Environmental Engineering Reference
In-Depth Information
∴
Zeroth moment decreases with
z
since solute is lost in chemical reaction.
d
c
d
s
,
m
1
(
z
)
=−
lim
s
→
0
d
c
d
s
=
d
c
0
d
s
c
0
z
e
λ
z
d
d
s
e
λ
z
where
+
v
D
0
A
−
1
/
2
4
D
0
d
A
d
d
s
=
−
2
2
D
0
1
/
2
0
and
+
d
s
.
Hence,
−
m
1
(0)e
λ
0
z
m
0
(0)
z
e
λ
0
z
m
1
(
z
)
=−
+
γ
solution in terms of moments.
µ
1
(
z
)
=
µ
1
(0)e
λ
0
z
γ
λ
0
z
−
z
3
R
k
p
2
(1
−
α
)
−
d
A
d
s
=
α
+
1
s
k
p
2
!
3
R
(1
−
α
)
+
k
+
α
d
d
s
=
γ<
lim
s
→
0
0
.
Exit of pulse concentration gradient (C.G.) is retarded by loss of reactant. Note that if we
are to get an output pulse,
k
must be very small so that we don't lose all reactant, or
z
must
be small.
From before:
K
a
→∞⇒
k
a
=
0 or non-reversible first-order reaction but
k
a
=
0
∂
2
c
i
∂
c
i
∂
D
i
β
2
r
∂
c
i
−
ρ
p
β
t
=
+
k
a
c
i
∂
r
2
∂
r
s
c
i
ρ
p
β
D
i
β
2
D
i
r
c
i
c
i
−
+
k
a
+
=
0
β
s
k
a
D
i
+
ρ
p
β
r c
i
2
c
i
+
−
r c
i
=
0
.
b
2
≡
k
a
ρ
p
D
i
Note: lim
s
→
0
=
≡
b
0
.
2
v
0
2
D
0
−
v
0
2
D
0
D
0
c
0
e
λ
z
c
(
z
)
=
where
λ
=
+
[
s
+
h
(
s
)]
Search WWH ::
Custom Search