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Peristaltic pumping in circular cylindrical tubes: a numerical study of fluid transport and its efficiency

Published online by Cambridge University Press:  21 April 2006

S. Takabatake ,
K. Ayukawa  and
A. Mori
S. Takabatake
Affiliation:
Department of Mechanical Engineering, Ehime University, Bunkyo-cho. Matsuyama, Ehime 790, Japan
K. Ayukawa
Affiliation:
Department of Mechanical Engineering, Ehime University, Bunkyo-cho. Matsuyama, Ehime 790, Japan
A. Mori
Affiliation:
Mitsubishi Heavy Industry Co. Ltd., Mihara Works, Itozaki-cho, Mihara, Hiroshima 723, Japan
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Abstract

A numerical method employing an upwind finite-difference technique is adopted for an investigation of peristaltic pumping in circular cylindrical tubes. such as some organs in the living body. Various peristaltic flows are calculated under conditions of finite wave amplitudes, finite wavelengths and finite Reynolds numbers, and the influence of the magnitude of these quantities on the flow is investigated. The fluid mechanics of peristaltic mixing and transport are studied in detail by analysing the reflux and the trapping phenomena. The mechanical efficiency of peristaltic pumping is also discussed, with reference to engineering and physiological applications. It is shown that quantitative differences are observed between the results obtained for flows in a circular cylindrical tube and a two-dimensional plane channel. However, for both cases the appearance of peristaltic reflux depends upon the Reynolds number and the wavenumber (mean tube radius/wavelength). Much greater peristaltic mixing and transport are realized in a circular tube than in a plane channel.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 193 , August 1988 , pp. 267 - 283
Copyright
© 1988 Cambridge University Press

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References

Ayukawa, K., Kawai, T. & Kimura, M. 1981 Streamlines and path lines in peristaltic flows at high Reynolds numbers. Bull. Japan Soc. Mech. Engrs 24, 948–955.Google Scholar
Ayukawa, K. & Takabatake, S. 1982 Numerical analysis of two-dimensional peristaltic flows (1st report; flow pattern). Bull. Japan Soc. Mech. Engrs 25, 1061–1069.Google Scholar
Böhme, G. & Friedrich, R. 1983 Peristaltic flow of viscoelastic liquids. J. Fluid Mech. 128, 109–122.Google Scholar
Brasseur, J. G., Corrsin, S. & Lu, N. Q. 1987 The influence of a peripheral layer of different viscosity on peristaltic pumping with Newtonian fluids. J. Fluid Mech. 174, 495–519.Google Scholar
Brown, T. D. & Hung, T. K. 1977 Computational and experimental investigations of two-dimensional nonlinear peristaltic flows. J. Fluid Mech. 83, 249–272.Google Scholar
Fung, Y. C. & Yih, C. S. 1968 Peristaltic transport. Trans. ASME E: J. Appl. Mech. 35, 669–675.Google Scholar
Greenspan, D. 1968 Lectures on the Numerical Solution of Linear, Singular, and Nonlinear Differential Equations, pp. 122–147. Practice-Hall.
Gupta, B. B. & Seshadri, V. 1976 Peristaltic pumping in non-uniform tubes. J. Biomech. 9, 105–109.Google Scholar
Hanin, M. 1968 The flow through a channel due to transversely oscillating walls. Israel J. Tech. 6, 67–71.Google Scholar
Jaffrin, M. Y. 1973 Inertia and streamline curvature effects on peristaltic pumping. Intl J. Engng Sci. 11, 681–699.Google Scholar
Jaffrin, M. Y. & Shapiro, A. H. 1971 Peristaltic pumping. Ann. Rev. Fluid Mech. 3, 13–36.Google Scholar
Li, C. H. 1970 Peristaltic transport in circular cylindrical tubes. J. Biomech. 3, 513–523.Google Scholar
Liron, N. 1976 On peristaltic flow and its efficiency. Bull. Math. Biol. 38, 573–596.Google Scholar
Longuet-Higgins, M. S. 1983 Peristaltic pumping in water waves. J. Fluid Mech. 137, 393–407.Google Scholar
Manton, M. J. 1975 Long-wavelength peristaltic pumping at low Reynolds number. J. Fluid Mech. 68, 467–476.Google Scholar
Pozrikidis, C. 1987 A study of peristaltic flow. J. Fluid Mech. 180, 515–527.Google Scholar
Rath, H. J. 1987 Ein Beitrag zur Berechnung einer peristaltischen Strömung in elastischen Leitungen. Acta Mech. 31, 1–12.Google Scholar
Shapiro, A. H., Jaffrin, M. Y. & Weinberg, S. L. 1969 Peristaltic pumping with long wavelengths at low Reynolds number. J. Fluid Mech. 37, 799–825.Google Scholar
Srivastava, L. M. & Srivastava, V. P. 1984 Peristaltic transport of blood: Casson model II. J. Biomech. 17, 821–829.Google Scholar
Stokes, G. G. 1847 On the theory of oscillatory waves. Trans. Camb. Phil. Soc. 8, 441–455.Google Scholar
Takabatake, S. & Ayukawa, K. 1982 Numerical study of two-dimensional peristaltic flows. J. Fluid Mech. 122, 439–465.Google Scholar
Takabatake, S., Ayukawa, K. & Okura, M. 1985 Numerical analysis of two-dimensional peristaltic flows (3rd report; pumping characteristics of peristaltic transport). Trans. Japan Soc. Mech. Engrs 51, 2365–2372 (in Japanese).Google Scholar
Tong, P. & Vawter, D. 1972 An analysis of peristaltic pumping. Trans. ASME E: J. Appl. Mech. 39, 857–862.Google Scholar
Yin, F. & Fung, Y. C. 1969 Peristaltic waves in circular cylindrical tubes. Trans. ASME E: J. Appl. Mech. 36, 579–587.Google Scholar
Zien, T. F. & Ostrach, S. 1970 A long wave approximation to peristaltic motion. J. Biomech. 3, 63–75.Google Scholar