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Clayey soils (Casagrande, 1983), glacial tills (Friborg, 1996)
Sand (Ahmad, 1964)
Berea sandstone (Zhu & Toksoz, 2012)
+
Saprolites (Revil et al., 2012)
Glass beads, sand gravel, sand till (Sheffer, 2007)
Glass beads (Pengra et al., 1999; Boleve et al., 2007)
Limestones (Pengra et al., 1999; Revil et al., 2007)
0
V
ˆ
Clayrock (Revil et al., 2005)
8
Alluvium (Jardani et al., 2007)
Sandstones (Pengra et al., 1999)
Jougnot et al. (2012) Unsaturated conditions-WR Approach
Jougnot et al. (2012) Unsaturated conditions-RP Approach
6
log
10
ˆ
0
V
Jardani et al. (2007)
= -9.23-0.82 log
10
k
0
4
Figure 1.11
Quasistatic charge density
Q
0
V
(excess pore charge moveable by the
quasistatic pore water flow) versus the
quasistatic permeability
k
0
for a broad
collection of core samples and porous
materials. This charge density is derived
directly from laboratory measurements of
the streaming potential coupling coefficient.
Data from Ahmad (1969), Bolève et al.
(2007), Casagrande (1983), Friborg (1996),
Jougnot et al. (2012), Jardani et al. (2007),
Pendra et al. (1999), Revil et al. (2005,
2007), Sheffer (2007), Revil et al. (2012),
and Zhu and Toksöz (2013). The effective
charge density
Q
0
+
+
+
2
0
-2
V
cannot be used to predict
the cation exchange capacity of the porous
material. We also show the smaller effect of
salinity.
-4
-20
-18
-16
-14
-12
-10
-8
-6
Permeability log
10
(
k
0
, m
2
)
charges (Marshall & Madden, 1959; Titov et al., 2004;
Leroy et al., 2008; Grosse, 2009). The total current den-
sity
J
can be decomposed into a contribution associated
with the electromigration of the charge carriers plus a
contribution associated with the
“
true
”
polarization of
the material:
same as the salinity dependence of the zeta potential,
ζ
.
The polarity of
Q
V
is opposite to the polarity of
, and
any change affecting the zeta potential would modify
the effective charge density
Q
V
in the same way.
A comparison between Equations (1.81) and (1.80)
implies that at first approximation we have the following
equivalence between the parameters:
Q
V
k
0
ζ
ε
ζ
F
.
f
N
q
i
J
i
+
∂
D
∂
J
=
1 82
t
i
=1
1.3 The complex conductivity
where
J
i
denotes the flux density of species
i
(the number
of species passing per unit surface area and per unit time)
and
D
is the displacement field associated with dielectric
polarization of the porous material. In nonequilibrium
thermodynamics, the flux densities
J
i
are coupled to
other transport mechanisms in the porous media. These
ionic fluxes are directly controlled by the gradient of the
electrochemical potentials, introduced in Section 1.1, and
In this section, we examine the second and third conse-
quences associated with the electrical double layer,
namely, the existence of surface conductivity and the
existence of low-frequency polarization associated with
the quadrature electrical conductivity. At low frequen-
cies (below few kHz), porous media and colloids are
not only conductive, but they store, reversibly, electrical
