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Non-steady peristaltic transport in finite-length tubes

Published online by Cambridge University Press:  26 April 2006

Meijing Li  and
James G. Brasseur
Meijing Li
Affiliation:
Department of Mechanical Engineering, Pennsylvania State University, University Park PA 16802, USA
James G. Brasseur
Affiliation:
Department of Mechanical Engineering, Pennsylvania State University, University Park PA 16802, USA
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Abstract

The classical lubrication-theory model of steady peristaltic transport of periodic sinusoidal waves in infinite-length tubes (Shapiro et al. 1969) is generalized to arbitrary wave shape and wavenumber in tubes of finite length. Whereas the classical model is steady in a frame of reference moving with the peristaltic waves, peristaltic transport in a finite-length tube is inherently non-steady. It may be shown, however, that pumping performance is independent of tube length if there exists an integral number of peristaltic waves in the tube. Three particularly interesting characteristics of non-steady peristalsis are described: (i) fluctuations in pressure and shear stress arise due to a non-integral number of waves in the finite-length tube; (ii) retrograde motion of fluid particles during peristaltic transport (reflux) has inherently different behaviour with single peristaltic waves as compared to multiple ‘train waves’, and (iii) finite tube length, the number of peristaltic waves and the degree of tube occlusion affect global pumping performance. We find that, whereas significant increases in pressure and shear stress result from the tube-to-wave length ratio being non-integral, global pumping performance is only slightly degraded by the existence of a non-integral number of waves in the tube during peristaltic transport. Furthermore, the extent of retrograde motion of fluid particles is much greater with single waves than with train waves. These results suggest that in the design and analysis of peristaltic pumps attention should be paid to the unsteady effects of finite tube length and to the differences between single and multiple peristaltic waves.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 248 , March 1993 , pp. 129 - 151
Copyright
© 1993 Cambridge University Press

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References

Barton, C. & Raynor, S. 1968 Peristaltic flow in tubes. Bull. Math. Biophys. 30, 663– 680.Google Scholar
Bohme, G. B. & 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 fluid. J. Fluid Mech. 174, 495– 519.Google Scholar
Brasseur, J. G. & Dodds, W. J. 1991 Interpretation of intraluminal manometric measurements in terms of swallowing mechanics. Dysphagia 6, 100– 119.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
Burns, J. C. & Parkes, T. 1967 Peristaltic motion. J. Fluid Mech. 29, 731– 743.Google Scholar
Dusey, M. P., Brasseur, J. G. & Li, M.-J. 1990 Analysis of a singularity inherent to the lubrication theory model of peristaltic pumping using a full Navier-Stokes simulation (abstract). Bull. Am. Phys. Soc. 35, 2245.Google Scholar
Fung, Y. C. & Yih, C. S. 1968 Peristaltic transport. Trans. ASME E: J. Appl. Mech. 35, 669– 675.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 on peristaltic pumping. Intl. J. Engng. Sci. 11, 681– 699.Google Scholar
Jaffrin, M. Y. & Meginniss, J. R. 1971 The hydrodynamics of roller pumps and their implication to hemolysis. Fluid Mechanics Laboratory, Publication No. 71-1. Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA.
Jaffrin, M. Y. & Shapiro, A. H. 1971 Peristaltic pumping. Ann. Rev. Fluid Mech. 3, 13– 36.Google Scholar
Latham, T. W. 1966 Fluid motions in a peristaltic pump. M.S. thesis, Massachusetts Institute of Technology, Cambridge, MA.
Liu, N. S. & Krause, E. 1979 Calculation of incompressible viscous flows in vessels with moving boundaries. Acta Mechanica 33, 21– 32.Google Scholar
Lykoudis, P. S. & Roos, R. 1970 The fluid mechanics of the ureter from a lubrication theory point of view. J. Fluid Mech. 43, 661– 674.Google Scholar
Rath, H. J. 1982 Peristaltic flow through a lobe-shaped tube. Intl. J. Mech. Sci. 24, 359– 367.Google Scholar
Roos, R. & Lykoudis, P. S. 1971 The fluid mechanics of the ureter with an inserted catheter. J. Fluid Mech. 46, 625– 630.Google Scholar
Shapiro, A. H. 1967 Pumping and retrograde diffusion in peristaltic waves. Proc. Workshop on Ureteral Reflux in Children. Natl. Acad. Sci. Washington, D.C.
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
Shukla, J. B. & Gupta, S. P. 1982 Peristaltic transport of a power-law fluid with variable consistency. Trans. ASME K: J. Biomech Engng 104, 182– 186.Google Scholar
Shukla, J. B., Parihar, R. S., Rao, B. R. P. & Gupta, S. P. 1980 Effects of peripheral-layer viscosity on peristaltic transport of a bio-fluid. J. Fluid mech. 97, 225– 237.Google Scholar
Stavitsky, D., Macagno, E. O. & Christensen, J. 1981 Finite-element analysis of flow induced by contractions like those of intestine. J. Biomech. 14, 183– 193.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. & Mori, A. 1988 Peristaltic pumping in circular cylindrical tubes: a numerical study of fluid transport and its efficiency. J. Fluid Mech. 193, 267– 283.Google Scholar
Taylor, G. I. 1951 analysis of the swimming of microscopic organisms. Proc. R. Soc. Lond. A 209, 447– 461.Google Scholar
Tong, P. & Vawter, D. 1972 An analysis of peristaltic pumping. Trans. ASME E: J. Appl. Mech. 39, 857– 862.Google Scholar
Weinberg, S. L., Eckstein, E. C. & Shapiro, A. H. 1971 An experimental study of peristaltic pumping. J. Fluid Mech. 49, 461– 497.Google Scholar
Yih, F. & Fung, Y. C. 1969 Peristaltic waves in circular cylindrical tubes. Trans. ASME E: J. Appl. Mech. 36, 579– 587.Google Scholar