Geoscience Reference
In-Depth Information
Electroosmotic permeability coefficient 1) .
Table 5.2.
10 9
Water content
k eo ×
Approximate
[m 2 s 1 V 1 ]
k h [m s 1 ] 2)
Material
[%]
10 10
London clay
52.3
5.8
10 10
Boston blue clay
50.8
5.1
10 9
Kaolin
67.7
5.7
10 8
Clayey silt
31.7
5.0
10 11
Na-Montmorillonite
170
2.0
10 10
2000
12.0
10 6
Fine sand
26.0
4.1
10 10
Silty clay, West Branch Dam
32.0
3.0-6.0
10 7
Clayey silt, Little Pic River, Ontario
26.0
1.5
1) From Mitchell and Soga (2005).
2) Hydraulic conductivity.
where A and B are experimentally determined constants, and C [mole m 3 ] is the total electrolyte
concentration. Accordingly, the zeta potential is controlled by the pH of the medium and the total
electrolyte concentration in the pore water. The point where the plot of the zeta potential versus
pH passes through the zero zeta potential is called the isoelectric point or Point of Zero Charge
(PZC).
The electroosmotic flow rate, Q [m 3 s 1 ], is expressed as:
Q
=
nV eo A
(5.7)
where n and A [m 2 ] are the porosity and the cross-sectional area of the soil. From Equations (5.4)
and (5.7) , we obtain:
Q = ( ( nεζ ) / µ ) EA
(5.8)
Similar to Darcy's law, Equation (5.8) can be expressed as:
Q =− k eo EA
(5.9)
where the coefficient k eo [m 2 s 1 V 1 ], is termed electroosmotic permeability. Comparing
Equation (5.8) with Equation (5.9) , the electroosmotic permeability coefficient ( k eo ) is given as:
k eo =
( nεζ )
(5.10)
10 8 m 2 s 1 V 1 ( Table
5.2 ). According to the Helmholtz-Smoluchowski theory and Equation (5.10) , k eo should be rel-
atively independent of pore size, and this is shown in Table 5.2 , but the hydraulic conductivity
( k h ) varies as the square of some effective pore size (Mitchell and Soga, 2005). Electroosmo-
sis acts more effectively in flowing water through fine-grained soil than hydraulically-driven
flow, since k eo is independent of pore size. It is easily demonstrated by the following exam-
ple proposed by Mitchell and Soga (2005). One can consider a fine sand and a clay of k h of
1
10 9 to 1
Mitchell and Soga (2005) reported that k eo ranges from 1
×
×
10 5 ms 1 and 1
10 10 ms 1 , respectively, and it is assumed that both soils have k eo values
×
×
10 9 m 2 s 1 V 1 . If hydraulic flow rates are equal in both soils, then ( i h
of 5
×
×
k h )
=
( E
×
k eo ),
where E is the electrical potential gradient or electric field strength. Hence, i h
( k eo / k h ) E .If E of
20 V m 1 is applied, i h is 0.01 for the fine sand and 1000 for the clay. It means that a hydraulic gra-
dient of only 0.01 can move water as effectively as an electrical gradient of 20 V m 1 in fine sand.
However, for the clay, a hydraulic gradient of 1000 would be needed to offset the electroosmotic
flow (Mitchell and Soga, 2005).
=
 
 
Search WWH ::




Custom Search