Environmental Engineering Reference
In-Depth Information
and Daniel 1994). On the other hand, ionic migration can occur in all soil
types, including sand and gravel, and is affected by ionic strength and pH
to a lesser extent compared to EO flow.
5.3.3 Charge Flux
Upon application of direct current to a saturated soil medium, the electric
field causes charge transport. The main components of charge flux in a sat-
urated soil medium are migration flux, and diffusion flux (due to the dif-
fusion of charged species). There is no contribution of the advective fluid
transport to the charge transport.
The current density in the pore fluid due to applied electrical gradient is
given by Ohm's law as:
)
(
*
(5.12)
I
=∇−
s
E
where, I is the electric current density (CL-2T-1),
-2
T
-1
), and
s
* is the effective elec-
tric conductivity of the porous medium given as:
N
species
∑
s
*
=
ZF
u
j
*
C
(5.13)
j
j
j
=
1
The migration charge flux can be related to the migration mass flux of
species using Faraday's law for equivalence of mass flux and charge flux as:
∑
N
∑
N
)
(
e
e
*
(5.14)
I
=
species
ZF
J
=
species
ZF
u
C
∇ −
E
j
i
j
j
j
j
=
1
j
=
1
Similar to the
migrational charge flux, the diffusional charge flux due to
the diffusional mass flux of charged species is evaluated using Faraday's law
of the equivalence of mass flux and charge flux as:
(
)
(5.15)
∑
N
∑
N
d
d
*
I
=
species
ZF
J
=
species
ZF
D
∇ −
C
j
i
j
j
j
j
=
1
j
=
1
The electrical neutrality of free pore fluid is preserved by:
∑
N
species
(5.16)
CZ
j
=
0
j
j
=
1
Search WWH ::
Custom Search