Environmental Engineering Reference
In-Depth Information
hydrophobia interactions, sequestration, ion-exchange, proton-transfer, coordination
reactions or covalent bond formation with soil or sediment organic matter, and (d)
diffusion into mineral or organic matter micropores. Several adsorption models can be
used to describe the adsorption of NMs on soils (Table 15.6).
In the soil literature, the distribution of a contaminant between the solid and
liquid phase is given by the partitioning model, which is equal to the Freundlich model
when n = 1 (Table 15.6). Selection of an adsorption isotherm will affect the mass
balance and the governing fate and transport equations (e.g., eqs. 15.13, 15.38). For
example, because transport rates in soil or porous media are usually very slow, we can
assume that the adsorption/desorption process is instantaneous. If the partitioning model
is used to represent the adsorption isotherm and the other Rj = 0, eq. 15.13 becomes:
L
dx
2
\ ~1
J
^ d
2
c
fT
^
^ d
2
c
-i
c
A
~\
/,, p
h
\
dc
„
dc
dc
dx
dc
dc
\
a
6 / dt
dt
—
+ u— = D
L
—-
(K
d
^)—
L
dx
2
or
R— + u— = D
L
—
(Eq. 15.42)
dx
dt
where 6 = the soil porosity, unitless; and R = (1+ Kdpb/6), the retardation coefficient. If
the Langmuir model is used and the other Rj = 0, eq. 15.13 becomes:
^
+
u
^
=DL
^£_(£!i)!lpl
(Eq. 15.43)
dx
2
6
dt
\ -1
;
dt
dx
Table 15.6
Commonly used sorption models for organic and inorganic solutes (Bhandari
Sorption Model
Mathematical Representation
Partitioning Model
S - K
d
C
,
Freundlich Model
S = K
r
c;
Langmuir Model
S = S
a
K
L
c,
/(i +
K
L
c,)
Brunauer-Emmett-Teller
„
S
a
K
EET
C
f
o — •
(BET) Model
(c, -
C.)[l +
(K
EET
-lXc./C.
Dual Mode Model
S
=
K
d
c,
+
Langmuir-Hinshelwood
N + s
s
« A ^ F + s
s
dN/dt = -K.S
S
N + KjA; dA/dt = k
a
S
s
N-K
d
A-K
r
A; S = S
s
o
- A
where,
S =
mass of solute (NMs) sorbed per unit dry mass of soil;
K
d
=
linear phase distribution constant;
C
e
=equilibrium concentration of NMs;
K
F
=
Freundlich adsorption coefficient;
n =
empirical coefficient
or fitting parameter to represent sorption energy and heterogeneity factor;
S
0
=
sorption capacity;
K
L
=
sorption energy factor for the Langmuir model;
K
BET
=
sorption energy factor for the BET model;
C, =
molar solubility of NMs;
n =
types of sorption-sites within heterogeneous SOM;
N=
NMs' concentration
in solution;
S, =
concentration of available sites for NM adsorption,
A =
concentration of adsorbed NPs;
F
=
concentration of fixed NP;
K
a
=
rate coefficient for adsorption;
Kj =
rate coefficient for desorption;
K
s
=
rate coefficient for reaction; < = elapsed time; and
S
S
o =
concentration of total sites for NP adsorption.
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