Environmental Engineering Reference
In-Depth Information
u
ei
is ionic species migration velocity (e.i., electromigration velocity),
given as:
1
∂
∂
Φ
1
(5.42)
uv
=−
F
ei
i
i
t
2
x
t
2
Comparison of experimental results with model predictions showed
good agreement for a case of acetic acid removal from a 40-cm length
kaolinite sample (Shapiro and Probstein, 1993).
Acar et al., (1989) presented a one dimensional model to estimate pH
distribution during EK driven mass transport in contaminated soil. The
model demonstrated the impact of electrolysis reactions on pH distribu-
tion during EK process. Alshawabkeh and Acar (1992) described a modi-
fied formulation accounting for the chemical reactions of adsorption/
desorption, precipitation/dissolution, and acid/base reactions. The gov-
erning equation of one dimensional mass transport due to applied electric,
hydraulic, and chemical gradient in their model is given as:
2
⎡
⎢
2
2
⎤
⎥
∂
nC
t
∂
∂
C
x
)
∂
Φ
∂
∂
h
x
(
i
=
D
i
+
Cuk
+
+
k
i
i
i
eo
h
∂
2
∂
x
2
2
(5.43)
+
∂
∂
c
x
)
∂
Φ
∂
∂
h
x
⎡
⎢
⎤
(
i
uk
+
+
k
⎥
+
nR
i
eo
h
i
∂
x
The left side of the equation, which is the mass conservation, is also
described as:
( )
∂
nC
x
=−∇
()
+
i
(5.44)
i
J
R
i
∂
t
Where, n is the porosity of the media,
J
i
is the total mass flux of species,
and
R
i
is the production rate of the
i
th
aqueous chemical species per unit
fluid volume due to chemical reactions such as sorption, precipitation-dis-
solution, oxidation/reduction, and aqueous phase reactions. Alshawabkeh
and Acar (1996) enhanced their model to predict the reactive transport of
hydrogen, lead, hydroxyl, and nitrate ions. The model accounts for lead
hydroxide precipitation/dissolution, lead sorption (assuming linear pH
dependent isotherm) and water equilibrium reactions. Comparisons of
experimental results with model predictions for different species transport
indicated that the model is capable of capturing different EK processes suc-
cessfully (Acar et al., 1997).
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