Membrane Gas Separation

List of symbols 
J
fl ux or permeation rate
D
diffusivity
C
gas concentration
C
2
, C
1
upstream and downstream gas concentration
p
2
, p
1
upstream and downstream pressure
L
membrane thickness
P
permeability
S
solubility
 
η
 
atomic surface density
 
σ
 
kinetic diameter
ε
well depth
d
theoretical pore size (between surface nuclei)
d
* 
experimental PALS pore size ( d minus electron cloud thickness)
W
difference in the potential energies outside and inside of the pore
 
λ
 
mean free path
d
min
minimum pore size for barrier - free transport
d
K
minimum pore size for dominant Knudsen transport
Δ
E
a
energy barrier for activation diffusion
Δ
H
a
enthalpy of adsorption for activation diffusion
Δ
E
S
energy barrier for surface diffusion
T
temperature
n
surface concentration of pore entrance sites
v
f
free volume
q
heat of adsorption
K
Henry ’ s law coeffi cient, K = K
0
exp( q / RT ), where K
0
is a constant
m
mass of gas molecule
τ
pore tortuosity
u¯ 
average molecular gas speed
 
ρ
 
g
probability that the molecule will travel towards a transition
 
ρ
 
E
probability that the molecule will pass through the transition

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Modelling Gas Separation in Porous Membranes 
107
u
velocity of the molecule through the transition
 
λ
 
jump length from the reactant cavity to the product cavity
R
resistance (= L / P )
l
pore length
x
K
fraction of pore length in which Knudsen dominates
ε
=
( z )
potential energy between two parallel planes