Transport in Nonuniform Media - Transport and Fate of Chemicals in Soils: Principles and Applications - page 307

redistribution coefficient where the linear equilibrium model was assumed:

b

SKC
d

=

(9.8)

where the exponent b is commonly less than unity for most reactive chem-
icals. Here, R1 represents a nonreactive layer and R2 represents a nonlin-
ear (Freundlich) adsorptive layer. These simulations were carried out for
a wide range of the Peclet or Brenner number ( B = qL /θ D ). We also exam-
ined the influence of the nonlinear Freundlich parameter b on the shape
of the BTCs. For most reactive chemicals, including pesticides and trace
elements, b is always less than unity (Selim and Amacher, 1997). Based
on these simulations, BTCs were not influenced by the layering sequences
regardless of the Brenner number B when nonlinear Freundlich adsorp-
tion was considered. This result is similar to that of Selim, Davidson, and
Rao (1977). Dispersion is dominant for the case where the Brenner number
is small, whereas convection becomes the dominant process for large B
values. The BTCs exhibit increasing retardation or delayed arrival, and
excessive tailing of the right-hand side of the BTCs for increasing values
of the nonlinear adsorption parameter b . In addition, the BTCs become
less spread (i.e., a sharp front) with increasing Brenner numbers. All such
cases provide similar observations, that is, the effects of nonlinearity of
adsorption are clearly manifested. Nevertheless, for all combinations of
b and the Brenner number B used in these simulations, the BTCs under
reverse layering orders showed no significant differences. In other words,
layering order is not important for solute breakthrough in layered soils
with nonlinear adsorption as the dominant mechanism in one of the lay-
ers. Zhou and Selim (2001) arrived at similar conclusions for layered soil
profiles when several retention mechanisms of the kinetic reversible and
irreversible types were considered.

9.4.3 Langmuir Model

To illustrate that the above finding is universally valid, other solute adsorp-
tion processes of the nonlinear type were investigated. The Langmuir
adsorption model is perhaps one of the most commonly used equilibrium
formulations for describing various reactive solutes in porous media,

ω
+ω

C

SS /

max =

(9.9)

(1 C )

where S max is the maximum amount sorbed and ω is the affinity coefficient.
We consider here simulated columns consisting of one nonreactive layer and
one reactive layer with a Langmuir-type adsorption mechanism. The simu-
lation results are shown in Figure 9.4. The combined first- and third-type