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9.3.4
Permeation Data
The main permeation data are collected in Tables 9.1 , 9.2 and Figure 9.10 . The data
presented are the mean values of six measurements with standard deviations.
Results 6 and 9 from Table 9.2 were obtained by using a newly designed permeation
cell with strong magnets on both sides of a membrane. The percentage of air enrichment
was directly measured, while the value of B in this case was just estimated. Values of
calculated oxygen content in the permeate originate from theoretical consideration [24] .
We can see that theoretical expectations are in really good agreement with experimental
data. But, if we present the measured oxygen content in the permeate as a function of the
magnetic induction (Figure 9.11 ) we can see the tendency of deviation from the linear
relationship.
All that might be due to the infl uence of a strong magnetic fi eld in which nitrogen and
oxygen form aggregates [36] which carry more nitrogen, and spoil, in a sense, the separa-
tion process.
-16
-14
-12
-10
-8
-6
-4
-2
0
0
1
2
3
4
5
6
7
t
ln[Q-Qs]
ln[2lc
0
/
Π
2
]
Figure 9.9 An example of late - time permeation curve according to Equation (9.23).
Reprinted with permission from Journal of Membrane Science, On the air enrichment by
polymer magnetic membranes by A. Rybak, Z. J. Grzywna and W. Kaszuwara, 336, 1 – 2,
79 – 85, Copyright (2009) Elsevier Ltd
Air Enrichment by Polymeric Magnetic Membranes
171
Table 9.1 Mass transport coeffi cients for various membranes
No. Membrane
B (mT) N
2
, pure
N
2
, in air
P
×
10
7
La(l)
Δ
c
0
P
×
10
7
La(l)
Δ
c
0
cm
cm
cm s cmHg
STP
2
3
(
) (
)
(s)
cm
cm
STP
3
3
(
)
cm
cm
cm s cmHg
STP
2
3
(
) (
)
(s)
cm
cm
STP
3
3
(
)
1
Flat EC
0.00
0.19
±
0.01
1.37
±
0.10 0.71
±
0.05
0.19
±
0.01
1.21
±
0.01 0.50
±
0.04
2
EC + 1.30 g
of Nd
0.00
0.22
±
0.01
1.23
±
0.10 0.73
±
0.07
0.22
±
0.01
1.31
±
0.01 0.39
±
0.04
3
EC + 1.23 g
of Nd
0.50
0.31
±
0.01
0.52
±
0.04 0.71
±
0.05
0.46
±
0.01
0.47
±
0.01 0.37
±
0.03
4
EC + 1.38 g
of Nd
0.79
0.34
±
0.01
1.03
±
0.10 0.73
±
0.07
0.94
±
0.01
0.35
±
0.01 0.37
±
0.03
5
EC + 1.49 g
of Nd
1.25
0.42
±
0.02
0.83
±
0.07 0.72
±
0.07
1.98
±
0.02
0.30
±
0.01 0.39
±
0.04
No
Membrane
B (mT) O
2
, pure
O
2
, in air
P
.
10
7
La(l)
Δ
c
0
P
.
10
7
La(l)
Δ
c
0
cm
cm
cm s cmHg
STP
2
3
(
) (
)
(s)
cm
cm
STP
3
3
(
)
cm
cm
cm s cmHg
STP
2
3
(
) (
)
(s)
cm
cm
STP
3
3
(
)
1
Flat EC
0.00
0.23
±
0.01
1.21
±
0.10 0.63
±
0.05
0.22
±
0.01
1.17
±
0.01 0.11
±
0.01
2
EC + 1.30 g
of Nd
0.00
0.24
±
0.01
1.35
±
0.10 0.60
±
0.05
0.22
±
0.01
1.26
±
0.01 0.12
±
0.01
3
EC + 1.23 g
of Nd
0.50
0.52
±
0.01
0.51
±
0.05 0.62
±
0.05
0.77
±
0.01
0.45
±
0.01 0.11
±
0.01
4
EC + 1.38 g
of Nd
0.79
0.63
±
0.01
0.56
±
0.06 0.63
±
0.05
2.23
±
0.01
0.32
±
0.01 0.11
±
0.01
5
EC + 1.49 g
of Nd
1.25
1.18
±
0.02
0.52
±
0.05 0.64
±
0.05
5.79
±
0.01
0.23
±
0.01 0.12
±
0.01
Source: Reprinted with permission from Journal of Membrane Science, On the air enrichment by polymer magnetic membranes by A. Rybak, Z. J. Grzywna and W. Kaszuwara,
336, 1 – 2, 79 – 85 Copyright (2009) Elsevier Ltd
*
Δ
c
0
was obtained using a late time permeation curve according to Equation (9.23) . Other methods mentioned above could be used only in the case of the suffi cient amount of
data, and for an ‘ ideal Fickian ’ description of a permeation process.
172
Membrane Gas Separation
0
0,000
t(s)
0,002
Q
a
(l, t)
0,004
La=1,17 s
La=0,45 s
La=0,32 s
La=0,23 s
Figure 9.10 Downstream absorption permeation curves for various polymer and
magnetic membranes. Points marked as: squares, magnetic membrane with B = 1.25 mT;
stars, magnetic membrane with B = 0.79 mT; triangles, magnetic membrane with
B = 0.50 mT; asterisk, plane EC membrane
Table 9.2 Comparison of measured and calculated air enrichment data for various
membranes
No
Membrane
B (mT)
Measured oxygen
content in permeate (%)
Predicted (calculated) oxygen
content in permeate (%)
1
EC
0.00
23.8
±
1.0
25.0
2
EC
0.0
0.00
22.1
±
1.1
25.0
3
EC
0.50
0.50
30.7
±
1.1
33.3
4
EC
0.79
0.79
40.7
±
1.1
38.2
5
EC
1.25
1.25
43.8
±
1.1
45.8
6
EC
2.25
2.25
55.6
±
1.4
62.5
7
PPO
0.00
37.4
±
1.2
–
8
PPO
1.70
1.70
54.1
±
1.4
–
9
PPO
2.70
2.70
61.9
±
1.5
–
9.4
Results and Discussion
We have found (Table 9.3 ) that EC fi lms for pure and mixed components as well as
EC + Nd/N
2
form ideal Fickian systems, while EC + Nd/N
2
air, EC + Nd/O
2
and EC + Nd/
O
2
air, do not. Based on that we can calculate D
¯ and
Δ
c
0
from the appropriate ‘ ideal ’
permeation curve to get a sort of a reference point for non - ideal cases.
We can separate the drift and diffusion in an overall fl ux assuming that the diffusional
contribution to the overall fl ux is magnetic fi eld independent.
Air Enrichment by Polymeric Magnetic Membranes
173
l
D
J
Bi
=
+
w
Bi
Δ
c
0
Δ
c
0
plane EC
drift
(9.24)
J
J
w
c
Bi
Bi
=
+
0
0
Δ
(9.25)
Here ‘ B
i
’ stands for magnetic induction of a membrane. The drift coeffi cient can be cal-
culated for an imposed induction B from equation:
w
J
J
c
Bi
Bi
=
−
0
0
Δ
(9.26)
and its values for different values of B are collected in Table 9.4 .
As can be seen from Table 9.5 (pure gases) the infl uence of drift is meaningful only
for oxygen, whose transport is strongly affected by the magnetic fi eld.
Quite a different situation happens for air transport through magnetic membranes (i.e.
with a nonzero induction), where much larger differences between the nitrogen and
oxygen diffusion coeffi cients were observed (Table 9.6 ). Surprisingly, it was found that
not only is oxygen transport affected by the magnetic fi eld, but the nitrogen diffusion is
as well.
0
10
20
30
40
50
60
70
2,5
2
1,5
1
0,5
0
B [mT]
oxygen content in permeate [%]
Figure 9.11 Dependence of the oxygen content in permeate vs. magnetic fi eld induction.
Points marked as rhombus were obtained in experiment, points marked as squares were
predicted by the theory
174
Membrane Gas Separation
Table 9.3 Diffusion coeffi cients for ideal, and non - ideal, Fickian systems
Membrane
Ideal Fickian system
N
2
pure
O
2
pure
N
2
in air
O
2
in air
D
¯
D
L
D
3
D
4
D
5
D
¯
D
L
D
3
D
4
D
5
D
¯
D
L
D
3
D
4
D
5
D
¯
D
L
D
3
D
4
D
5
10
5
(cm
2
/s)
10
5
(cm
2
/s)
10
5
(cm
2
/s)
10
5
(cm
2
/s)
Flat EC
0.8
±
0.2
0.8
±
0.2
1.1
±
0.2
0.9
±
0.1
1.1
±
0.2
1.1
±
0.1
1.0
±
0.1
1.1
±
0.2
1.0
±
0.1
1.2
±
0.1
0.9
±
0.2
0.9
±
0.2
1.1
±
0.4
0.9
±
0.1
1.1
±
0.2
0.9
±
0.1
0.9
±
0.1
1.4
±
0.2
1.0
±
0.1
1.2
±
0.1
EC + 1.30 g
Nd
1.3
±
0.2
1.1
±
0.2
1.4
±
0.3
1.3
±
0.2
0.9
±
0.2
out of the case
out of the case
out of the case
EC + 1.38 g
Nd
1.4
±
0.3
1.0
±
0.2
1.3
±
0.3
1.1
±
0.2
0.9
±
0.2
out of the case
out of the case
out of the case
Membrane
Non - ideal Fickian system
N
2
pure
O
2
pure
N
2
in air
O
2
in air
D
¯
D
L
D
3
D
4
D
5
D
¯
D
L
D
3
D
4
D
5
D
¯
D
L
D
3
D
4
D
5
D
¯
D
L
D
3
D
4
D
5
10
5
(cm
2
/s)
10
5
(cm
2
/s)
10
5
(cm
2
/s)
10
5
(cm
2
/s)
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