Environmental Engineering Reference
In-Depth Information
10
4
21
s
s
�
�
�
�
(17)
(
)
( )
( )
2
V rR
,
= πqe s
3
FC
M
x
−
FC
M x
-
€
‚
€
‚
FC
FC
11
5
ƒ
„
ƒ
„
32
R
R
-
where r is the distance between the an atom and the nearest point on the cylinder,
R the radius of the nanotube,
x
= r/R the ratio of distance to radius and θ the same
surface number density as above. Here the following integrals are used:
π
1
( )
∫
Mx
=
d
ϕ
(18)
(
)
2
n
n
2
1
+− ϕ
x
2
x
cos cos
0
Simpson integration is used to get the final potential. For simplicity of program-
ming, the following expression was adopted to represent the results of the integra-
tion
����������
10
4
4
4
4
V rR
(, )
s
s
s
s
s
=
a
+
b
+
c
+
d
+
e
€‚€‚€‚€‚€‚
e ƒ„ƒ„ƒ„ƒ„ƒ„
(19)
10
4
3
2
R
R
R
R
R
where a-e are constants dependent on the kind of fluid and the R radius of the
nanotubes. They can be determined from the numerical integration. To binary
system, the selectivity is defined as
**
21
rr
xy
/
/
pb
S
=
1
2
=
rr
(20)
**
xy
2
2
pb
12
where
x
refers to a pore mole fraction and
y
to a bulk mole fraction. The subscripts
of
x
and
y
refers to different components in the mixture. is the reduced number
density of the bulk fluid. is that of the pore fluid [1, 131, 139, 143, 144, 145].
1.2.1.3 THEORETICAL MODELS FOR ADSORPTION INTEGRAL
CALCULATING
Strongly activated carbons possess a broad distribution of micropores because
some walls between adjacent micropores burn off. In this case the DR and DA
equations cannot give a satisfactory representation of adsorption data. Based on
the equations mentioned before that describe adsorption in uniform micropores,
Izotova and Dubinin proposed the following two-term equation for description of
adsorption on solids with bimodal microporous structure:
2
2
��
A
��
A
0
I
0
II
aa
=
exp
−
B
-
+
a
exp
−
B
-
€‚
€‚
mi
mi
I
mi
II
ƒ„
b
ƒ„
b
(21)
-
-
Here parameters and correspond to micropores and and correspond to super mi-
cropores. Eq. (21) has been often applied to describe adsorption on non- uniform
microporous solids. The model studies showed that Eq. (21) is especially suit-
able for description of adsorption on microporous solids that possess two types
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