Environmental Engineering Reference
In-Depth Information
electromigration (
v
em
), and the electroosmotic (
v
eo
) velocities given in sum-
mation as the advective velocity (
v
adv
):
(2.11)
v
=+
v
v
adv
em
eo
and, from Eqs. 2.4 & 2.7,
v
where,
v
=
z F
Φ
eVt
hs
The electromigration velocity in equation 2.11 is the speed of ion move-
ment in the pore water caused by an electric field in infinitely dilute solu-
tions. In the pore fluids with finite ion concentrations, which more closely
resemble the electrochemical systems of contaminated clays, the influence
of the inter-ionic attraction should be considered. Generalized ion mobil-
ity that accounts for the possibility of interactions between the ionic spe-
cies can be used to modify the electrochemical potentials of individual ions
in the flux term [Eq. 2.9] when strong chemical reactions between ionic
species are considered (Newman, 1991). The resulting relative electric field
due to the retardation effects of dissymmetrical ionic atmosphere during
ion transport was considered in Cao's model (1997) as described below.
The electroosmotic component of the electrokinetic transport is depended
on the electroosmotic velocity of the fluid flow. The classical H-S equation
expresses this parameter as a function of the field gradient. Due to the
tight coupling between the ion concentrations and electric potential - as
the ions contribute to the local electric potential themselves - the use of
H-S electro-osmotic velocity in transport determination in clay soils can
result in nonlinear predictions (Ravian and Zaslavsky, 1967; Chu, 2005).
Hence, uncoupling this parameter from the electric potential using the
surface conductivity
s
s
, and the resulting proportion of the current trans-
ferred over the solid-liquid interface
i
s
, provide an intrinsic electroosmotic
velocity dependent on clay surface properties only, as first introduced by
Khan (1991) in equation 2.8.
The model predicted distribution and evolution of bulk conductivity,
s
b
and field strength,
E,
in kaolinite clay containing Pb(NO
3
)
2
at the initial
concentration of 0.05M in its pore fluid are presented in Figures 2.4 and 2.5,
respectively (Cao, 1997). In Figure 2.4, the normalized distribution of the
conductivity (normalized by the initial conductivity of
0.28
Siemens/m)
shows a consistent decrease in the conductivity at the cathode region, and
a steady spread of the lower conductivity towards the anode area over time.
Part of this result is attributed to the decrease of dissolved lead concentra-
tion, which prevail over the increase of H+ concentration. The change of
the conductivity is influenced by combination of three factors: (i) the initial
=
⎡
⎤
⎥
⋅
i
A
em
i
i
s
s
⎢
eo
n
s
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