Fundamentals of Haemodynamics - Computational Hemodynamics: Theory, Modelling and Applications - page 69

Fig. 4.2 Relative viscosity is taken as the ratio of the viscosity of blood to that of water at 37 °C,
3

µ − −−

11

≈× a Relative viscosity as a function of haematocrit fraction. b Relative
viscosity as a function of the vessel diameter for different haematocrit fractions. c Dynamic vis-
cosity as a function shear rate for blood with 48 % haematocrit fraction. Data for figures from
(Bernaschi et al. 2013; Pries et al. 1992; Westerhof et al. 2010)

0.7 10 kgm s

water

Blood flows continuously through the network of vessels in the cardiovascular
system. These vessels vary in size from the smallest vessels in the capillary network
to the large heart chambers. The viscosity is also influenced by vessel diameter
due to shear stresses caused by its walls. The viscosity decreases gradually for a
vessel diameter decreasing from 3 mm down to 1 mm (Fig. 4.2c ). In these vessel
diameters, the effects on red blood cells are not significant and the viscosity remains
relatively constant. Blood can then be considered as a homogeneous fluid with New-
tonian properties in larger arteries�
When the vessel diameter is in the micron range, there is a rapid decrease in the
viscosity with decreasing vessel diameter from 1000 µm down to 10 µm. In these
small vessels, the red blood cells move towards the centre of the vessel, leaving the
plasma to remain close to the walls. This reduces the blood viscosity and this effect
called the “Fahraeus-Lindqvist effect” extends down to vessels with diameters of
about 7 µm (Fig. 4.2c ). At the smallest vessels the inner diameter is about the same