Abstract
An axisymmetric flow of a power law fluid through circular tubes under constant pressure gradient with the flow parameters varying radially is analyzed theoretically. The main finding is that for the Fahraeus-Lindqvist (F-L) effect to occur, it is necessary to have at least one of the parametersK (consistency) andn (index) as a discontinuous function ofr in the absence of wall slip; and with slip condition the parameters could be continuous functions ofr under specific conditions. In both the cases the existence of more than one discontinuity cannot be ruled out. The results obtained are consistent with experimental findings of blood flow through narrow tubes.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature
Bugliarello, G. and J. W. Hayden. 1962. “High Speed Microcinematographic Studies of Blood Flowin Vitro”Nature 138, 981.
—— and J. Sevilla. 1970. “Velocity Distribution and other Characteristics of Steady and Pulsatile Blood Flow in Fine Glass Tubes.”Bioheology 7, 85.
——, C. Kapur and G. C. Hsiao. 1965. “The Profile Viscosity and other Characteristics of Blood Flow in a Nonuniform Shear Field.” InProc. 4th Int. Congress on Rheology. Part 4, A. L. Copley (Ed.), p. 351. New York: Interscience.
Chathurani, P. and V. S. Upadhya. 1979. “A Two Fluid Model for Blood Flow Through Small Diameter Tubes.”Biorheology 16, 109.
Dintenfass, L. 1967. “Inversion of the Fahraeus-Lindqvist Phenomenon in Blood Flow Through Capillaries of Diminishing Radius.”Nature 215, 1099.
Fahraeus, R. and Lindqvist, T. 1931. “The Viscosity of the Blood in Narrow Capillary Tubes.”Am. J. Physiol. 96, 562.
Fung, Y. C. 1981. InBiomechanics, pp. 80, 66, 149. Berlin: Springer Verlag.
Gaehtgens, P. 1980. “Flow of Blood Through Narrow Capillaries: Rheological Mechanisms Determining Capillary Hematocrit and Apparent Viscosity.”Biorheology 17, 183.
Gupta, B. B., K. M. Nigam and M. Y. Jaffarin. 1981 “A Three Layer Semi-empirical Model for Flow of Blood and other Particulate Suspensions through Narrow Tubes.”Trans. Am. Soc. mech. Engrs, J. biomech. Engng 104, 129.
Haynes, R. H. 1960. “Physical Basis of the Dependence of Blood Viscosity on Tube Radius.”Am. J. Physiol. 198, 1193.
Lamb, H. 1932.Hydrodynamics, 6th edn, p. 586. Cambridge: Cambridge University Press.
Lighthill, J. M. 1972. “Physiological Flyid Dynamics a Survey.”J. Fluid Mech. 52, 475.
Majhi, S. N. and L. Usha. 1983. “n-layered Poiseuille Flow and Sigma Effect.” InProc. International Symposium on Physiological Fluid Dynamics (in press).
Poiseuille, J. L. H. 1840, 1841. RecherebesC.r. Acad. Sci. Paris 11, 961, 1041;12, 112.
Segre, G. and A. Silberberg. 1962. “Behaviour of Macroscopic Rigid Spheres in Poiseuille Flow, Part 2.”J. Fluid Mech. 14, 475.
Shukla, J. B., R. S. Parihar and B. R. P. Rao. 1980a. “Effects of Stenosis on Non-Newtonian Flow of Blood in an Artery.”Bull. math. Biol.,42, 283.
——, S. P. Gupta and R. S. Parihar. 1980b. “Biorheological Aspects of Blood Flow through Artery with Mild Stenosis: Effects of Peripheral Layer.”Biorheology 17, 403.
Ware, J. H., F. Y. Sorrell and R. M. Felder. 1974. “A Model of Steady Blood Flow.”Biorheology 11, 97.
Whitmore, R. L. 1968.Rheology of the Circulation, p. 67. Oxford: Pergamon Press.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Majhi, S.N., Usha, L. A mathematical note on the fahraeuslindqvist effect in power law fluid. Bltn Mathcal Biology 47, 765–769 (1985). https://doi.org/10.1007/BF02469303
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02469303