Biomedical Engineering Reference
In-Depth Information
due to slip on the surface of the solute molecule. If the solute is not spherical but ellipsoid, with
dimensions
a
and
b
, the characteristic diameter can be estimated as:
,
ln
a þ
!
:
p
a
2
2
p
b
2
a
2
b
2
s
i
¼
(2.38)
b
Example 2.6
(
Diffusion coefficient of a large molecule in water
). Fibrinogen is a protein that plays
a key role in blood clotting. Fibrinogen significantly increases the risk of stroke. This protein molecule
has a rod shape of 67 nm in length and 2.2 nm in diameter. Estimate the diffusion coefficient of
fibrinogen in water at 25
C. Dynamic viscosity of water at this temperature is
m ¼
10
3
Pa
0.903
$
s.
10
9
m and
Solution.
The large molecule can be assumed to have the ellipsoid shape with
a
¼
67
10
9
nm. According to
(2.38)
, the characteristic diameter of a fibrinogen molecule is:
b
¼
2.2
2
p
a
2
b
2
a
!
s
¼
p
a
2
b
2
þ
ln
b
q
67
10
9
2
2
10
9
2
(2.39)
2
:
2
10
8
m
s
¼
q
¼
3
:
26
:
0
1
67
10
9
2
2
10
9
2
10
9
67
þ
:
2
@
A
ln
10
9
2
:
2
Thus, based on the Stokes-Einstein equation
(2.37)
, the diffusion coefficient of fibrinogen is:
10
23
k
B
T
3
pm
water
s
fibrinogen
¼
1
:
38
ð
25
þ
273
Þ
10
11
m
2
D
¼
10
8
¼
1
:
48
=
sec
:
10
3
3
p
0
:
903
3
:
26
The diffusion of a large molecule in water is about six orders slower than that of gases.
2.2.3.3 Diffusion coefficient of electrolytes
Salts and many other molecules dissolve in water to form cations and anions. However, they do not
diffuse as a single molecule, because different ions have different diffusion coefficients.
Tables 2.3 and
Diffusion coefficients of typical cations in water at 25
C (in 10
9
m
2
/sec)
[7]
Table 2.3
H
D
Li
D
Na
D
K
D
Rb
D
Cs
D
Ag
D
NH
4
D
Ca
2D
Mg
2D
La
3D
9.31
1.03
1.33
1.96
2.07
2.06
1.65
1.96
0.79
0.71
0.62
Diffusion coefficients of typical anions in water at 25
C (in 10
9
m
2
/sec)
[7]
Table 2.4
OH
L
F
-
Cl
-
Br
-
I
-
NO
3
D
CH
3
COO
-
B(C
6
H
5
)
4
-
SO
4
2L
CO
3
2L
5.28
1.47
2.03
2.08
2.05
1.90
1.09
0.53
1.06
0.92
Search WWH ::
Custom Search