Sorption Isotherms - Transport and Fate of Chemicals in Soils: Principles and Applications - page 9

1.5

Normal

Delta Dirac
g(ζ)=1

1.0

Lognormal

0.5

Exponential

0.0

k

0.0 1.0 2.0 3.0

Anity Cooecient (ζ )

FIGURE 1.2
Probability distribution function for normal, log-normal, and exponential distributions and
delta Dirac function.

In addition to the above shortcomings, another concern is the adoption of
the Langmuir assumption for all solutes and soils. Although the Langmuir
assumption is physically meaningful, it does not always describe isotherms
for many solute species. In fact, for most if not all organic compounds, sorp-
tion isotherms cannot be described based on the Langmuir assumption.
As an example, the atrazine isotherms for various smectites are shown in
Figure 1.3 (Laird et al., 1992). These isotherms illustrate their linearity as well
as extensive differences (i.e., heterogeneity) among the different smectites.
Deviation from the Langmuir assumption, where maximum sorption is
assumed, is likely due to multiple factors. It is possible that limited solubility
of various trace elements and organic compounds in aqueous systems is one
such factor.
In the following discussion, we deviate from the well-accepted Langmuir
assumption as the governing sorption isotherm function and adopt the
linear-type governing function. Specifically, we consider that for each con-
stituent i of the soil system, sorption follows a simple linear form such that

Γζ (,) CCkC =ζ = where k = ζ

(1.11)

i i i i i

As a result, the isotherm equation for a heterogeneous system can be writ-
ten as

n

=χ
=

S (,) k C

(1.12)

i

i 1