Biomedical Engineering Reference
In-Depth Information
and the turbulent shear stress equation:
x j 1 @
u j
@
@
u i
u i u j
τ
5 μ
2 ρ
ij
@
x i
where u i u j is the turbulent inertia tensor. For any turbulent flow, this term cannot be
neglected, but it is also not known prior to the calculation, as it only involves the turbulent
fluctuations which are random. This quantity can only be resolved after the flow has
occurred and the fluctuations can be measured with respect
to the mean velocity.
Turbulent flows will be discussed in further details in Chapter 13.
Because one cannot discretely define the properties of turbulent flows, most biofluid
mechanics engineers discuss the common characteristics of turbulence. The first common
property of turbulent flows is that they are random and therefore statistical methods are
needed to characterize the flow properties. In non-turbulent flows, we typically make the
assumption that there is no mass transfer between fluid laminae. However, in turbulent
flows there is diffusion between laminae that increases the momentum flux, the heat trans-
fer and mass transfer, within the fluid. Turbulent flows also are characterized by large
inertial forces as compared to the internal viscous forces (this is quantified by the
Reynolds number, which will be discussed later). Turbulent flows also require a large
amount of energy to maintain the turbulence. This is induced by the lamina mixing, which
causes viscous shear forces to perform work on neighboring fluid elements. This work
increases the internal energy of the fluid but decreases the kinetic energy of the fluid.
Therefore, turbulent flows are typically dissipative; without an external energy input, they
tend to return to laminar flow conditions.
5.11 DISEASE CONDITIONS
5.11.1 Arteriosclerosis/Stroke/High Blood Pressure
In Section 4.6, we began a discussion of coronary artery disease and myocardial infarc-
tion as instigated through a plaque formation. Here we will more fully discuss the disease
of arteriosclerosis and how it is manifested within the arterial system. In general, arterio-
sclerosis can be characterized by a thickening and a stiffening of the arterial wall. As we
have discussed in this chapter, a decrease in the cross-sectional area of blood vessels can
have multiple effects in the body. Flow can accelerate around the constriction, causing
enhanced shear stresses or pressure gradients within the fluid. Flow can also be stagnated
around the constriction if the pressure gradient is not large enough to overcome the
enhanced resistance to flow. Flow can separate from the wall, which also decreases the
mean fluid velocity and may enhance recirculation zone formation. When a mean flow
velocity decreases, there is the potential for a reduction in the tissue oxygenation along
with a decrease in the glucose delivered to cells. Also, stiffening of the arterial wall
decreases the compliance of the vessel, and it may not be able to withstand the high pres-
sure forces that act on the vessel. Arteriosclerosis is manifested in two main forms: calcifi-
cation of the arterial wall or atherosclerosis. Calcification is associated with the deposition
of calcium salts between the tunica intima and the tunica media and a breakdown of
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