Free Access
Issue
Math. Model. Nat. Phenom.
Volume 6, Number 5, 2011
Complex Fluids
Page(s) 67 - 83
DOI https://doi.org/10.1051/mmnp/20116504
Published online 10 August 2011
  1. J. Baranger, A. Machmoum. Existence of approximate solutions and error bounds for viscoelastic fluid flow: characteristics method. Comput. Methods Appl. Mech. Engrg. , 148 (1997), No. 1-2, 39–52. [CrossRef] [MathSciNet] [Google Scholar]
  2. J. Baranger, D. Sandri. Finite element approximation of viscoelastic fluid flow: existence of approximate solutions and error bounds. I. Discontinuous constraints. Numer. Math., 63 (1992), No. 1, 13–27. [CrossRef] [MathSciNet] [Google Scholar]
  3. R.B. Bird, R.C. Armstrong, O. Hassager. Dynamics of Polymeric Liquids. Wiley-Interscience, 1987. [Google Scholar]
  4. J.R. Blake, P.G. Vann, H Winet. A model of ovum transport. J. Theor. Biol., 102 (1983), No. 1, 145–166. [CrossRef] [PubMed] [Google Scholar]
  5. S. Boyarski, C. Gottschalk, E. Tanagho, P. Zimskind. Urodynamics: Hydrodynamics of the Ureter and the Renal Pelvis. Academic Press, New York, 1971. [Google Scholar]
  6. A. Brooks, T. Hughes. Streamline Upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering, 32 (1982), No. (1-3), 199–259. [CrossRef] [MathSciNet] [Google Scholar]
  7. J.C. Chrispell, V.J. Ervin, E.W. Jenkins. A fractional step [theta]-method approximation of time-dependent viscoelastic fluid flow. Journal of Computational and Applied Mathematics, 232 (2009), No. 2, 159–175. [CrossRef] [MathSciNet] [Google Scholar]
  8. K. Connington, Q. Kang, H. Viswanathan, A. Abdel-Fattah, S. Chen. Peristaltic particle transport using the lattice boltzmann method. Phys. of Fluids, 21 (2009), No. 5, 053301. [CrossRef] [Google Scholar]
  9. A.W. El-Kareh, L.G. Leal. Existence of solutions for all deborah numbers for a non-Newtonian model modified to include diffusion. Journal of Non-Newtonian Fluid Mechanics, 33 (1989), No. 3, 257–287. [CrossRef] [Google Scholar]
  10. O. Eytan, D. Elad. Analysis of intra-uterine fluid motion induced by uterine contractions. Bull. Math. Biol., 61 (1999), No. 2, 221–238. [CrossRef] [PubMed] [Google Scholar]
  11. O. Eytan, A.J. Jaffa, J. Har-Toov, E. Dalach, D. Elad. Dynamics of the intrauterine fluid-wall interface. Ann. Biomed. Engr., 27 (1999) No. 3, 372-9. [CrossRef] [Google Scholar]
  12. L. Fauci. Peristaltic pumping of solid particles. Comp. & Fluids, 21 (1992), No. 4, 583–598. [CrossRef] [Google Scholar]
  13. L. Fauci, R. Dillon. Biofluidmechanics of reproduction. Annu. Rev. Fluid. Mech., 38 (2006), No. 1, 371–394. [CrossRef] [Google Scholar]
  14. B.E. Griffith, C.S. Peskin. On the order of accuracy of the immersed boundary method: Higher order convergence rates for sufficiently smooth problems. Journal of Computational Physics, 208 (2005), No. 1, 75–105. [CrossRef] [MathSciNet] [Google Scholar]
  15. R. Guy, A. Fogelson. A wave propagation algorithm for viscoelastic fluids with spatially and temporally varying properties. Comput. Methods Appl. Mech. Engr., 197 (2008), No. 1, 2250–2264. [CrossRef] [Google Scholar]
  16. F. H. Harlow, J. E. Welch. Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys. of Fluids, 8 (1965), No. 12, 2182–2189. [NASA ADS] [CrossRef] [Google Scholar]
  17. E. J. Hinch. Uncoiling a polymer molecule in a strong extensional flow. Journal of Non-Newtonian Fluid Mechanics, 54 (1994), No. C, 209–230. [CrossRef] [Google Scholar]
  18. T.K. Hung, T.D. Brown. Solid-particle motion in two-dimensional peristaltic flows. J. Fluid Mech, 73 (1976), No. 1,77–96. [CrossRef] [Google Scholar]
  19. M. Y. Jaffrin and A. H. Shapiro. Peristaltic pumping. Annu. Rev. Fluid Mech., 3 (1971), No. 1, 13–37. [CrossRef] [Google Scholar]
  20. M. Y. Jaffrin, A. H. Shapiro, S. L. Weinberg. Peristaltic pumping with long wavelengths at low reynolds number. J. Fluid Mech., 37 (1969), No. 4, 799–825. [CrossRef] [Google Scholar]
  21. J. Jimenez-Lozano, M. Sen, P. Dunn. Particle motion in unsteady two-dimensional peristaltic flow with application to the ureter. Phys. Rev. E, 79 (2009), No. 4, 041901. [CrossRef] [Google Scholar]
  22. J. Kim, P. Moin. Application of a fractional-step method to incompressible Navier-Stokes equations. J. Comp. Physics, 59 (1985), No. 2, 308–323. [CrossRef] [MathSciNet] [Google Scholar]
  23. G. Kunz, D. Beil, H. Deiniger, A. Einspanier, G. Mall, G. Leyendecker. The uterine peristaltic pump. normal and impeded sperm transport within the female genital tract. Adv. Exp. Med. Biol., 424 (1997), No. 1, 267–277. [CrossRef] [PubMed] [Google Scholar]
  24. R.G. Larson. The Structure and Rheology of Complex Fluids. Oxford University Press, 1998. [Google Scholar]
  25. M. Li, J. Brasseur. Non-steady peristaltic transport in finite-length tubes. J. Fluid Mech., 248 (1993), No. 1, 129–151. [CrossRef] [Google Scholar]
  26. C.Y. Lu, P.D. Olmsted, R.C. Ball. Effects of nonlocal stress on the determination of shear banding flow. Phys. Rev. Lett., 84 (2000), No. 4, 642–645. [CrossRef] [PubMed] [Google Scholar]
  27. C.S. Peskin. The immersed boundary method. Acta Numerica, 11 (2002), 479–517. [CrossRef] [MathSciNet] [Google Scholar]
  28. C. Pozrikidis. A study of peristaltic flow. J. Fluid Mech. 180 (1987), 180:515. [Google Scholar]
  29. J.M. Rallison. Dissipative stresses in dilute polymer solutions. Journal of Non-Newtonian Fluid Mechanics, 68 (1997), No. 1, 61–83. [CrossRef] [Google Scholar]
  30. S. Takabatake, K. Ayukawa, A. Mori. Peristaltic pumping in circular cylindrical tubes: a numerical study of fluid transport and its efficiency. J. Fluid Mech., 194 (1988), 193:267. [Google Scholar]
  31. J. Teran, L. Fauci, M. Shelley. Peristaltic pumping and irreversibility of a Stokesian viscoelastic fluid. Phys. of Fluids, 20 (2008), No. 7, 073101. [CrossRef] [Google Scholar]
  32. J. Teran, L. Fauci, M. Shelley. Viscoelastic fluid response can increase the speed and efficiency of a free swimmer. Phys. Rev. Letters, 104 (2010), No. 3, 038101. [CrossRef] [Google Scholar]
  33. B. Thomases, M. Shelley. Transition to mixing and oscillations in a Stokesian viscoelastic flow. Phys. Rev. Lett., 103 (2009), No. 9, 094501. [CrossRef] [PubMed] [Google Scholar]

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