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Peristaltic Transport in a Finite Circular Pipe

  • H. Ramkissoon
  • L. K. Antanovskii
Conference paper
  • 173 Downloads
Part of the Fluid Mechanics and its Applications book series (FMIA, volume 43)

Abstract

A viscous flow in a long pipe of a circular cross-section, driven by a time-dependent pressure drop at the ends of the pipe and the deformation of the pipe walls, is investigated. This kind of a flow is relevant to the peristaltic transport of blood, with the effect of the oscillating pressure gradient due to the heart pumping included. An explicit solution is obtained within the framework of lubrication theory approximation, and some numerical simulations to illustrate the model are carried out. In order to account for inertia effects, an approximation based on an a priori parabolic flow pattern across the pipe, is also derived.

Keywords

Pipe Wall Lubrication Theory Parabolic Profile Peristaltic Transport Peristaltic Flow 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Rath, H.J. (1980). Peristaltische Stromungen, Springer-Verlag, Berlin.CrossRefGoogle Scholar
  2. [2]
    Provost, A.M. and Schwartz, W.H. (1994). A theoretical study of viscous effects in peristaltic pumping, J. Fluid Mech., 279: 177–195.MathSciNetADSzbMATHCrossRefGoogle Scholar
  3. [3]
    Pozrikidis, C. (1987). A study of peristaltic flow, J. Fluid Mech., 180: 515–527.ADSCrossRefGoogle Scholar
  4. [4]
    Takabatake, S., Ayukawa, K. and Mori, A. (1988). Peristaltic pumping in circular cylindrical tubes: a numerical study of fluid transport and its efficiency. J. Fluid Mech., 193: 267–283.ADSCrossRefGoogle Scholar
  5. [5]
    Brasseur, J. G. Corrsin, S. and Lu, N.Q (1987). The influence of peripheral layer of different viscosity on peristaltic pumping with Newtonian fluids. J. Fluid Mech., 174: 495–519.ADSCrossRefGoogle Scholar
  6. [6]
    Bohme, G. and Friedrich, R. (1983). Peristaltic flow of vicoelastic liquids. J. Fluid Mech., 128: 109–122.ADSCrossRefGoogle Scholar
  7. [7]
    Shapiro, A.H., Jaffrin, M.Y. and Weinberg, S.L. (1969). Peristaltic pumping with long wavelengths at low Reynolds number. J. Fluid Mech., 37: 799–825.ADSCrossRefGoogle Scholar
  8. [8]
    Brown, T.D. and Hung, T.K. (1977). Computational and experimental investigations of two-dimensional nonlinear peristaltic flows. J. Fluid Mech., 83:249-272.Google Scholar
  9. [9]
    Chow, T.S. (1970). Peristaltic transport in a circular cylindrical pipe. Trans. ASMEJ: J.Appl Mech., 37: 901–905.zbMATHCrossRefGoogle Scholar
  10. [10]
    Fung, Y.C. and Yih, C.S. (1968). Peristaltic transport. Trans. ASMEJ: J. Appl. Mech., 35: 669–675.ADSzbMATHCrossRefGoogle Scholar
  11. [11]
    Shukla, J.B. and Gupta, S.P. (1982). Peristaltic transport of a power-law fluid with variable consistency. Trans. ASME K: J. Biomech. Engng., 104: 182–186.CrossRefGoogle Scholar
  12. [12]
    Jaffrin, M.Y. and Shapiro, A.H. (1971). Peristaltic pumping. Ann. Rev. Fluid Mech., 3: 13–36.ADSCrossRefGoogle Scholar
  13. [13]
    Awon, M. P. Review of the literature with formulation of a theory for regulation of blood supply. (Private communication).Google Scholar
  14. [14]
    Kapitsa, P. L. (1948). Wave flow of thin layers of viscous liquid. Zh. Eksper. Teoret. Fiz., 18(1): 3–28.Google Scholar
  15. [15]
    Levich, V.G. (1967). Physico-Chemical Hydrodynamics. Prentice-Hall, Englewood Cliffs, NJGoogle Scholar
  16. [16]
    Demekhin, E.A. and Shkadov, V. Ya. (1984). On three-dimensional unsteady waves in a moving liquid film. Izv. AN Nauk SSSR Ser. Mekh. Zhidk. Gaza, 5:21–27.Google Scholar
  17. [17]
    Antanovskii, L.K. (1987). Generalized equations for a flow in a film on a plane wall. Dinamika Sploshnoi Sredy, 81: 37–42. [In Russian].Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1998

Authors and Affiliations

  • H. Ramkissoon
    • 1
  • L. K. Antanovskii
    • 2
  1. 1.Department of Mathematics & Computer ScienceThe University of the West IndiesTrinidad (W.I.)Trinidad
  2. 2.Modflow International Dty LtdVictoriaAustralia

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