Environmental Engineering Reference
In-Depth Information
)
+∇−
)
(
(
(5.3)
J
=∇−
k hk
E
w
h
eo
The total one-dimensional fluid flux can therefore be found as:
∂
∂
h
x
∂
∂
E
x
(5.4)
J
=−
k
−
k
w
h
eo
Under combination of applied hydraulic and electrical gradients, con-
solidation of soil is expected to take place and influence the hydraulic
conductivity value (
k
h
) (Acar, et al., 1997). However, in the mathemati-
cal formulation of the process,
k
h
is generally assumed to be constant in
time and space because of: (i) the lack of theoretical mechanisms that can
describe and capture the effect of pore fluid chemistry on soil fabric and
consequently the hydraulic conductivity, and (ii) the uncertainties in eval-
uating the hydraulic conductivities are more significant than the changes
expected in its values. Also, the value of
k
eo
is usually assumed to be con-
stant during the EK process as long as there is no change in the concentra-
tion of ions or pH of the pore fluid, which is not always a valid assumption
(Gray and Mitchell, 1967; Lorenz, 1969; Hunter, 1981).
The ratio of coefficient of EO permeability (
k
eo
) to hydraulic conduc-
tivity (
k
h
) significantly affects the contribution of each applied gradient
to the total flux. Soil type, microstructure, and pore fluid conditions are
among the factors that impact this ratio. In coarse-grained soils this ratio
is very small due to almost non-existing EO flow and relatively high
hydraulic conductivities (>10
-3
cm/sec), whereas in fine-grained soils the
ratio becomes significant as is usually in the order of 10
-5
(cm
2
/V.sec),
while is less than 10
-5
cm/sec (10
-7
cm/sec for clayey soils) (Acar et al.,
1997).
5.3.2 Mass Flux
Different coupled potential gradients cause the mass flux of chemical spe-
cies relative to pore fluids in porous media. Diffusional mass flux (i.e.,
mass transport due to chemical concentration gradient) and migrational
mass flux (i.e., mass transport of charged species due to an electric poten-
tial gradient) are the main components that contribute to the mass flux of
chemical species in porous media. Advection (i.e., species transport by the
flowing fluid) is another component of mass flux of dissolved species, as
well as surface neutral micelles and immiscible fluids.
Search WWH ::
Custom Search