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The influence of a peripheral layer of different viscosity on peristaltic pumping with Newtonian fluids

Published online by Cambridge University Press:  21 April 2006

James G. Brasseur ,
Stanley Corrsin  and
Nan Q. Lu
James G. Brasseur
Affiliation:
Department of Chemical Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA Current address: Department of Mechanical Engineering, Clemson University, Clemson, SC 29634-0921, USA.
Stanley Corrsin
Affiliation:
Department of Chemical Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA
Nan Q. Lu
Affiliation:
Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA
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Abstract

The analysis by Shapiro et al. (1969) of a two-dimensional peristaltic pump at small Reynolds number and with long wavelengths is extended to include a Newtonian peripheral layer adjacent to the wall to simulate the effect of a coating in physiological flows. An earlier analysis by Shukla et al. (1980) violates mass conservation because of an incorrect deduction of the interface shape. We present a detailed analysis of the effect of the peripheral layer on the fluid motions, the pumping characteristics, and the phenomena of reflux and trapping. For prescribed wall motion, a peripheral layer more viscous than the inner fluid improves pumping performance, while a less-viscous outer layer degrades performance. Even a very thin peripheral layer may substantially reduce pumping if the viscosity in this layer is very low relative to the inner region. The effects of the peripheral layer on reflux and trapping depend on the conditions which are held fixed while making the comparison. However, the general trend with decreasing peripheral-layer viscosity is towards an overall decrease in trapping, a decrease in reflux with fixed total volume flow rate, but an increase in reflux with fixed pressure head.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 174 , January 1987 , pp. 495 - 519
Copyright
© 1987 Cambridge University Press

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References

Birkhoff, G. & MacLane, S. 1963 A Survey of Modern Algebra. MacMillan.
Buthaud, H. 1971 The influences of unsymmetry, wall slope, and wall motion on peristaltic pumping at small Reynolds number. M.S. thesis, Department of Mechanics, The Johns Hopkins University
Jaffrin, M. Y. 1973 Inertia and streamline curvature 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
Lykoudis, P. S. & Roos, R. 1970 The fluid mechanics of the ureter from a lubrication point of view. J. Fluid Mech. 43, 661–674.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
Shukla, J. B. & Gupta, S. P. 1982 Peristaltic transport of a power-law fluid with variable consistency. Trans. ASME K: J. Biomech. Engng 104, 182–186Google 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
Taylor, G. I. 1951 Analysis of the swimming of microscopic organisms. Proc. R. Soc. Lond. A 209, 447–461.Google Scholar