Biomedical Engineering Reference
In-Depth Information
considerably changed by the presence of the polymers. At zero shear rate, the vis-
cosity is given by an expression of the type
n
η η
=
[1
+
a c
( [ ]) ]
η
s
Above the threshold
c
*
= 1/[
h
], the effect of the transported polymers becomes
important. This point is illustrated in Figure 6.11.
6.2.5.2 Diffusion Constant
In Chapter 5, we introduced the Einstein relation for the diffusion of the particles
k T
B
D
=
6
(6.23)
π η
R
H
Substituting (6.19) in (6.23) yields
k T
1
D
B
0
D
( )
φ
=
=
(6.24)
5
6
π
R
é
5
ù
H
1
+
φ
η
1
+
φ
0
ê
ú
2
2
ë
û
The relative change in
D
is
D
( )
φ
-
D
5
2
0
» -
φ
D
0
For the typical value
f
= 0.02, the relative change of
D
is -5%.
6.2.5.3 Density
The density of the buffer fluid is a function of the concentration. Using the defini-
tion of the volume fraction, the density is
ρ φρ
=
+
(1
-
φ ρ
)
(6.25)
P
L
Figure 6.11
Comparison between concentration free and a concentration of polymers (alginate)
c
= 2
g
/
l
.
P
in
= 100 Pa,
w
= 100
m
m,
d
= 100
m
m (COMSOL).
