Letter | Published:

The Flow of Blood through Narrow Tubes

Abstract

IN a recent letter, one of us1 has shown that the flow of the blood of several species in a single capillary tube of radius R and length L follows an equation recently proposed by Casson2 for varnishes and inks. where P is pressure, V is volume flow/see, k 0, and k 1 are constants. When k 0 becomes zero, this equation reduces to the well-known equation of Poiseuille, since the terms in parenthesis represent the stress and shear rate respectively, at the wall of the tube. When k 0 has finite values, however, it is a measure of a yield-value or critical shearing stress which, as pressure is raised, will be first reached at the capillary wall. As pressure still further increases, the critical distance (r 0) from the centre at which this occurs, will steadily diminish. A similar phenomenon was studied many years ago for the Bingham equation, which differs from Casson's equation only in the absence of square roots; when Buckingham3 and, independently, Reiner4 evaluated the correct equation of flow for such a system where p is the pressure corresponding to the yield-value given by p = 2Lk 0 2/R.

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References

  1. 1

    Scott Blair, G. W., Nature, 183, 613 (1959).

  2. 2

    Casson, N., Chap. 5 of “The Rheology of Disperse Systems”, ed. C. C. Mill. (Pergamon Press, London, 1959).

  3. 3

    Buckingham, E., Proc. Amer. Soc. Test. Mater., 21, 1154 (1921).

  4. 4

    Reiner, M., Kolloidzschr., 39, 80 (1926).

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