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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- τ0 :
limiting shear stress (yield stress)
- τ0 :
analog of plastic viscosity
- μpl :
human plasma viscosity
- \(\dot \gamma\) :
- m, n :
nonlinearity parameters of the rheological model
- R :
thickness of the wall layer of human plasma
- r :
- 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 =τ0/τ 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 :
- l :
- 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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B. M. Smol'skii, Z. P. Zhul'man, and V. M. Gorislavets, Rheodynamics and Heat Transfer in Nonlinear Viscoplastic Materials [in Russian], Minsk (1970).
N. N. Firsov, Macro- and Micro-Rheology of Human Blood in Norm and Pathology [in Russian], Doctoral Dissertation in Biological Sciences, Moscow (1983).
R. H. Haynes, Amer. J. Physiology,198, No. 6, 1195 (1960).
G. M. Kostin, Change in Rheological Properties of Human Blood in the Acute Poisoning Cases [in Russian], Candidate's Dissertation in Medicine, Moscow (1976).
B. Folkov and E. Neil, Blood Circulation, New York, Oxford University Press, London-Toronto (1971).
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
- Blood Flow
- Flow Velocity
- Shear Rate
- Volume Blood
- Flow Curve