Skip to main content

The effect of microstructure on the rheological properties of blood

Bulletin of Mathematical Biology volume 38, pages 135–159 (1976)Cite this article

Abstract

The micromorphic theory of Eringen is applied to study the tube flow of blood. The blood is considered to be a deformable suspension, with constitutive relations of the form of those of simple microfluids. By means of energy consideration, a relation is established between the local concentration parameter and the measure of rotationality involving both macro-and micromotions. The tube flow problem is then solved with some analyses on viscosity coefficients and boundary conditions. The results obtained indicate an integrated explanation of various important physical phenomena associated with blood flow, such as the tube size dependence of the apparent viscosity and the non-uniform concentration distribution over a tube cross section.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

43,34 €

Price includes VAT (Finland)
Tax calculation will be finalised during checkout.

Literature

  • Acre, E. L., A. N. Bulygin and E. V. Kuvshinskii. 1965 “Assymetrie Hydromechanies,”PMM,29, 297–308.

    Google Scholar 

  • Ariman, T. 1971. “On the Analysis of Blood Flow.”J. Biomech.,4, 185–192.

    Article  Google Scholar 

  • Barbee, J. H. and G. R. Coeklet. 1971. “Prediction of Blood Flow in Tubes with Diameters as Small as 29 Microns.”Microvascular Res.,3, 17–21.

    Article  Google Scholar 

  • Batchelor, G. K. 1967.An Introduction to Fluid Dynamics. Cambridge University Press.

  • —— 1970. “The Stress System in a Suspension of Force-Free Particles.“J. Fluid Mech.,”41, 545–570.

    MATH  MathSciNet  Article  Google Scholar 

  • Bretheron, F. P. 1962. “The Motion of Rigid Particles-Shear Flow at Low Reynolds Number.”J. Fluid Mech.,14, 284–304.

    MathSciNet  Article  Google Scholar 

  • Bugliarello, G. and J. Sevilla. 1970. “Velocity Distribution and Other Characteristics of Steady and Pulsatile Blood Flow in Fine Glass Tubes.”Biorheology,7, 85–107.

    Google Scholar 

  • Charm, S. E., G. S. Kurland and S. L. Brown. 1968. “The Influence of Radial Distribution and Marginal Plasma Layer or the Flow of Red Cell Suspensions.”Biorheology,5, 15–43.

    Google Scholar 

  • Cowin, S. C. 1972. “On the Polar Fluid as a Model for Blood Flow in Tubes.”Biorheology,9, 23–25.

    Google Scholar 

  • Dix, F. J. and F. W. Scott Blair. 1940.J. Appl. Physiol.,11, 574.

    MATH  Article  Google Scholar 

  • Eringen, A. C. 1964. “Simple Micro fluids.”Int. J. Engng. Sci.,2, 205–217.

    MATH  MathSciNet  Article  Google Scholar 

  • ——. 1966. “Theory of Mieropolar Fluids.”J. Math. Mech.,16, 1–18.

    MathSciNet  Google Scholar 

  • —. 1967. “Mechanics of Mieromorphie Continua.”Mechanics of Generalized Continua (Ed. E. Kröner), Springer-Verlag, pp. 18–35.

  • ——. 1970. “Balance Laws of Micromorphic Mechanics.”Int. J. Engng. Sci.,8, 819–828.

    MATH  Article  Google Scholar 

  • ——. 1972. “Micromorphic Description of Turbulent Channel Flow.”J. Math. Analysis Applic.,39, 253–266.

    Article  Google Scholar 

  • —— and E. S. Suhubi. 1964. “Nonlinear Theory of Simple Micro-Elastic Solids.”Int. J. Engng. Sci.,2, 189–203.

    MATH  MathSciNet  Article  Google Scholar 

  • Giesekus, H. 1962. “Stromungen mit Konstantem Gesehwindigkeitsgradienten und die Bewegung von darin suspendiertin Teilchen.”Rheol. Acta.,2, 101–122.

    Article  Google Scholar 

  • Goddard, J. D. and C. Miller. 1967. “Nonlinear Effects in the Rheology of Dilute Suspensions.”J. Fluid Mech.,28, 657–673.

    Article  Google Scholar 

  • Goldman, A. J., R. G. Cox and H. Brenner. 1967. “Slow Viscous Motion of a Sphere Parallel to a Plane Wall.”Chem. Engng. Sci.,22, 637–652.

    Article  Google Scholar 

  • Goldsmith, H. L. and S. G. Mason. 1967.Rheology,4, 85.

    Google Scholar 

  • Happel, J. and H. Brenner. 1965.Low Reynolds Number Hydrodynamics. Prentice-Hall.

  • Haynes, R. H. 1961.Soc. Rheol. Trans.,5, 85.

    Article  Google Scholar 

  • Houssay, B. A. 1955.Human Physiology, McGraw-Hill.

  • Kirwan, A. C. and M. S. Chang. 1970. “Cylindrical Flow of a Fluid Containing Deformable Structures.”Int. J. Engng. Sci.,8, 731–741.

    MATH  Article  Google Scholar 

  • Kuroda, D., Y. Mishiro, I. Wada and J. Tokushima. 1958.Expl. Med.,4, 73.

    Google Scholar 

  • Landau, L. D. 1959.Fluid Mechanics, p. 69.

  • Mason, S. G., H. Brenner and C. E. Chaffey. 1965.Rheol. Acta,4, 65.

    Google Scholar 

  • Scott-Blair, G. W. 1958. “The Importance of the Sigma Phenomenon in the Study of the Flow of Blood.”Rheol. Acta.,1, 123–126.

    Article  Google Scholar 

  • Segré, G. and A. Silberberg. 1962. “Behaviour of Macroscopic Rigid Spheres in Poiseuflle Flow.”J. Fluid Mech.,14, 115–157.

    MATH  Article  Google Scholar 

  • Seshadri, V. and S. P. Sutera. 1968. “Concentration Changes of Suspensions of Rigid Spheres Flowing Through Tubes.”J. Colloid Interface Sci.,27, 101–110.

    Article  Google Scholar 

  • Truesdell, E. 1960.Handbuch der Physik III/1,363.

  • Vand, V. J. 1948. “Viscosity of Solutions and Suspensions.”J. phys. Chem.,52, 277–321.

    Article  Google Scholar 

  • Wayland, H. 1967. “Rheology and the Microcirculation.”Gastroenterology,52, 342–355.

    Google Scholar 

Download references

Author information

Affiliations

  1. National Tsing-Hua University, Hsin-Chu, Taiwan, China

    C. K. Kang

  2. Princeton University, Princeton, N.J., U.S.A.

    A. C. Eringen

Authors
  1. C. K. Kang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. C. Eringen
    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

Kang, C.K., Eringen, A.C. The effect of microstructure on the rheological properties of blood. Bltn Mathcal Biology 38, 135–159 (1976). https://doi.org/10.1007/BF02471753

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02471753

Keywords

  • Rheological Property
  • Apparent Viscosity
  • Viscosity Coefficient
  • Tube Flow
  • Concentrate Suspension