Peristaltic pumping of solid particles immersed in a viscoelastic fluid

Mathematical Modelling of Natural Phenomena

Volumn 6, Issue 5, 2011, Pages 67-83

  Chrispell, J ^a,b   Fauci, L ^a,b  

^a Tulane University   (United States)

^b TULANE UNIVERSITY   (United States)

Author keywords

Oldroyd B; Peristaltic pumping; Viscoelastic fluid

Indexed keywords

BIOLOGICAL PROCESS; BIOLOGICAL SETTINGS; GOVERNING EQUATIONS; IMMERSED BOUNDARY; KIDNEY STONE; NAVIER STOKES; NONLINEAR CONSTITUTIVE EQUATIONS; OLDROYD-B; PERISTALTIC PUMPING; PERISTALTIC TRANSPORT; POLYMER STRESS; SOLID PARTICLES; STRESS TENSORS; TEMPORAL EVOLUTION; VISCO-ELASTIC FLUID; WEISSENBERG NUMBER;

BIOLOGY; FLUIDS; NONLINEAR EQUATIONS; PUMPS; STEADY FLOW; VISCOELASTICITY;

TRANSPORT PROPERTIES;

EID: 80051779979     PISSN: 09735348     EISSN: 17606101     Source Type: Journal    
DOI: 10.1051/mmnp/20116504     Document Type: Article

References (33)

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.
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.
3. R.B. Bird, R.C. Armstrong, O. Hassager. Dynamicsof Polymeric Liquids. Wiley-Interscience, 1987.
4. J.R. Blake, P.G. Vann, H Winet A model of ovum transport. J. Theor. Biol., 102 (1983), No. 1, 145-166.
5. S. Boyarski, C. Gottschalk, E. Tanagho, P.Zimskind. Urodynamics: Hydrodynamics of the Ureter and the Renal Pelvis. Academic Press,New York, 1971.
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 inApplied Mechanics and Engineering, 32 (1982), No. (1-3), 199-259. (Pubitemid 13490980)
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.
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.
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. (Pubitemid 20625140)
10. O. Eytan, D. Elad Analysis of intra-uterine fluid motion induced by uterine contractions. Bull. Math. Biol., 61 (1999), No. 2, 221-238. (Pubitemid 29187982)
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. (Pubitemid 129647578)
12. L. Fauci Peristaltic pumping of solid particles. Comp. & Fluids, 21 (1992), No. 4, 583-598. (Pubitemid 23558189)
13. L. Fauci, R. Dillon Biofluidmechanics of reproduction. Annu. Rev. Fluid. Mech., 38 (2006), No. 1, 371-394. (Pubitemid 43240181)
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. (Pubitemid 40714214)
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.
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.
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.
18. T.K. Hung, T.D. Brown Solid-particle motion in two-dimensional peristaltic flows. J. Fluid Mech, 73 (1976), No. 1,77-96.
19. M. Y. Jaffrin and A. H. Shapiro Peristaltic pumping. Annu. Rev. Fluid Mech., 3 (1971), No. 1, 13-37.
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.
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.
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.
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. (Pubitemid 27479703)
24. R.G. Larson. The Structure and Rheology of ComplexFluids. Oxford University Press, 1998.
25. Li, J. Brasseur Non-steady peristaltic transport in finite-length tubes. J. Fluid Mech., 248 (1993), No. 1, 129-151.
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.
27. C.S. Peskin The immersed boundary method. Acta Numerica, 11 (2002), 479-517.
28. C. Pozrikidis A study of peristaltic flow. J. Fluid Mech. 180 (1987), 180:515.
29. J.M. Rallison Dissipative stresses in dilute polymer solutions. Journal of Non-Newtonian Fluid Mechanics, 68 (1997), No. 1, 61-83.
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.
31. J. Teran, L. Fauci, M. Shelley Peristaltic pumping and irreversibility of a Stokesian viscoelastic fluid. Phys. of Fluids, 20 (2008), No. 7, 073101.
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.
33. B. Thomases, M. Shelley Transition to mixing and oscillations in a Stokesian viscoelastic flow. Phys. Rev. Lett., 103 (2009), No. 9, 094501.