Agriculture Reference
In-Depth Information
n
−
1
i
l
∂
()
S
t
θ
ρ
∑
2
i
=
kC
α
C
−+
(
k
kS
) ()
( 7. 2 3)
3,
i
i
ij
,
j
4,
i
s i
,
2
i
∂
j
=
1
∂
()
S
t
si
=
kS
()
( 7. 2 4)
si
,
si
∂
∂
()
S
θ
ρ
irri
=
k
C
( 7. 2 5 )
irri
,
i
∂
t
When competition is ignored, that is, α
i
,
j
for all
j
≠
i
, Equation 71 holds for
single-species
n
th-order kinetic sorption. Examples of the capability of this
approach to describe the transport of the competitive arsenate and phos-
phate behavior in soil columns are presented in a subsequent section.
7.7 Competitive Langmuir Model
The Langmuir equation can be extended to account for competitive sorption
of multiple heavy metals in multicomponent systems. In the multicompo-
nent Langmuir approach, one assumes that there is only one set of sorp-
tion sites for all competing ions. Furthermore, the model also assumes that
the presence of competing ions does not affect the sorption affinity of other
ions. Because of these overly simplified assumptions, the modeling ability of
the model is rather limited. It should be noted that with the assumption of
a fixed number of reaction sites, the surface complexation model described
in this chapter gives Langmuir-type adsorption isotherms under constant
pH and ionic strength. For time-dependent sorption of competing ions, the
multicomponent second-order kinetic equation was proposed in the form of:
l
∂
∂
=λ
θ
S
t
∑
i
()
CS
−
S
−λ
()
S
( 7. 2 6 )
fi
i
max
j
bi i
ρ
i
=
1
Under equilibrium conditions, Equation 7.26 yields:
() ()
()
()
=λ
λθ
fi
K
Li
λρ
( 7. 2 7 )
fi
bi
where λ
f
and λ
b
(h
-1
) are the forward and backward rate coefficients, respectively.
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