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Rheological factor and Fahraeus-Lindqvist effect

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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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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


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


Rcynolds number

l :

characteristic size



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