Membrane Gas Separation

9.5
Conclusions 
It is clear that the idea of ‘ magnetic membranes ’ works. There are, however, some obsta-
cles that depend on the kind of membrane used, especially when the stronger magnetic 

---

Table 9.5  Diffusion coeffi cients for pure gases 
Membrane
B 
(mT)
N 
2
pure
O 
2
pure
 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)
Flat EC
0.00
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
EC + 1.30 g 
Nd
0.00
0.9
±
0.2
1.3
±
0.22
1.5
±
0.3
1.1
±
0.2
1.0
±
0.2
1.2
±
0.1
2.2
±
0.2
3.4
±
0.5
0.6
±
0.1
0.9
±
0.1
EC + 1.30 g 
Nd
0.50
1.3
±
0.2
1.1
±
0.2
1.4
±
0.3
1.3
±
0.2
0.9
±
0.2
2.5
±
0.2
6.1
±
0.6
5.2
±
0.5
0.8
±
0.1
1.0
±
0.1
EC + 1.38 g 
Nd
0.79
1.4
±
0.3
1.0
±
0.2
1.3
±
0.3
1.1
±
0.2
0.9
±
0.2
3.0
±
0.3
8.6
±
0.8
7.2
±
0.7
0.9
±
0.1
1.5
±
0.1
EC + 1.49 g 
Nd
1.25
1.8
±
0.3
1.5
±
0.3
1.6
±
0.3
1.0
±
0.2
1.1
±
0.2
5.6
±
0.5
14.3
±
1.0
13.7
±
1.1
1.4
±
0.1
3.4
±
0.3
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 

---

Table 9.6  Diffusion coeffi cients for nitrogen and oxygen in air 
Membrane
B 
(mT)
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
 
10 
5
(cm 
2
/s)
10 
5
(cm 
2
/s)
Flat EC
0.00 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 + 1.30g 
Nd
0.00 1.0
±
0.2
2.5
±
0.4
4.1
±
0.8 0.1
±
0.05 0.8
±
0.1
0.9
±
0.1
2.8
±
0.2
3.1
±
0.3 0.05
±
0.01 0.6
±
0.1
EC + 1.30 g 
Nd
0.50 2.2
±
0.4
6.5
±
1.2
5.6
±
1.0 0.7
±
0.1
0.4
±
0.1
3.2
±
0.3
6.8
±
0.6
8.1
±
0.3
1.0
±
0.1
0.5
±
0.05
EC + 1.38 g 
Nd
0.79 4.5
±
0.9 11.7
±
2.2 12.2
±
2.4 1.2
±
0.2
1.0
±
0.2
9.4
±
0.9 18.6
±
1.2 25.5
±
2.7
2.5
±
0.2
1.8
±
0.15
EC + 1.49 g 
Nd
1.25 8.9
±
1.8 24.2
±
4.2 25.8
±
4.4 2.0
±
0.4
2.6
±
0.4 22.5
±
1.9 42.9
±
3.8 51.7
±
5.2
5.0
±
0.4
4.9
±
0.4

---

178
Membrane Gas Separation
Table 9.7  Dependence of the fl ux vs. membrane side A, B for various membranes 
No.
Membrane
B (mT)
N 
2
pure
O 
2
pure
N 
2
in air
O 
2
in air
J 
A
J 
B
J 
A
J 
B
J 
A
J 
B
J 
A
J 
B
10 
4
cm
cm s
STP
3
2
(
)
1
EC + 1.30 g 
of Nd
0.00
5.41
5.28
8.50
8.58
6.25
6.26
1.65
1.66
2
EC + 1.23 g 
of Nd
0.50
4.77
5.16
6.99
8.66
5.85
6.05
2.55
2.69
3
EC + 1.38 g 
of Nd
0.79
4.04
4.89
7.24
8.97
7.79
8.05
4.85
5.18
4
EC + 1.49 g 
of Nd
1.25
2.16
3.40
7.72
9.56
8.76
9.06
6.85
7.44
fi eld acts. For example, the creation of N 
2
- O 
2
- O 
2
clusters modifi es the air enrichment 
leading to a less effective process in the case of EC membranes. A careful selection of 
the polymeric matrix can result in a ‘ magnetic membrane ’ with better properties. Formation 
of these aggregates can be the reason for the difference between theoretical expectations 
and experimental data for oxygen content in the permeate. It means that we have to take 
into account the infl uence of some kind of the ‘ reaction ’ between oxygen and nitrogen in 
a strong magnetic fi eld, using for example the Smoluchowski equation with reaction term 
for theoretical predictions. 
One more problem should be discussed in further investigations. We assumed in our 
preliminary mathematical description that membranes are homogeneous. However, the 
method of preparing membranes with magnetic powder by casting suggests that we deal 
with regular heterogeneous membranes. That is why a mathematical description in further 
studies should take into account the ‘ directional ’ mass transport properties. Diffusion of 
a penetrant in the membrane where diffusion properties are changing in the x - direction 
should be expressed in the transport equation by the functional form of the diffusion and 
drift coeffi cients, i.e. D 
ij
  ( x ) and w ( x ) in Equation (9.1) .
Acknowledgements 
The authors would like to thank The Ministry of Science and Higher Education for pro-
viding fi nancial support under the project N N508 409137.
List of Symbols 
x
position (cm)
l
thickness of membrane (cm)
t
time (s)
D
diffusion coeffi cient for a one component system (cm 
2
/s)

---

Table 9.8  Mass transport coeffi cients for membranes based on PPO matrix 
Membrane
B 
(mT)
N 
2
pure
O 
2
pure
P
 D
¯
 
D 
L
 
D 
3
 
D 
4
 
D 
5
  P
 D
¯
 
D 
L
 
D 
3
 
D 
4
 
D 
5
 
.
10 
10
cm
cm
cm s cmHg
STP
2
3
(
) (
)
10 
7
(cm 
2
/s)
10 
10
cm
cm
cm s cmHg
STP
2
3
(
) (
)
10 
7
(cm 
2
/s)
Plane PPO
0.00
2.70
±
0.25
1.8
±
0.4
1.6
±
0.3
1.9
±
0.4
1.5
±
0.3
1.6
±
0.3
10.01
±
1.11
1.2
±
0.2
1.3
±
0.2
1.2
±
0.3
1.4
±
0.1
1.5
±
0.2
PPO + 1.80 g 
Nd
1.70
32.50
±
2.98
3.3
±
0.6
2.9
±
0.5
3.0
±
0.6
2.9
±
0.5
3.4
±
0.7
144.0
±
8.2
13.3
±
1.1
17.9
±
1.2
28.1
±
2.3
5.3
±
0.5
14.7
±
1.2
Membrane
B 
(mT)
N 
2
in air
O 
2
in air
P
 D
¯
 
D 
L
 
D 
3
 
D 
4
 
D 
5
  P
 D
¯
 
D 
L
 
D 
3
 
D 
4
 
D 
5
 
.
10 
10
cm
cm
cm s cmHg
STP
2
3
(
) (
)
.
10 
7
(cm 
2
/s)
.
10 
10
cm
cm
cm s cmHg
STP
2
3
(
) (
)
10 
7
(cm 
2
/s)
Plane PPO
0.00
3.07
±
0.34
1.8
±
0.3
1.8
±
0.3
1.9
±
0.3
1.4
±
0.1
1.4
±
0.2
10.25
±
1.12
1.4
±
0.1
1.3
±
0.1
1.6
±
0.2
1.2
±
0.1
1.2
±
0.1
PPO + 1.80 g 
Nd
1.70
54.30
±
5.01
22.7
±
1.1
10.3
±
0.9
51.6
±
3.1
13.0
±
1.0
3.0
±
0.2
241.0
±
15.0
73.1
±
6.8
29.3
±
2.2
169.0
±
14.3
41.7
±
3.0
8.8
±
0.8

---

180
Membrane Gas Separation
w
drift coeffi cient (cm/s)
c
1
( x , t )
concentration at position x and time t for oxygen
c
2
( x , t )
concentration at position x and time t for nitrogen
D 
ij
 
diffusion coeffi cients for mixtures, i,j = 1 (oxygen), = 2 (nitrogen)
D
¯
mean diffusion coeffi cient (cm 
2
/s)
J
S
diffusive mass fl ux in stationary state (
cm
cm s
STP
3
2
)
J
A,B
diffusive mass fl ux in stationary state on various membrane 
sides A, B
L
a
( l )
time lag (s)
D
L
diffusion coeffi cient calculated using time lag method (cm 
2
/s)
P
permeation coeffi cient (
cm
cm
STP
3
2
)/(cm 
3
cmHg s)
 
Δ
 p
pressure difference (cmHg)
S
sorption coeffi cient (
cm
cm cmHg
STP
3
3
)
c
0
initial concentration at position x = 0 (
cm
cm
STP
3
3
)
D
3
diffusion coeffi cient calculated using D 1 – D 8 system (cm 
2
/s)
D
4
diffusion coeffi cient calculated using D 1 – D 8 system (cm 
2
/s)
D
5
diffusion coeffi cient calculated using D 1 – D 8 system (cm 
2
/s)
J
a
( l , t )
diffusive mass fl ux at position x = l
Q
a
( l , t )
penetrant mass which is fl owing out from the membrane (
cm
cm
STP
3
2
)
Q l t
S
a
,
( )
penetrant mass which is fl owing out from the membrane in stationary 
state (
cm
cm
STP
3
2
)
EC
ethylcellulose
PPO
poly(2,6 – dimethyl - 1,4 - phenylene oxide)
Nd
neodymium powder
J
0
oxygen fl ux for pure EC membrane
J
B
 
i
 
oxygen fl ux for magnetic membrane with appropriate magnetic 
induction
w
B
 
i
 
drift coeffi cient
 
Δ
 c
0
equilibrium concentration of oxygen
B  
i
 
magnetic induction, i = 0.50, 0.79 and 1.25 mT, respectively
k
0
a reaction rate constant
k ( x )
the distribution function of an active, reaction points
f ( c )
the reaction kinetic term