Agriculture Reference
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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
Ω
(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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