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κ
1
κ
2
1.0
0
0.001
0.01
0.1
0.01
0.1
1
0.8
0.6
0.4
0.2
0
0
1
2
3
4
5
6
7
8 9 0
V/V
o
FIGURE 8.9
Effluent concentration distributions for different values of κ
1
and κ
2
using the SOMIM model.
(From H. M. Selim and M. C. Amacher. 1997.
Reactivity and Transport of Heavy Metals in Soils
.
Boca Raton, FL: CRC Press. With permission.)
spherical diffusion and for first-order kinetic (mobile-immobile) models.
Estimates for α are based on the assumption of average aggregate sizes of
0.01, 0.01, and 0.005 cm for Windsor, Olivier, and Cecil soils used, respec-
tively. In addition,
D
a
for Cr(VI) diffusion was assumed to be 10
-9
cm
2
sec
-2
for all three soils. Barber (1984) compiled diffusion coefficients for a num-
ber of ions in soils with values for phosphate (H
2
PO
4
-
) ranging from 10
-8
to
10
-11
cm
2
sec
-1
(for water
D
a
= 10
-6
cm
2
sec
-1
). Since chromate and phosphate
κ
1
κ
2
ω
--
1.0
0
0
0.01
0.02
0.1
10
1
0.8
0.6
0.4
0.2
0
0
1
2
3
4
5
6
7
8
V/V
o
FIGURE 8.10
Effluent concentration distributions for different values of the parameter ω using the SOMIM
model. Values of κ
1
and κ
2
are also shown. (From H. M. Selim and M. C. Amacher. 1997.
Reactivity and Transport of Heavy Metals in Soils
. Boca Raton, FL: CRC Press. With permission.)
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