Agriculture Reference
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800
Isotherms- Linear Assumption
-ree-Phase n = 3
600
Two-Phase n = 2
400
Linear n = 1
200
0
0
20
40
60
80
Concentration (mg/L)
FIGURE 1.4
Linear, two-, and three-phase isotherms based on the linear model assumption.
where
n
λ=
F ii
(1.16)
i
=
1
This equation resembles that of S = K d C , where λ is a weighted average of
the affinity coefficient of all constituents. Based on the above we present, in
Figure 1.4, three isotherms: linear, two-, and three-phase isotherms, where
two ( n = 2) and three ( n = 3) constituents were assumed. There are numerous
examples in the literature of two- and three-phase isotherms.
Extending the analysis to a soil matrix having ten constituents results in
the nonlinear isotherms shown in Figure  1.5. In both isotherms, ten equal
fractions were assumed, where the affinity varied linearly from 30 to 100 for
isotherm A and 50 to 100 for isotherm B. The isotherms illustrate nonlinear
Freundlich-type behavior with the exponent parameter b < 1; b = 0.59 and
0.46 for isotherms A and B, respectively. A complete isotherm with a greater
number of constituents may be regarded as the sum of all individual iso-
therms in a similar manner to that for Langmuir isotherms described above.
The only exception is that all isotherms are subject to the constraint given
by the piece-wise continuous function, Equation 1.13. Based on these results,
Freundlich behavior can be described without the constraint of the log-nor-
mal distribution of site affinities.
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