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Freundlich equation, followed by estimating the competition coefficients α
i,j
through fitting the experimental isotherms of binary and ternary mixtures
to the SRS equation (Roy, Hassett, and Griffin, 1986a). The competition coef-
icients α
i,j
in the SRS equation represent the relative selectivity of the sorbent
to the heavy metal species. It is demonstrated that the SRS equation with
competition coefficients estimated through nonlinear least squares optimi-
zation successfully describes the experimental competitive adsorption iso-
therms of Ni and Cd on three different soils (Liao and Selim, 2010). Gutierrez
and Fuentes (1993) employed the SRS equation to represent the competitive
adsorption of Sr, Cs, and Co in Ca-montmorillonite suspensions. They found
that the SRS competition coefficients α
i,j
obtained from experimental data
on binary mixtures successfully predicted the competitive adsorption of the
ternary mixture Sr-Cs-Co. Similarly, Bibak (1997) found that values of the
SRS competitive coefficients obtained from binary sorption experiments suc-
cessfully predicted sorption data of the ternary solute mixture Cu-Ni-Zn.
The SRS equation was successfully used to describe competitive sorption of
Cd, Ni, and Zn on a clay soil by Antoniadis and Tsadilas (2007). In addition,
the SRS equation was also used by Wu et al. (2002) in representing the com-
petitive adsorption of molybdate, sulfate, selenate, and selenite on γ-Al
2
O
3
surface where relative affinity coefficients were used instead of competitive
coefficients. The relative affinity coefficients were calculated as the ratios of
the proton coefficients of competing anions. The simulation result showed
that the sorption affinity of anions on γ-Al
2
O
3
surface decreased in the order
of MoO
4
2-
> SeO
3
2-
> SeO
4
2-
> SO
4
2-
.
7.6 Competitive Multireaction Model (CMRM)
The kinetic (time-dependent) sorption models of the Freundlich type given
were developed to simulate the sorption of solutes during their transport in
soils and aquifers (Selim, 1992). Zhang and Selim (2007) extended the equi-
librium Freundlich approach to account for kinetic competitive or multiple-
component systems. Specifically, the model accounts for equilibrium and
kinetic adsorption in a way similar to the SRS equation described above.
This model represents a modification of the multireaction and transport
model (MRTM), which accounts for equilibrium and kinetic retention of the
reversible and irreversible type as discussed in Chapter 5. MRTM accounts
for linear as well as nonlinear reaction processes of equilibrium and/or
kinetic (reversible and irreversible) type. The model version discussed here
is that with reversible as well as irreversible sorption of the concurrent and
consecutive type. Here
S
e
represents the amount retained on equilibrium
sites (mg kg
-1
);
S
1
and
S
2
represent the amount retained on reversible kinetic
sites (mg kg
-1
);
S
s
represents the amount retained on consecutive irreversible
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