Agriculture Reference
In-Depth Information
m
∂
∂
C
x
mm
0
=
vC
− Θ
D
(
xt
=>
0,
t
)
(8.50)
p
m
∂
∂
C
x
=
0(
xLt
=
,
≥
)
(8. 51)
These conditions are similar to those described earlier for the transport
of a solute pulse (input) in a uniform soil having a finite length
L
where a
steady water flux
v
was maintained constant. The soil column is considered
as having uniform retention properties as well as having uniform ρ and Θ.
It is further assumed that equilibrium conditions exist between the solute
present in the soil solution of the mobile water phase (i.e., interaggregate)
and that present in the immobile (or interaaggregate) phase. This necessary
condition is expressed by Equations 8.47 and 8.48. Uniform initial condi-
tions were assumed along the soil column. It is assumed that an input heavy
metal solution pulse having a concentration
C
o
was applied at the soil surface
for a time duration
t
p
and was then followed by a solute-free solution. As a
result, at the soil surface, the third-type boundary conditions were those of
Equations 8.49 and 8.50. In a dimensionless form, the boundary conditions
can be expressed as:
m
D
c
x
∂
∂
mm
1
=−Θ
c
(
XTT
=<
0,
)
(8.52)
p
m
D
c
x
∂
∂
mm
0
=−Θ
c
(
XTT
=>
0,
)
(8.53)
p
and at
x
=
L
, we have
m
∂
∂
c
x
=
0(
XLT
=
,
>
)
(8.54)
where
T
p
is dimensionless time of input pulse duration of the applied solute
and represents the amount of applied pore volumes of the input solution.
8.4.2 Sensitivity Analysis
Figures 8.9 through 8.12 are examples of simulated BTCs to illustrate the
sensitivity of the proposed second-order reaction, when incorporated into
the mobile-immobile concept, to various model parameters. As shown,
several features of the mobile-immobile concept dominate the behavior of
solute transport and thus the shape of simulated BTCs. For this reason, we
restrict the discussion here to the influence of parameters pertaining to the
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