. 34 (1989) 113–146. [Google Scholar]
  2. R.A. Adams and J.J.F. Fournier, Sobolev Spaces. Academic Press, Cambridge, MA (2003). [Google Scholar]
  3. E.C. Bingham, Fluidity and Plasticity. McGraw-Hill, New York, NY (1922). [Google Scholar]
  4. F. Boyer and P. Fabrie, Eléments d’analyse pour l’étude de quelques modèles d’écoulements de fluides visqueux incompressibles. Springer, Berlin (2005). [Google Scholar]
  5. F. Boyer and P. Fabrie, Mathematical Tools for the Study of the Incompressible Navier-Stokes Equations and Related Models. Springer, Berlin (2013). [CrossRef] [Google Scholar]
  6. B. Button, L.-H. Cai, C. Ehre, M. Kesimer, D.B. Hill, J.K. Sheehan, R.C. Boucher and M. Rubinstein, Periciliary brush promotes the lung health by separating the mucus layer from airway epithelia. Science (N.Y.) 337 (2012) 937–941. [CrossRef] [PubMed] [Google Scholar]
  7. G. Carbou and P. Fabrie, Boundary layer for a penalization method for viscous incompressible flow. Differ. Equ. 8 (2003) 1453–1480. [Google Scholar]
  8. P. Carreau, Rheological equations from molecular network theories. Trans. Soc. Rheol. 16 (1972) 99–127. [CrossRef] [Google Scholar]
  9. R. Chatelin, D. Anne-Archard, M. Murris-Espin, D. Sanchez, M. Thiriet, A. Didier and P. Poncet, Chapter 5 – Modeling cystic fibrosis and mucociliary clearance. In: Modeling of Microscale Transport in Biological Processes, edited by S.M. Becker. Academic Press, Cambridge, MA (2017) 113–154. [CrossRef] [Google Scholar]
  10. R. Chatelin, D. Anne-Archard, M. Murris-Espin, M. Thiriet and P. Poncet, Numerical and experimental investigation of mucociliary clearance breakdown in cystic fibrosis. J. Biomech. 53 (2017) 56–63. [CrossRef] [PubMed] [Google Scholar]
  11. R. Chatelin and P. Poncet, A hybrid grid-particle method for moving bodies in 3D stokes flow with variable viscosity. SIAM J. Sci. Comput. 35 (2013) B925–B949. [Google Scholar]
  12. R. Chatelin and P. Poncet, Hybrid grid–particle methods and penalization: a Sherman–Morrison–Woodbury approach to compute 3D viscous flows using FFT. J. Comput. Phys. 269 (2014) 314–328. [Google Scholar]
  13. R. Chatelin and P. Poncet, A parametric study of mucociliary transport by numerical simulations of 3D non-homogeneous mucus. J. Biomech. 49 (2016) 1772–1780. [CrossRef] [PubMed] [Google Scholar]
  14. R. Chatelin, D. Sanchez and P. Poncet, Analysis of the penalized 3D variable viscosity stokes equations coupled to diffusion and transport. ESAIM: M2AN 50 (2016) 565–591. [CrossRef] [EDP Sciences] [Google Scholar]
  15. G.-H. Cottet, R. Hildebrand, P. Koumoutsakos, C. Mimeau, I. Mortazavi and P. Poncet, Passive and active flow control using vortex methods. In: 6th International Conference on Vortex Flows and Vortex Models. Nagoya, Japan (November 2014). [Google Scholar]
  16. G.H. Cottet and P.D. Koumoutsakos, Vortex Methods: Theory and Practice. IOP Publishing, Bristol (2001). [Google Scholar]
  17. M.V. D’Angelo, H. Auradou, C. Allain and J.-P. Hulin, Pore scale mixing and macroscopic solute dispersion regimes in polymer flows inside two-dimensional model networks. Phys. Fluids 19 (2007) 033103. [CrossRef] [Google Scholar]
  18. A. Decoene, S. Martin and B. Maury, Microscopic modelling of active bacterial suspensions. MMNP 6 (2011) 98–129. [EDP Sciences] [Google Scholar]
  19. L. Diening, Theoretical and numerical results for electrorheological fluids. Ph.D. thesis, University of Frieburg, Germany (2002). [Google Scholar]
  20. L. Diening, P. Harjulehto, P. Hästö and M. Ruzicka, Lebesgue and Sobolev spaces with variable exponents. In: Vol. 2017 of Lecture Notes in Mathematics. Springer Berlin Heidelberg, Berlin, Heidelberg (2011). [CrossRef] [Google Scholar]
  21. L. Diening, P. Hästö and A. Nekvinda, Open problems in variable exponent Lebesgue and Sobolev spaces. In: FSDONA04 Proceedings, Milovy. Czech Republic, Citeseer 3858(2004). [Google Scholar]
  22. G. Duvaut and J.L. Lions, Les inéquations en mécanique et en physique. Dunod, Paris (1972). [Google Scholar]
  23. J.V. Fahy and B.F. Dickey, Airway mucus function and dysfunction.New England J. Med. 363 (2010) 2233–2247. PMID: 21121836. [CrossRef] [PubMed] [Google Scholar]
  24. C. Foias and R. Temam, Remarques sur les équations de navier-stokes stationnaires et les phénomènes successifs de bifurcation. Ann. Scuola Norm. Superiore Pisa - Classe di Scienze 5 (1978) 29–63. [Google Scholar]
  25. J.L.M.S. Ganter, M. Milas and M. Rinaudo, On the viscosity of sodium poly(styrene sulphonate), a flexible polyelectrolyte. Polymer 33 (1992) 113–116. [Google Scholar]
  26. D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order. Springer Berlin Heidelberg, Berlin, Heidelberg (1983). [CrossRef] [Google Scholar]
  27. H. Giesekus, A simple constitutive equation for polymer fluids based on the concept of deformation dependent tensorial mobility. J. Non-Newtonian Fluid Mech. 11 (1982) 69–109. [CrossRef] [Google Scholar]
  28. J.L. Guermond, P. Minev and J. Shen, An overview of projection methods for incompressible flows. Comput. Methods Appl. Mech. Eng. 195 (2006) 6011–6045. [Google Scholar]
  29. W.H. Herschel and R. Bulkley, Konsistenzmessungen von Gummi-Benzollösungen. Kolloid Z. 39 (1926) 291–300. [CrossRef] [Google Scholar]
  30. C.P. Kelco, Keltrol/Kelzan, Xanthan gum book 8th edition (March 2007). [Google Scholar]
  31. M. Krotkiewski, I.S. Ligaarden, K.-A. Lie and D.W. Schmid, On the importance of the stokes-brinkman equations for computing effective permeability in karst reservoirs. Commun. Comput. Phys. 10 (2011) 1315–1332. [Google Scholar]
  32. S.K. Lai, Y.-Y. Wang, D. Wirtz and J. Hanes, Micro- and macrorheology of mucus. Adv. Drug Delivery Rev. 61 (2009) 86–100. [CrossRef] [Google Scholar]
  33. P. Lindqvist, Notes on the p-Laplace Equation. University of Jyväskylä (2006). [Google Scholar]
  34. J.-L. Lions, Quelques méthodes de résolution des problemes aux limites non linéaires. In Vol. 31. Dunod Paris (1969). [Google Scholar]
  35. J.L. Lions, E. Magenes, Problèmes aux limites non homogènes et applications In Vol. 1. (1968). [Google Scholar]
  36. J.J. Monaghan, Extrapolating B splines for interpolation. J. Comput. Phys. 60 (1985) 253–262. [Google Scholar]
  37. J. Nečas, Les méthodes directes en théorie des équations elliptiques. Academia, San Francisco, CA (1967). [Google Scholar]
  38. B. Noetinger, L. Hume, R. Chatelin and P. Poncet, The effective viscosity of a random mixture of fluids. Phys. Rev. Fluids 3 (2017) 014103. [Google Scholar]
  39. J.G. Oldroyd, On the formulation of rheological equations of state. Proc. Roy. Soc. London 200 (1950) 523–541. [CrossRef] [MathSciNet] [Google Scholar]
  40. E. Puchelle, J.M. Zahm and D. Quemada, Rheological properties controlling mucociliary frequency and respiratory mucus transport. Biorheology 24 (1987) 557–563. PMID: 3502756. [PubMed] [Google Scholar]
  41. M. Le Ravalec, B. Noetinger and L.H. Hu, The FFT moving average (FFT-MA) generator: an efficient numerical method for generating and conditioning gaussian simulations. Math. Geol. 32 (2000) 701–723. [Google Scholar]
  42. M.J. Sanderson and M.A. Sleigh, Ciliary activity of cultured rabbit tracheal epithelium: beat pattern and metachrony. J. Cell Sci. 47 (1981) 331–347. [PubMed] [Google Scholar]
  43. D.J. Smith, E.A. Gaffney and J.R. Blake, Modelling mucociliary clearance. Respir. Physiol. Neurobiol. 163 (2008) 178–188. [CrossRef] [PubMed] [Google Scholar]
  44. G.A. Stahl and D.N. Schulz, Water-Soluble Polymers for Petroleum Recovery. Springer US (2012). [Google Scholar]
  45. P. Swarztrauber and R. Sweet, Efficient FORTRAN subprograms for the solution of elliptic partial differential equations (abstract). SIGNUM Newsl. 10 (1975). [CrossRef] [Google Scholar]
  46. M.D. Torres, B. Hallmark, D. Ian Wilson and L. Hilliou, Natural giesekus fluids: shear and extensional behavior of food gum solutions in the semidilute regime. AIChE J. 60 (2014) 3902–3915. [Google Scholar]
  47. E. Zeidler, Nonlinear Functional Analysis and its Applications II/B. Springer New York, New York, NY (1990). [Google Scholar]
  48. L. Zhong, M. Oostrom, M.J. Truex, V.R. Vermeul and J.E. Szecsody, Rheological behavior of xanthan gum solution related to shear thinning fluid delivery for subsurface remediation. J. Hazard. Mater. 244–245 (2013) 160–170. [Google Scholar]

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