Abstract
Flow of blood is analyzed under the assumptions of Deakin (1967b, 1968). It is found that for physiological values of hematocrit, there is little variation of erythrocyte concentration with radial distance. This conclusion is compared with those of other analyses, and an experiment is proposed which would decide between the various theories.
Similar content being viewed by others
Literature
Bugliarello, G. and J. W. Hayden. 1963. “Detailed Characteristics of the Flow of Blood in Vitro.”Trans. Soc. Rheol. 7, 209–230.
Casson, N. 1959. “A Flow Equation for Pigment-Oil Suspensions of the Printing Ink Type.” InRheology of Disperse Systems, C. C. Mill, Ed. London and New York. Pergamon Press, 84–103.
Cokelet, G. R., E. W. Merrill, E. R. Gillilland, H. Shin, A. Britten and R. E. Wells, Jr. 1963. “The Rheology of Human Blood: Measurement near and at Zero Shear-Rate.”Trans. Soc. Rheol. 7, 303–318.
Deakin, M. A. B. 1967a. “Erythrocyte Distribution in Arterial Blood-Flow: I. Basic Equations and Anisotropic Effects.”Bull. Math. Biophys.,29, 549–563.
— 1967b. “Erythrocyte Distribution in Arterial Blood-Flow: II. The Hypothesis of Minimal Energy Dissipation.” —Ibid.,29, 565–574.
— 1967c. “Erythrocyte Distribution in Arterial Blood-Flow: III. Physiological Considerations.” —Ibid.,29, 649–656.
— 1968. “Erythrocyte Distribution in Arterial Blood-Flow: IV. Simplification of the Proposed Equations.” —Ibid.,30, 27–34.
Goldsmith, H. L. and S. G. Mason. 1962. “The Flow of Suspensions through Tubes I. Single Spheres, Rods and Discs.”J. Colloid. Sci.,17, 448–476.
— 1965. “Further Comments on the Radial Migration of Spheres in Poiseuille Flow.”Biorheology,3, 33–36.
Jeffery, G. B. 1922. “The Motion of Ellipsoidal Particles Immersed in a Viscous Fluid.”Proc. Roy. Soc.,102A, 161–179.
Jones, A. L. 1966. “On the Flow of Blood in a Tube.”Biorheology,3, 183–188.
Segré, G. and A. Silberger. 1961. “Radial Particle Displacements in Poiseuille Flow of Suspensions.”Nature,189, 209–210.
——. 1962. “Behaviour of Macroscopic Rigid Spheres in Poiseuille Flow.”J. Fl. Mech.,14, 115–135, 136–157.
Silberberg, A. 1966. “The Tubular Pinch Effect in the Circulation of Blood.”Biorheology,4, 29–30.
Steiner, E. H. 1958. “A New Rheological Relationship to Express the Flow Properties of Melted Chocolate.”Rev. Intern. de la Chocolaterie,13, 290–308.
Taylor, M. G. 1955. “The Flow of Blood in Narrow Tubes. II. The Axial Stream and its Formation as Determined by Changes in Optical Density.”Aust. J. Exp. Biol. Med. Sci.,33, 1–16.
von Bertalanffy, L. 1960. “Principles and Theory of Growth.” InFundamental Aspects of Normal and Malignant Growth, W. W. Nowinski, Ed. New York: Elsevier Publishing Company. 137–304 (see pp. 151–155).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Deakin, M.A.B., Jones, A.S. Erythrocyte distribution in arterial blood flow: V. Flow with minimal energy dissipation. Bulletin of Mathematical Biophysics 30, 241–252 (1968). https://doi.org/10.1007/BF02476693
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02476693