Environmental Engineering Reference
In-Depth Information
The van't Hoff equation is
=
CRT
(strictly valid for dilute solutions).
(9.37)
Using equation (9.35)
m
b
=
C
m
C
b
;
p
b
=
C
p
C
b
.
(9.38)
We can write the solvent flux as
K
C
p
C
b
−
b
C
m
=
C
b
+
b
J
P
(9.39)
K
−
b
C
m
C
p
C
b
=
P
C
b
−
.
(9.40)
Note
:
C
m
−
C
p
e
+
(
v
p
/
D
)
δ
C
p
=
(9.41)
C
b
−
C
m
−
C
p
C
m
−
C
p
C
b
−
C
p
=
C
p
·
(9.42)
C
b
C
b
−
C
b
e
+
(
v
p
/
D
)
δ
R
obs
.
=
(9.43)
Substituting,
K
−
b
e
(
v
p
/
D
)
δ
R
obs
.
J
=
P
(9.44)
Note
: the solvent flux is a function of
bulk feed osmotic pressure
degree of concentration polarization
observed rejection.
Specific correlations for concentration polarization using
flat sheet membranes
have
been derived [15].
Laminar flow
C
m
C
b
=
ε
o
)
1
/
3
1
.
536(
+
1
ε
o
1
.
(9.45)
Near channel entrance
5
1
exp
1
/
2
ε
o
3
C
m
C
b
=
ε
o
+
−
−
+
.
1
(9.46)
Far downstream
C
m
C
b
=
1
o
+
1
,
(9.47)
3
σ
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