Biomedical Engineering Reference
In-Depth Information
FIGURE 5.16 Flow separation (region enclosed by dashed lines) downstream of a bifurcation and a stenosis
(rapid area expansions). Flow separates from the wall partially due to the skewing of the velocity profile toward
one of the walls of the blood vessel. By quantifying the pressure gradient along the wall, the likelihood for flow
separation can be predicted.
Flow separation is a common occurrence at bifurcations (especially within the arterial
circulation where the pressures/velocities are high) and near the wall when there are
rapid geometric changes that expand the cross-sectional area of the blood vessel. Flow sep-
aration is a phenomenon that occurs when the fluid pulls away from the wall forming a
region that has very slow flow associated with it ( Figure 5.16 ). The fluid in this region typ-
ically forms a recirculation pattern in which the fluid is trapped within that area. Flow
separation occurs when the fluid velocity is relatively fast and cannot expand with the
geometry rapidly. The formation of recirculation zones is a property of all viscous fluids
and cannot be ignored in physiological settings. The fluid that is trapped within the recir-
culation zone stays within the recirculation zone because it cannot overcome the flowing
fluid pressure to reenter the mainstream flow. In general, this occurs when the angle
between the main fluid flow direction and the wall is relatively large.
Also, a common way to generate flow separation in biofluids mechanics problems is
when there is an adverse pressure gradient causing convection throughout the fluid lami-
nae. In a pressure-driven viscous flow, the momentum equation at the wall is
2 u
@
1
μ
@
p
y 2 y 5 0 5
@
@
x
To maintain the flow regime without recirculation zones, the wall curvature must have the
same sign as the pressure gradient. Under normal conditions, the pressure gradient @ p
@
is
x
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