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c= C
C o
(6.19)
S
S max
s=
(6.20)
Φ
= S max
(6.21)
qL
D Θ
P=
(6.22)
where T is dimensionless time equivalent to the number of pore volumes
leached through a soil column of length L , and P is the Peclet number
(Brenner, 1962). Given the above variables, Equations 6.15, 6.7, and 6.8 are
rewritten in dimensionless form, respectively, as (Selim and Amacher, 1988):
2
c
T
+Ω
s
T
+
s
TP
=
1
c
X
c
X
1
2
κ
s
(6.23)
2
s
T
1
= κΦ κ
c
(6.24)
s
11
2
1
s
T
2
= κΦ κ
c
(6.25)
s
32
4
2
where
= S
C o
ρ
Θ
max
(6.26)
k
Θ
L
s
=
κ
(6.27)
s
q
2
2
k
Θ
ρ
C L
q
k
Θ
ρ
C L
q
1
o
3
o
κ =
and
κ =
(6.28)
1
3
Here, κ s , κ 1 , κ 2 , κ 3 , and κ 4 are dimensionless kinetic rate coefficients that
incorporate q and L . As will be shown in a later section, these dimensionless
variables (including Ω, c , s , and ϕ) represent a convenient way to study the
sensitivity of the model to reduced variables.
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