Membrane Gas Separation

9.2
Formulation of the Problem 
To separate gas mixtures one should take into account one of two (partly interrelated) 
factors by which gas components could differ, and which lead to an effective separation: 
solution - diffusion properties and molecular size differences of the components. Separation 
can be based on differences of molecular size, i.e. in the medium (a membrane) that 
behaves like a molecular sieve. In cases of similar sized molecules, like oxygen and 
nitrogen, the separation in polymer membranes can be also accomplished due to the dif-
ferences thermodynamic properties of the penetrants. The gas mixture is made to pass 
through the membrane by applying a pressure difference on either side of the membrane 
(which causes the chemical potential gradient within the membrane). Differences in per-
meability result not only from diffusivity differences of the various gas species but also 
from differences in physico - chemical interactions of these species within the polymer 
[27] . A challenge with air, when separation by polymer membrane is concerned, is to 
provide conditions for differences (other than solution 
- 
diffusion) in mass transport 
between oxygen and nitrogen. The necessary differences can appear by introduction of a 
magnetic fi eld which actively infl uences the oxygen transport, and is supposed to be 
neutral to nitrogen. A magnetic fi eld gives rise to the ‘ drift term ’ in the overall oxygen 
transport, i.e. a deterministic term of a value dependent on the magnetic fi eld induction. 
We consider a model of the mass transport system consisting of one or two gases, per-
meating through a dense membrane of thickness l . At the membrane boundaries for x = 0 
and x = l , concentrations c
0
and 0 are posed, respectively (Figure 9.1 ).
The fi rst approximation to the mathematical description reads
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
c
t
D
c
x
D
c
x
w
c
x
c
t
D
c
x
D
c
1
11
2
1
2
12
2
2
2
1
2
21
2
1
2
22
2
2
=
+
±
=
+
∂∂
x
l
2
0
⎧
⎨
⎪⎪
⎩
⎪
⎪
< <
∈
+
x
t
R
,
(9.1)
for initial and boundary conditions (indexes 1 and 2 refer to oxygen and nitrogen, 
respectively). 

---

Air Enrichment by Polymeric Magnetic Membranes
161
c x
c x
c
t
c
c
t
c
c l t
c l t
1
2
1
01
2
02
1
2
0
0
0
0
0
0
0
0
,
,
,
,
,
,
(
)
=
(
)
=
( )
=
( )
=
( )
=
( )
=
The experiment enabled the measurement of the permeation rates
[25] 
, whereas the 
composition of mixture was determined using a gas chromatograph.