Agriculture Reference
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where S 1 and S 2 are the amounts of solute retained by sites I and sites II,
respectively, ST T is the total amount of solute retained by the soil matrix (mg
kg -1 ), and k 1 , k 2 , k 3 , and k 4 are the associated rate coefficients (h -1 ). The nonlin-
ear parameters n and m are considered to be less than unity and n m . For
the case n = m = 1, the retention reactions are of the first-order type and the
problem becomes a linear one.
This two-site approach was also considered for the case where type I sites
were assumed to be in equilibrium with the soil solution, whereas type II sites
were considered to be of the kinetic type. Such conditions may be attained
when the values of k 1 and k 2 are extremely large. Under these conditions, a
combination of equilibrium and kinetic retention is (Selim, Davidson, and
Mansell, 1976):
1 =
n
S
K
C
(5.4)
f
Θ
ρ
S
t
2
=
m
k
C
k S
(5.5)
3
4
2
Jardine, Parker, and Zelazny (1985) found that the use of the equilib-
rium and kinetic two-site model provided good predictions of BTCs for
Al in kaolinite at different pH values. Selim, Davidson, and Mansell (1976)
found that the two-site model yielded improved predictions of the exces-
sive tailing of the desorption or leaching side and the sharp rise of the
sorption side of the BTCs in comparison with predictions using single-
reaction equilibrium or kinetic models. The two-site model has been used
by several scientists, including DeCamargo, Biggar, and Nielsen (1979),
Nkedi-Kizza et al. (1984), Jardine, Parker, and Zelazny (1985), and Parker
and Jardine (1986), among others. The model proved successful in describ-
ing the retention and transport of several dissolved chemicals, including
Al, P, K, Cr, Cd, 2,4-D, atrazine, and methyl bromide. However, there are
some inherent disadvantages of the two-site model. First, the reaction
mechanisms are restricted to those that are fully reversible. Moreover, the
model does not account for possible consecutive-type solute interactions
in the soil system.
5.2 Multireaction Models
A schematic representation of the multireaction model is shown in Figure 5.4.
In this model we consider the solute to be present in the soil solution phase
(C) and in five phases representing solute retained by the soil matrix as S e , S 1 ,
S 2 , S 3 , and S irr . We further assume that S e , S 1 , and S 2 are in direct contact with
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