Environmental Engineering Reference
In-Depth Information
Where,
r
is the bulk dry density of the soil,
S
i
is the adsorbed concentration
of the component per unit mass of the soil solids. The reversible term (
∂
∂
S
t
) is
often used to describe the adsorption rate (Kirkner and Reeves, 1988; Davis
and Kent, 1990). The equilibrium partitioning between the adsorbed phase
and the aqueous phase of the chemical components are commonly measured
under controlled temperature and applied pressure, and the resulting corre-
lations of
S
i
versus
C
i
are called adsorption isotherms. Different equilibrium
models are used to describe sorption of heavy metals in soils. Assuming
instantaneous equilibrium in sorption reactions and linear isotherms:
i
∂
∂
S
C
i
=
K
di
(5.24)
i
Where,
K
di
is the distribution coefficient of species i. Retardation factor
(
R
di
) is also introduced and used in modeling species transport to account
for linear sorption expressed as:
K
n
R
=+
1
r
di
(5.25)
di
The retardation factors of species i (
R
di
) define the relative rate of trans-
port of a non-sorped species to that of a sorped species. For a non-sorped
species,
R
di
= 1. Simple isotherm sorption models ignore the potential
effects of variations in pH, solute composition and ionic strength, redox
potential, or processes such as competitive adsorption. Alternatively, more
robust and complicated sorption models include ion-or ligand-exchange,
mass action models, and surface complexation models are also reported
in the literature (Kirkner and Reeves, 1988; Davis and Kent, 1990; Stumm
and Morgan, 1995; Bethke, 1996).
5.3.5.2 Aqueous reactions
In aqueous phase reactions, any complex j is the product of i's reactant
components expressed as:
N
c
∑
j
= 1,2,…,N
x
(5.26)
aC
↔
X
ij
i
j
i
=
1
where,
C
i
is the chemical formula for component i,
X
j
is the chemical for-
mula for the complex
j
,
a
ij
is the stoichiometric coefficient in complex
j
for
component
i
. The law of mass action implies that:
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