Geoscience Reference
In-Depth Information
pore fluid, the soil's porosity and the soil's electrical permittivity. The coefficient of
electroosmotic permeability is given by Equation (7.1):
V
t
n
E
εζ
q
=
L
A
(7.1)
where:
ζ
=
zeta potential
=
V
t
viscosity of the pore fluid
=
n
soil porosity
ε
=
soil electrical permittivity
A
=
gross cross-sectional area perpendicular to water flow
L
=
length
q
=
flow rate
Hydraulic conductivity,
k
h
, is significantly affected by the pore size and distribution
in the medium, but
k
e
, based on Helmholtz-Smoluchowski theory, depends mainly
on
ζ
.
The value of
k
e
is assumed to be constant during the electrokinetic process as
long as there is no change in the concentration of ions or pH of the pore fluid (Gray
and Mitchell, 1967). Based on Hemholtz-Smoluchowski theory,
ζ
and the charge
distribution in the fluid adjacent to the soil surface play important roles in determining
the electroosmotic flow.
Das (2008) reported that Schmid (1951) proposed a theory in contrast to the
Helmholtz-Smoluchowski theory. It was assumed that the capillary tubes formed by
the pores between clay particles are small in diameter and results in the excess cations
would be uniformly distributed across the pore cross-sectional area (Figure 7.5). Based
on this theory:
n
r
2
A
o
F
8
V
t
E
L
A
q
=
(7.2)
where:
r
=
pore radius
A
o
=
volume charge density
F
=
Faraday constant
n
=
porosity
A
=
gross cross-sectional area perpendicular to water flow
L
=
length
V
t
=
Viscosity
=
q
flow rate
However, the most widely used electroosmotic flow equation for the soil system
is proposed by Casagrande (1949):
q
=
k
e
i
e
A
(7.3)
