Transport in Nonuniform Media - Transport and Fate of Chemicals in Soils: Principles and Applications - page 305

sorption or exchange reactions with the solid matrix. Sorption or exchange
has been described by either instantaneous equilibrium or a kinetic reaction
where concentrations in solution and sorbed phases vary with time. Linear,
Freundlich, and one- and two-site Langmuir equations are perhaps the most
commonly used to describe equilibrium reactions. In the subsequent sections
we discuss Freundlich and Langmuir reactions and their use in describing
equilibrium retention. This is followed by kinetic-type reactions and their
implication for single and multireaction retention and transport models.

9.4.1 Linear Adsorption

Figure 9.2 shows a comparison of breakthrough curves (BTCs) for a two-
layered soil column with reverse layering orders. Here we report results for
a layered soil column where one layer is nonreactive ( R = 1) and the other is
linearly adsorptive. For the case of linear adsorption, a dimensionless retar-
dation factor can be obtained from Equation 9.1 and is given by:

=+ ρ

K d

R (9.5)

θ

where K d is a redistribution coefficient where the linear equilibrium model
was assumed:

SKC
d

=

(9.6)

For the case where K d = 0, the retardation factor R equals 1 and solute is
considered nonreactive. The BTC for the case R1 → R2 where the nonre-
active layer was first encountered (top layer) was similar to that when the

1.0

LINEAR

1st and 3rd try

0.8

0.6

R1 R2

0.4

R2 R1

0.2

0.0

0 10 20 30

Pore Volume (V/Vo)

FIGURE 9.2
Simulated breakthrough results for a two-layered soil column under different layering orders
(R1 → R2 and R2 → R1). Here R1 is a nonreactive layer and R2 is a reactive layer with linear
adsorption.