Biomedical Engineering Reference
In-Depth Information
F
Forchheimer constant
g
Acceleration due to gravity
v
p
J
Unit vector oriented along the pore velocity vector,
J
=
|
v
p
|
K
Permeability of the porous medium
P
Pressure
f
P
Average pressure
Re
m
Mean Reynolds number,
ρu
m
d/µ
t
Time
Average velocity vector
v
p
Pore velocity vector
V
Velocity vector in the parent vessel
T
p
Period
Greek symbols
ε
Porosity of the porous medium
µ
Dynamic viscosity
ν
Kinematic viscosity
ρ
Density
Subscripts
f
v
Fluid
6.2 Introduction
Porous media theory has been utilized to improve our understanding of trans-
port processes. There are numerous practical applications that can be modeled
or approximated as a transport through porous media: catalytic reactors, elec-
tronic cooling, geothermal systems, thermal insulation, drying technology, and
packed-bed heat exchangers. These applications have been discussed by Nield
and Bejan [1], Vafai [2], Hadim and Vafai [3], and Vafai and Hadim [4], Vafai
and Tien [5,6], and Vafai [7,8]. Vafai and Tien [6] presented a comprehensive
analysis of the generalized transport through porous media and developed a
set of governing equations utilizing the local volume averaging technique. The
use of porous media theory for modeling biomedical phenomena has resulted
in significant advances in biofilms, drug delivery, computational biology, brain
aneurysms filled with endovascular coil, medical imaging, porous scaffolds for
tissue engineering, and diffusion processes in the extracellular space (ECS).
6.3 Physics of Cerebral Aneurysms
Cerebral aneurysms are pathological segmental dilatations of the cerebral
arteries. On microscopic examination, cerebral aneurysms show weakening
of their vessel walls with thinning of the tunica media and the disruption of
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