Geoscience Reference
In-Depth Information
Table 5.1.
Diffusion coefficient, ionic mobility at infinite dilution and effective ionic mobility in soil.
Metal
Molecular diffusion coefficient
Ionic mobility
Effective ionic mobility
10 10
[m 2 s 1 ] 1)
10 8
[m 2 s 1 V 1 ]
u i
10 9
[m 2 s 1 V 1 ] 2)
species
D i
×
u i
×
×
Li +
10.3
4.01
5.62
Na +
13.3
5.18
7.25
K +
19.6
7.63
10.7
Rb +
20.7
8.06
11.3
Cs +
20.5
7.98
11.2
Be 2 +
5.98
4.66
6.52
Mg 2 +
7.05
5.49
7.69
Ca 2 +
7.92
6.17
8.64
Sr 2 +
7.9
6.15
8.61
Ba 2 +
8.46
6.59
9.22
Pb 2 +
9.25
7.20
10.09
Cu 2 +
7.13
5.55
7.77
Fe 2 +
7.19
5.60
7.84
Cd 2 +
7.17
5.58
7.82
Zn 2 +
7.02
5.47
7.65
Ni 2 +
6.79
5.29
7.40
Fe 3 +
6.07
7.09
9.93
Cr 3 +
5.94
6.94
9.72
Al 3 +
5.95
6.95
9.73
1) Values from Mitchell (1993) and Mitchell and Soga (2005).
2) Values calculated using 0.4 porosity ( n ) and 0.35 tortuosity ( τ ) (Kim et al ., 2009a).
coefficient, D i [m 2 s 1 ], in free solution and ionic mobility, u i (Alshawabkeh and Acar, 1996;
Kim et al ., 2002a; Mitchell and Soga, 2005):
u i
=
( D i
|
z i
|
F ) / ( RT )
(5.1)
where z i is the charge of species i , F is Faraday's constant (96,485 C/mole electrons), R is
the universal gas constant (8.3144 J K 1 mole 1 ), and T is the absolute temperature [K]. The
ionic mobilities in the free solution range from 10 8
to 10 7 m 2 s 1 V 1 , except for protons
10 7 m 2 s 1 V 1 ). However, the effective ionic
mobility, u i [m 2 s 1 V 1 ] in soil is substantially lower relative to that ( u i ) in solution due to the
effect of porosity ( n ) and tortuosity ( τ ). The effective mobility, u i , is defined as follows:
10 7 m 2 s 1 V 1 ) and hydroxyl ions (2
(4
×
×
u i
=
nτu i
(5.2)
where n and τ are the porosity and tortuosity of soil, respectively. The tortuosity factors reported
in different studies are as low as 0.01 and as high as 0.84, and they usually range from 0.20
to 0.50 (Shackelford, 1990). Table 5.1 presents the diffusion coefficients, ionic mobilities, and
effective ionic mobilities of representative metal ions. The typical effective ionic mobilities in
clayey soils, which are targeted to electrokinetics, range from 3
10 8 m 2 s 1 V 1
(Mitchell, 1991; 1993; Mitchell and Soga, 2005). The effective ionic mobility is affected by
several factors, such as the electric conductivity and ionic strength of the pore water, the charge
of the ion, and temperature. For electromigrative velocity of species i in soils, V em , i , can be
calculated by using effective ionic mobility, u i , and electric field strength E [V m 1 ]:
10 9
×
to 1
×
u i E
V em , i
=
(5.3)
 
 
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