Fundamentals of Haemodynamics - Computational Hemodynamics: Theory, Modelling and Applications - page 71

4.5 Blood Flow Properties

Blood flow through the cardiovascular network of vessels is essentially a form of
internal flow since the fluid is wall-bounded. Within this class of flow, a number of
flow properties exist including velocity, pressure, and shear stress. Furthermore the
blood flow can be steady or unsteady, laminar or turbulent, or in linear or curved
arteries. Each of these fluid dynamics properties is discussed.

4.5.1 Shear Force

Unlike solids, a fluid cannot resist an applied force and instead it reacts by deform-
ing continuously under the action of the force, while its viscosity tries to resist the
deformation. When blood is moving across the non-moving artery, a resultant shear
stress occurs due to the fluid particles moving past one another at different veloci-
ties, causing a friction-like effect. If its velocity is the same, and all fluid particles
move together then no shear stress is found. To understand shear stress we consider
a 3D rectangular fluid element next to a stationary vessel boundary wall shown in
Fig. 4.3 . The fluid velocity is zero at the wall surface, but increases in velocity away
from the wall. Each layer of fluid moves faster than the one below it, creating fric-
tion between them. This friction acts as a force resisting the motion, which is the
viscosity.
Experimental observations made by Sir Isaac Newton showed that for certain
fluids under laminar flows, the shear force is proportional to the velocity u , and the
area A, and inversely proportional to their distance from the wall y ,

u
FA y = µ

(4.3)

where the proportionality factor is the dynamic viscosity μ . Therefore fluids that
behave according to Eq. 4.3 are known as Newtonian fluids. Earlier we saw that for

Fig. 4.3 Shear stress and velocity gradient arising from an applied force deforming a rectangular
fluid element