Agriculture Reference
In-Depth Information
absence of an electrostatic term in the empirical models, whereas it is man-
datory in mechanistic models. Mechanistic models, also known as chemical
models, are expected to provide a close representation of the real adsorption
phenomenon in the soil system. Nevertheless, due to the complexity of chem-
ical model, empirical models are utilized in most solute studies with soils
and geological media. Moreover, empirical models have been widely used
in soil science and environmental studies related to metal and anion adsorp-
tion and pesticide retention in soils. A listing of such models is presented in
Table 1.1. These models do not take into consideration the electrostatic influ-
ence of the electrically charged surfaces in the solution, or the influence of
changes in surface charges due to the composition of the soil solution. In the
empirical model, the model form is chosen a posteriori from the observed
adsorption data and to enable a satisfying fitting of the experimental data
TABLE 1.1
Selected Equilibrium and Kinetic Type Models for Heavy Metal
Retention in Soils
Model
Formulation
a
Equilibrium Type
Linear
S
=
K
d
C
Freundlich
S
=
K
f
C
b
General Freundlich
S
/
S
ma
x
= [ω
C
/(1 + ω
C
)]
β
Rothmund-Kornfeld ion exchange
S
i
/
S
T
=
K
RK
(
C
i
/
C
T
)
n
Langmuir
S
/
S
max
= ω
C
/[1 + ω
C
]
General Langmuir Freundlich
S
/
S
max
= (ω
C
)
β
/[1 + (ω
C
)
β
]
Langmuir with Sigmoidicity
S
/
S
max
= ω
C
/[1 + ω
C
+ σ/
C
]
Kinetic Type
First-order
∂∂=θρ−
St k
/
( /)
CkS
f
b
n
∂∂=θρ−
St k
/
( /)
CkS
n
th order
f
b
∂∂= θρ −
St
/
k
( /)(
C
C
)
Irreversible (sink/source)
s
p
∂∂=θρ
St k
/
( /)
CS
(
−
S
)
Second-order irreversible
s
max
(
)
∂∂=θρ
St k
/
( /)
C SSkS
−
−
Langmuir kinetic
f
max
b
Elovich
∂
S
/∂
T
=
A
Exp (−
Bs
)
Power
St KC
nm
∂∂=θρ
/
( /)
(
)
∂∂=θρ−
St K
/
( /) CC*
Mass transfer
a
A, B, b, C
*,
C
p
, K, K
d
, K
RK
, k
b
, k
f
, k
s
, n, m, S
max
, ω, β, and σ are adjustable
model parameters, ρ is bulk density, Θ is volumetric soil water content,
C
T
is total solute concentration, and
S
T
is total amount sorbed of all
competing species.
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