Sorption Kinetics - Transport and Fate of Chemicals in Soils: Principles and Applications - page 38

Rarely are all these steps followed in the course of a single study and other
experiments are often required to identify a mechanism(s). This is often
achieved largely based on trial and error process of testing and retesting to
eliminate alternate observed rate functions.

2.1 Modeling of Kinetic Sorption
Kinetic models represent slow reactions where the amount of solute sorption
or transformation is a function of contact time. Most commonly encountered
is the first-order kinetic reversible reaction for describing time-dependent
adsorption/desorption in soils. Others include linear irreversible and non-
linear reversible kinetic models. Recently, combinations of equilibrium and
kinetic-type (two-site) models, and consecutive and concurrent multireac-
tion-type models have been proposed.

2.1.1 First-Order and Freundlich Kinetics

The first-order kinetic approach is perhaps one of the earliest single forms
of reactions used to describe the sorption versus time for several dissolved
chemicals in soils. This may be written as:

∂
∂

S
t

θ
ρ

= k CkS −

(2.1)

f b

where the parameters k f and k b represent the forward and backward rates
of reactions (h -1 ) for the retention mechanism, respectively. The first-order
reaction was first incorporated into the classical convection-dispersion equa-
tion by Lapidus and Amundson (1952) to describe solute retention during
transport under steady-state water flow conditions. Integration of Equation
2.1 subject to initial conditions of C = C i and S = 0 at t = 0, for several C i values,
yields a system of linear sorption isotherms. That is, for any reaction time, t ,
a linear relation between S and C is obtained.
There are numerous examples in the literature on kinetics of pesticides and
other organic sorption on various soils. Examples are shown in Figure 2.3 for
imidocloprid that illustrate experimental observations where sorption over
time appears linear (Jeong and Selim, 2010).
It was argued that such apparent linear behavior is not surprising for a
number of reasons, including that the concentration range of the solute in
solution and the adsorption optima are not attained. In addition, Selim (2011;
2012) suggested that linear behavior is also due to the uniform or homoge-
neous nature of the sorbing matrix. It is safe to consider organic matter as