Agriculture Reference
In-Depth Information
two regions, for example,
k
m
s
and
k
im
s
in Equations 8.5 and 8.6, respectively.
However, such a distinction in reaction coefficients was not incorporated in
this model and a common parameter
k
s
was thus used.
The retention mechanism associated with the mobile and immobile phases
of Equations 8.3 and 8.4 was considered as an equilibrium linear sorption by
van Genuchten and Wierenga (1976) and was extended to the nonlinear or
Freundlich type by Rao et al. (1979). Recently, multiple ion retention expressed
on the basis of ion-exchange equilibrium reactions was successfully incorpo-
rated into the mobile-immobile model by van Eijkeren and Lock (1984) and
Selim, Schulin, and Flühler (1987). Here, it is considered that reversible solute
reactions are governed by the second-order kinetic approach. Specifically, the
rates of reaction for
S
m
and
S
im
were considered as (Selim and Amacher, 1988):
ρ
∂
∂
m
S
t
m
=
Θ
m
m
−ρ
m
k
C
k S
(8.23)
1
2
and
ρ
∂
∂
im
S
t
im
=
im
im
-
ρ
im
Θ
k
C
k S
(8.24)
1
2
where
k
1
and
k
2
are forward and backward rate coefficients (day
-1
), respec-
tively. Here φ
m
and φ
im
represent the vacant or unfilled sites (μg per gram
soil) within the dynamic and the stagnant regions, respectively. In addition,
the terms φ
m
and φ
im
can be expressed as:
m
=
S
−
m
=f
SS
−
m
m
S
(8.25)
max
max
im
=
− =− −
im
(1
f
)
im
im
S
SS
S
(8.26)
max
max
where
S
max
,
S
max
m
, and
S
max
im
are the total number of sites in the soil matrix,
total sites in the dynamic region, and the total in the less accessible region
(mg/kg soil), respectively. These terms are related by:
=
S
+
S
S
m
im
max
(8.27)
max
max
We also assume
S
max
to represent the combined total of occupied and unoc-
cupied sites, that is, maximum adsorption capacity of an individual soil, and
it is regarded as an intrinsic property of the soil.
An important feature of the second-order retention approach (Equations
8.23 and 8.24) is that similar reaction rate coefficients (
k
1
and
k
2
) associ-
ated with the dynamic and stagnant regions were chosen. Specifically, it is
assumed that the retention mechanism is equally valid for the two regions of
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