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Computational and experimental investigations of two-dimensional nonlinear peristaltic flows

Published online by Cambridge University Press:  12 April 2006

Thomas D. Brown  and
Tin-Kan Hung
Thomas D. Brown
Affiliation:
Department of Orthopaedic Surgery, University of Pittsburgh, Pennsylvania 15261
Tin-Kan Hung
Affiliation:
Departments of Civil Engineering and Neurosurgery, University of Pittsburgh, Pennsylvania 15261
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Abstract

An implicit finite-difference technique employing orthogonal curvilinear co-ordinates is used to solve the Navier–Stokes equations for peristaltic flows in which both the wall-wave curvature and the Reynolds number are finite (§2). The numerical solutions agree closely with experimental flow visualizations. The kinematic characteristics of both extensible and inextensible walls (§3) are found to have a distinct influence on the flow processes only near the wall. Without vorticity, peristaltic flow observed from a reference frame moving with the wave will be equivalent to steady potential flow through a stationary wavy channel of similar geometry (§4). Solutions for steady viscous flow (§5) are obtained from simulation of unsteady flow processes beginning from an initial condition of potential peristaltic flow. For nonlinear flows due to a single peristaltic wave of dilatation, the highest stresses and energy exchange rates (§6) occur along the wall and in two instantaneous stagnation regions in the bolus core. A series of computations for periodic wave trains reveals that increasing the Reynolds number from 2[sdot ]3 to 251 yields a modest augmentation in the ratio of flow rate to Reynolds number but induces a much greater increase in the shear stress (§7.1). The transport effectiveness is markedly reduced for pumping against a mild adverse pressure drop (§7.2). Increasing the wave amplitude will lead to the development of travelling vortices within the core region of the peristaltic flow (§7.3).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 83 , Issue 2 , 22 November 1977 , pp. 249 - 272
Copyright
© 1977 Cambridge University Press

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References

Brown, C. H., Lemuth, R. F., Hellums, J. D., Leverett, L. G. & Alfrey, C. P. 1975 Response of human platelets to shear stress. Trans. Am. Soc. Artif. Int. Organs 21, 35–38.Google Scholar
Brown, T. D. 1976 Computational and experimental studies of two-dimensional nonlinear peristaltic pumping. Ph.D. thesis, Carnegie-Mellon University.
Eckstein, E. 1970 Experimental and theoretical pressure studies of peristaltic pumping. S.M. thesis, Massachusetts Institute of Technology.
Fung, Y. C. & Yih, C. S. 1968 Peristaltic transport. 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
Harlow, F. H. & Welch, J. E. 1965 Numerical calculation of viscous incompressible flow of fluid with free surface. Phys. Fluids. 8, 2182–2189.Google Scholar
Hung, T. C., Hochmuch, R. M., Joist, J. H. & Sutera, S. P. 1976 Shear-induced aggregation and lysis of platelets. Trans. Am. Soc. Artif. Int. Organs 22, 285–291.Google Scholar
Hung, T.-K. 1970 Vortices in pulsatile flows. Proc. 5th Int. Cong. Rheol. vol. 2, pp. 115–127.
Hung, T.-K. & Brown, T. D. 1976 Solid-particle motion in two-dimensional persistaltic flows. J. Fluid Mech. 73, 77–97.Google Scholar
Hung, T.-K. & Brown, T. D. 1977 An implicit finite-difference method for solving the Navier-Stokes equation using orthogonal curvilinear coordinates. J. Comp. Phys. 23, 343–363.Google Scholar
Jaffrin, M. Y. 1973 Inertia and streamline curvature effects on peristaltic pumping. Int. 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. M.I.T. Fluid Mech. Lab. Publ. no. 71–1.Google Scholar
Jaffrin, M. Y. & Shapiro, A. H. 1971 Peristaltic pumping. Ann. Rev. Fluid Mech. 3, 13–35.Google Scholar
Macagno, E. O. & Hung, T.-K. 1967a Pressure, Bernouilli sum and momentum and energy relations in a laminar zone of separation. Phys. Fluids 10, 78–92.Google Scholar
Macagno, E. O. & Hung, T.-K. 1967b Computational and experimental study of a captive annular eddy. J. Fluid Mech. 28, 43–64.Google Scholar
Mittra, T. K. & Prasad, S. N. 1973 On the influence of wall properties and Poiseuille flow in peristalsis. J. Biomech. 6, 681–693.Google Scholar
Negrin, M. P., Shack, W. J. & Lardner, T. J. 1974 A note on peristaltic pumping. J. Appl. Mech. 96, 520–521Google 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
Taylor, G. I. 1951 Analysis of the swimming of microscopic organisms. Proc. Roy. Soc. A 209, 447–461.Google Scholar
Thom, A. & Apelt, C. J. 1961 Field Computations in Engineering and Physics. Van Nostrand.
Tong, P. & Vawter, D. 1972 An analysis of peristaltic pumping. J. Appl. Mech. 39, 857–862.Google Scholar
Welch, J. E., Harlow, F. H., Shannon, J. P. & Daly, B. J. 1966 The MAC method: a computing technique for solving viscous, incompressible, transient fluid-flow problems involving free surfaces. Los Alamos Sci. Lab. Rep. LA-3425.Google Scholar
Yin, F. C. P. & Fung, Y. C. 1971 Comparison of theory and experiment in peristaltic transport. J. Fluid Mech. 47, 93–113.Google Scholar