Environmental Engineering Reference
In-Depth Information
Ri
L
Ri
L
(2.6)
E
==
ss
bb
vk Ri
L
=
k
t
i
A
ss
eo
s
(2.7)
=
eo
eo
s
n
s
vA Q
Ki
(2.8)
==
eo
eo
s
where, k eo is the H-S coefficient of electroosmotic conductivity; i, i s and i b
are the total, surface and bulk currents (Amps or C/s ), respectively; R s and
R b (Ohm) are the surface and the bulk resistances; and
σ s is the surface
conductivity ( l -1 Siemens or l -1 Ohm -1 ; where l represents the unit of length);
t is the tortuosity; n is the porosity; A is the total area ( A low = nA ). The rela-
tion between the resistance and conductivity is given as: R s =L'/(σ s A low ) , and
the tortuosity term t is included to augment L ( L' = L t ) because the electric
currents may follow a tortuous path through the length, L of the electro-
chemical cell for which the pore walls are assumed lined up with connected
electric double layers. In this model, K emerges as a factor that relates vol-
ume rate of electroosmotic flow of fluid movement per electrical charge.
Shang et al., (1995) looked at the relation of conductivity and apparent
polarization in several wet clay systems, where they found that the sur-
face conductivity and the apparent permittivity decreased significantly
when the volume fraction of the particles was increased beyond 0.3. They
also found that the conductivity of the bulk fluid was at least an order of
magnitude higher than the surface conductivity (=> R b /R s
0.1), and that
the surface conductivity increased when the clay was remolded (=> R b /
R sr
0.2-0.5). These findings support Khan's (1991) “parallel resistances”
model when the flow direction is implicitly taken to be the direction of
the electric current flow. Because the electroosmotic velocity representa-
tion using the surface conductivity, s s, would require fully developed elec-
tric double layers with connectivity, increasing the dry clay content would
inhibit the connectivity of the electric double layers, and hence cause the
reduction in the measurement of the surface conductivity for the overall
system. The remolding of wet clay pastes has been shown to reduce the
repulsion between particles and cause them align in a face-to-face orienta-
tion (Mitchell, 1993; Quigley, 1980), and therefore, possibly increase the
connectivity of the electric layers in edge-to-edge correspondence. It fol-
lows than the preferential alignment of the particles in the direction of
the electrical field help increase the surface conductivity, as was shown by
Shang and co-workers (1995).
 
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