Blood flow: theory, effective viscosity and effects of particle distribution

Bulletin of Mathematical Biology
J C Chow

Abstract

A study is made of blood flow by assuming that the blood constitutes a suspension of cells in plasma instead of a simple homogeneous fluid. A macroscopic theory governing the motion of plasma in a plasma-cell system is derived from the local volume averaging method for a system without mass transfer between the phases, and its characteristic length is much larger than the size of the cells. The equations governing the motion of the local averaged fluid quantities include one additional term in the equation of motion and two additional terms in the energy equation. These terms represent, respectively, the force exerted upon the fluid by the particles, and the rate of heat transfer and work kone upon the fluid by the particles. The theory is applied to obtain the effective viscosity as the explicit function of the volume concentration of the cells by assuming that the cells behave like rigid spherical particles with slip-collision, and the plasma is an compressible Newtonian fluid. Comparison with existing experimental results shows a good agreement. The theory is also used to obtain the effects of cell distribution upon the overall effective viscosity in a circular tube. The quantitative result shows that there is a decrease in ...Continue Reading

References

Apr 1, 1974·Archives of Internal Medicine·P P KlugP Radice
Dec 1, 1969·The Bulletin of Mathematical Biophysics·T F Zien
Mar 1, 1969·The Bulletin of Mathematical Biophysics·M M Lih
Sep 1, 1965·Journal of Applied Physiology·E W MerrillE W Salzman
Oct 1, 1969·Journal of Biomechanics·Y C Fung

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Citations

Mar 9, 2012·Computer Methods in Biomechanics and Biomedical Engineering·T A BégN Rahimzadeh
Feb 1, 1983·Circulation Research·J Melbin, A Noordergraaf

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