Agriculture Reference
In-Depth Information
where
m
im
=
C
C
=
C
C
m
,
im
c
c
(8.36)
0
0
s
m
=
S
m
/
S
max
,
s
im
=
S
im
/
S
max
, Φ
m
= φ
m
/
S
max
, Φ
im
= φ
im
/
S
max
, (8.37)
P
=
vL
/
D
Θ,
(8.38)
= α
L
/
v
(1 - μ),
(8.39)
μ = Θ
m
/Θ,
(8.40)
X
=
x
/
L
,
(8.41)
T
=
vt
/
L
Θ,
(8.42)
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). In addition, we have defined:
Ω =
S
max
ρ/
C
o
Θ,
(8.43)
κ
s
=
k
s
Θ
L
/
v
,
(8.44)
κ
1
=
k
1
Θ
2
C
o
L
/ρ
v
,
(8.45)
κ
2
=
k
2
Θ
L
/
v
.
(8.46)
Here, κ
s
, κ
1
, and κ
2
are dimensionless kinetic rate coefficients that incorporate
v
and
L
.
8.4.1 Initial and Boundary Conditions
The corresponding initial and boundary conditions associated with the sec-
ond-order mobile-immobile model can be expressed as:
C
m
=
C
im
=
C
i
(
t
= 0, 0 <
x
<
L
)
(8.47)
S
m
=
S
im
=
S
i
(
t
= 0, 0 <
x
<
L
)
(8.48)
m
∂
∂
C
x
mm
vC
=
vC
− Θ
D
(
xt
=<
,
t
)
(8.49)
o
p
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