Skip to main content
SpringerLink
Log in

Interaction of peristaltic motion with Poiseuille flow

  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

The effect of Poiseuille flow on peristaltic transport has been investigated in a two-dimensional mathematical model of peristalsis for the case when the wall of the channel executes a sinusoidal motion of small amplitude. Closed-form solutions have been obtained for limiting values of Reynolds number and the Poiseuille flow parameter, while the method of Frobenius series solution has been used for the general case. It is found that the mean flow reversal is strongly dependent on the Poiseuille flow. The position of flow reversal may change drastically from the center of the channel to the boundaries. Numberical results are reported for various values of the physical parameters of interest.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literature

  • Barton, C. and S. Raynor. 1968. “Peristaltic Flow in Tubes.”Bull. Math. Biophysics,30, 663–680.

    MATH  Google Scholar 

  • Boyarsky, S. and P. Labay. 1972.Ureteral Dynamics. Baltimore: Williams & Wilkins.

    Google Scholar 

  • Burns, J. C. and T. Parkes. 1967. “Peristaltic Motion.”J. Fluid Mech.,29, 731–743.

    Article  Google Scholar 

  • Chow, T. S. 1970. “Peristaltic Transport in a Circular Cylindrical Pipe.”J. Appl. Mech.,37, 901–905.

    MATH  Google Scholar 

  • Fung, Y. C. and C. S. Yih. 1968. “Peristaltic Transport.”35, 669–675.

    MATH  Google Scholar 

  • Ince, E. L. 1956.Ordinary Differential Equations. p. 396. New York: Dover Publications.

    Google Scholar 

  • Li, Chin-Hsiu. 1970. “Peristaltic Transport in Circular Cylindrical Tubes.”J. Biomech.,3, 513–523.

    Article  Google Scholar 

  • Mittra, T. K. 1971. “Effect of Wall Properties and Poiseuille Flow on Peristalsis”,Ph. D. dissertation, University of Mississippi.

  • Prasad, S. N. and C. Herrmann. 1970. “Stability of a Cantilevered Bar Subjected to a Transverse Follower Force of Fluid Jet.”Ingenieur-Archiv. 39, 341–356.

    Article  MATH  Google Scholar 

  • Shapiro, A. S., M. Jaffrin and S. L. Weinberg. 1968. “Peristaltic Pumping with Long Wavelength at Low Reynolds Numbers.”J. Fluid Mech.,37, 799–825.

    Article  Google Scholar 

  • Tong, P. and D. Vawter. 1972. “An Analysis of Peristaltic Pumping.”J. Appl. Mech.,39, 857–862.

    Google Scholar 

  • Yin, F. and Y. C. Fung. 1969. “Peristaltic Waves in Circular Cylindrical Tubes.”,36, 579–587.

    Google Scholar 

  • Zien, T. F. and S. A. Ostrach. 1970. “Long Wave Approximation to Peristaltic Motion.”J. Biomech.,3, 63–75.

    Article  Google Scholar 

Download references

Author information

Author notes

  1. T. K. Mittra

    Present address: Westinghouse Astronuclear Laboratory, 15236, Pittsburgh, Pennsylvania

Authors and Affiliations

  1. Biomathematics Program, North Carolina State University, 27607, Raleigh, North Carolina

    T. K. Mittra

  2. Department of Civil Engineering, University of Mississippi, 38677, University, Mississippi

    S. N. Prasad

Authors
  1. T. K. Mittra
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. N. Prasad
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mittra, T.K., Prasad, S.N. Interaction of peristaltic motion with Poiseuille flow. Bltn Mathcal Biology 36, 127–141 (1974). https://doi.org/10.1007/BF02458598

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02458598

Keywords

Search

Navigation