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Rheological factor and Fahraeus-Lindqvist effect

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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.

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Abbreviations

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

u p :

velocity of human plasma

ΔP/L :

pressure gradient in vessel

Q p :

volume flow rate of human plasma

Q b :

volume flow rate of blood

u 0 :

quasisolid core velocity

τδ :

shear stress at the plasma-blood interface

τ w 0 w :

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

ū b :

mean velocity of blood flow

ū b :

mean velocity of plasma flow

c f :

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

References

  1. 1.

    V. A. Levtov, S. A. Regirer, and N. Kh. Shadrina, Blood Rheology [in Russian], Moscow (1982).

  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.

  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).

  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).

  5. 5.

    R. H. Haynes, Amer. J. Physiology,198, No. 6, 1195 (1960).

  6. 6.

    G. M. Kostin, Change in Rheological Properties of Human Blood in the Acute Poisoning Cases [in Russian], Candidate's Dissertation in Medicine, Moscow (1976).

  7. 7.

    B. Folkov and E. Neil, Blood Circulation, New York, Oxford University Press, London-Toronto (1971).

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Additional information

Academic-Scientific Complex “A. V. Luikov Heat and Mass Transfer Institute, Academy of Sciences of Belarus,” Minsk, Belarus. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 3, pp. 416–426, May–June, 1995.

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Shul'man, Z.P., Markova, L.V. & Makhanek, A.A. Rheological factor and Fahraeus-Lindqvist effect. J Eng Phys Thermophys 68, 353–363 (1995). https://doi.org/10.1007/BF00859048

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Keywords

  • Blood Flow
  • Flow Velocity
  • Shear Rate
  • Volume Blood
  • Flow Curve