Environmental Engineering Reference
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and
!
3
k
p
R
(1
−
α
)
−
sinh
bR
+
bR
cosh
bR
h
(
s
)
=
1
sinh
bR
α
k
p
R
D
i
bR
cosh
bR
+
−
s
→
0
e
λ
z
)
m
0
(
z
)
=
s
→
0
c
(
z
)
lim
=
(lim
s
→
0
c
0
)
m
0
(0)
(lim
3
k
p
R
(1
−
α
)
−
sinh
b
0
R
+
b
0
R
cosh
b
0
R
lim
b
h
(
s
)
=
1
sinh
Rb
0
≡
h
0
α
k
p
R
D
i
!
→
b
0
bR
cosh
bR
+
−
2
v
0
2
D
0
−
v
0
2
D
0
D
0
h
0
≤
m
0
(0)e
λ
0
z
h
0
(
z
)
=
where
λ
0
≡
+
0
.
∴
m
0
(
z
) decreases with increasing
z
.
C.3
Question
C.1 Breakthrough curves in ion-exchange columns. Experiments are proposed for a col-
umn packed with H
+
/
Na
+
ion-exchange resin. The resin has been totally regenerated
with acid. A step function of sodium-chloride solution is injected into the column
at time
t
0. Sketch output curves of concentration vs time for the Cl
−
,Na
+
, and
H
+
ions. It is proposed that only a pH meter at the outlet is needed to get informa-
tion about the breakthrough curves and of pore diffusion and kinetics. Discuss this
possibility and its significance.
=
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