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Rheological factor and Fahraeus-Lindqvist effect

  • Z. P. Shul'man
  • L. V. Markova
  • A. A. Makhanek
Article

Abstract

Human blood flow in a microvessel with regard for the fahraeus-Lindquist effect is considered in an approximation of a two-layer model. The blood flow curve is described by the generalized equation of a nonlinear viscoplastic medium. Analytical expressions are derived for the volume blood flow velocity, effective blood viscosity, maximum flow velocity, and mean shear rate.

Keywords

Blood Flow Flow Velocity Shear Rate Volume Blood Flow Curve 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notation

τ

shear stress

τ0

limiting shear stress (yield stress)

τ0

analog of plastic viscosity

μpl

human plasma viscosity

\(\dot \gamma\)

shear rate

m, n

nonlinearity parameters of the rheological model

R

vessel radius

δ

thickness of the wall layer of human plasma

r

current radius

up

velocity of human plasma

ΔP/L

pressure gradient in vessel

Qp

volume flow rate of human plasma

Qb

volume flow rate of blood

u0

quasisolid core velocity

τδ

shear stress at the plasma-blood interface

τw0w

relative thickness of the quasisolid core of a viscoplastic flow

μe

total effective viscosity of human plasma and blood

f, φ, ψ

functions accounting for blood plasticity

ūb

mean velocity of blood flow

ūb

mean velocity of plasma flow

cf

drag coefficient

Re

Rcynolds number

l

characteristic size

ρ

density

ū

mean velocity of blood flow and the wall plasma layer

\(< \dot \gamma >\)

mean shear rate

μa

asymptotic value of the viscosity at a high shear rate

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References

  1. 1.
    V. A. Levtov, S. A. Regirer, and N. Kh. Shadrina, Blood Rheology [in Russian], Moscow (1982).Google Scholar
  2. 2.
    C. Gazley, in: Heat and Mass Transfer [in Russian], Collected Papers of the All-Union Conference, Minsk, Vol. 9. Pt. 1 (1972), pp. 3–22.Google Scholar
  3. 3.
    B. M. Smol'skii, Z. P. Zhul'man, and V. M. Gorislavets, Rheodynamics and Heat Transfer in Nonlinear Viscoplastic Materials [in Russian], Minsk (1970).Google Scholar
  4. 4.
    N. N. Firsov, Macro- and Micro-Rheology of Human Blood in Norm and Pathology [in Russian], Doctoral Dissertation in Biological Sciences, Moscow (1983).Google Scholar
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    R. H. Haynes, Amer. J. Physiology,198, No. 6, 1195 (1960).Google Scholar
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    G. M. Kostin, Change in Rheological Properties of Human Blood in the Acute Poisoning Cases [in Russian], Candidate's Dissertation in Medicine, Moscow (1976).Google Scholar
  7. 7.
    B. Folkov and E. Neil, Blood Circulation, New York, Oxford University Press, London-Toronto (1971).Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • Z. P. Shul'man
  • L. V. Markova
  • A. A. Makhanek

There are no affiliations available

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