Mathematical Model of the Single-File Flow of Red Blood Cells in Capillaries

  • Chapter
Recent Contributions to Fluid Mechanics

Abstract

An important ingredient for the analysis of the blood flow in the microcirculation is that the suspension of red cells in the plasma should not be treated as a continuum. In capillaries whose diameters range from 3 to 8 μm, the cells flow in single file. In larger vessels the flow is characterized by a distribution of red cells over the intraluminal cross-section. Extensive experimental studies for the latter flow regime have been done by Barbee and Cokelet (3). A theoretical description of this flow, however, has not been developed.

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

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

eBook
USD 9.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Albrecht, K.H.; Gaehtgens, P.; Pries, A.; Heuser, M.: The Fåhraeus effect in narrow capillaries (i.d. 3.3 to 11.0 μm). Microvasc. Res. 18 (1979), 33–47.

    Article  Google Scholar 

  2. Aroesty, J.; Gross, J.F.: Convection and diffusion in the microcirculation. Microvasc. Res. 2 (1970), 247–267.

    Article  Google Scholar 

  3. Barbee, J.H.; Cokelet, G.R.: Prediction of blood flow in tubes with diameters as small as 29 μ. Microvasc. Res. 3 (1971), 17–21.

    Article  Google Scholar 

  4. Bruns, F.W.: Numerical calculation on cree** flow in a closed cylindrical cavity. Computers and Fluids 7 (1979), 257–265.

    Article  MATH  MathSciNet  Google Scholar 

  5. Deen, W.M.; Robertson, C.R.; Brenner, B.M.: Concentration polarization in an ultrafiltering capillary. Biophysical J. 14 (1974), 412–431.

    Article  ADS  Google Scholar 

  6. Gaehtgens, P.; Dührssen, C; Albrecht, K.A.: Motion, deformation, and interaction of blood cells and plasma during flow through capillary tubes. Blood Cells 6 (1980), 799–812.

    Google Scholar 

  7. Gross, J.F.; Aroesty, J.: Mathematical models of capillary flow: A critical review. Biorheology 9 (1972), 225–264.

    Google Scholar 

  8. Papenfuss, H.-D.: Die Mechanik der Blutströmung und der Flüssigkeitsaustausch in der Mikrozirkulation. Habilitationsschrift, Ruhr-Universität Bochum (1979).

    Google Scholar 

  9. Papenfuss, H.-D.; Gross, J.F.: The interaction between transmural fluid exchange and blood viscosity in narrow blood vessels. Biorheology 14 (1977), 217–228.

    Google Scholar 

  10. Prothero, J.; Burton, A.C.: The physics of blood flow in capillaries. I. The nature of the motion. Biophysical J. 1 (1961), 565–575.

    Article  ADS  Google Scholar 

  11. Schlichting, H.: Grenzschicht-Theorie. 5. Auflage. Verlag G. Braun, Karlsruhe (1965).

    MATH  Google Scholar 

  12. Schmid-Schoenbein, G.W.; Zweifach, B.W.: RBC velocity profiles in arterioles and venules of the rabbit omentum. Microvasc. Res. 10 (1975), 153–164.

    Article  Google Scholar 

  13. Tözeren, H.; Skalak, R.: The steady flow of closely fitting incompressible elastic spheres in a tube. J. Fluid Mech. 87 (1978), 1–16.

    Article  MATH  ADS  Google Scholar 

  14. Tözeren, H.; Skalak, R.: Flow of elastic compressible spheres in tubes. J. Fluid Mech. 95 (1979), 743–760.

    Article  MATH  ADS  Google Scholar 

  15. Van Dyke, M.: Perturbation Methods in Fluid Mechanics. The Parabolic Press, Stanford, Cal. (1975).

    MATH  Google Scholar 

  16. Zien, T.-F.: Hydrodynamics of bolus flow — an analytical approach to blood flow in capillaries. Bull. Math. Biophys. 31 (1969), 681–694.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1982 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Papenfuss, HD., Gross, J.F. (1982). Mathematical Model of the Single-File Flow of Red Blood Cells in Capillaries. In: Haase, W. (eds) Recent Contributions to Fluid Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-81932-2_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-81932-2_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-81934-6

  • Online ISBN: 978-3-642-81932-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Navigation