Agriculture Reference
In-Depth Information
At large time (
t
→ ∞) when both sites achieve local equilibrium yield the
following expressions hold. For type 1 sites:
=
Θ
ρ
S
C
k
k
1
1
Θφ −ρ=
C
0,
or
=
ω
k
k
S
(6.36)
1
2
1
1
φ
2
and for type 2 sites:
=
Θ
ρ
S
C
k
k
2
3
Θφ −ρ=
C
0,
or
=
ω
k
k
S
(6.37)
3
4
2
2
φ
4
Here ω
1
and ω
2
represent equilibrium constants for the retention reactions
associated with type 1 and type 2 sites, respectively. These formulations are
analogous to expressions for the original second-order formulation, except-
ing that ω
1
and ω
2
are functions of the vacant sites ϕ.
In the following analysis we followed similar overall structure for the second-
order formulation to that described earlier where three types of retention sites
are considered with one equilibrium-type site (
S
e
) and two kinetic-type sites,
S
1
and
S
2
. Therefore, we have ϕ now related to the sorption capacity (
S
max
) by:
S
=φ+++
S
SS
(6.38)
max
e
1
2
The governing retention reactions can be expressed as (Ma and Selim, 1998):
ρ=Θφ
SKC
e
(6.39)
d
ρ
∂
S
t
1
∂
=Θφ−ρ
C
k
k
S
(6.40)
1
2
1
ρ
∂
S
t
2
k
∂
=Θφ−ρ
C
(
k
+
)
S
(6.41)
k
3
4
4
2
ρ
∂
S
t
irr
∂
=Θ
C
k
(6.42)
s
The unit for
K
e
is cm
3
μg
-1
,
k
1
and
k
3
have a derived unit of cm
3
μg
-1
h
-1
;
k
2
,
k
4
,
k
5
, and
k
s
are assigned a unit of h
-1
.
6.5 Experimental Data on Retention
The input parameter
S
max
of the second-order model is a major param-
eter and represents the total sorption of sites.
S
max
, which is often used
to characterize reactive chemical sorption, can be quite misleading if the
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