Transport - Transport and Fate of Chemicals in Soils: Principles and Applications - page 74

Equation 3.33 is commonly known as the convection-dispersion equation
(CDE) for solute transport in porous media and is applicable for fully saturated
and partially saturated water contents and under transient and steady flow.
For conditions where steady water flow is dominant, q and Θ are constants
over space and time, that is, for uniform Θ in the soil, the simplified form of
the CDE for nonreactive chemicals is

2

∂
∂

C
t

C
z

∂
∂

C
z

∂
∂

= D − v (3.34)

2

where v is the pore-water velocity ( q z /Θ).

3.2.4 Equilibrium Linear and Nonlinear Sorption

Linear or linearized equilibrium sorption isotherms are the simplest form
of solute retention. Here it is assumed that the amount retained by the soil
( S ) is related to solute concentration in solution ( C ) by an expression of the
linear form:

S= K C

(3.35)

d

where K d is the distribution coefficient (cm 3 g -1 ). This simple assumption of
linear adsorption generally is valid for most pesticides and solutes of low
affinity to the soils and at low concentrations. Incorporation of the linear
form into the CDE yields:

2

∂
∂

C
t

C
z

∂
∂

C
z

∂
∂

R = D − v

(3.36)

2

where R is the retardation factor:

=+ ρ
Θ

R (3.37)

K d

If there is no solute retention by the soil, K d becomes zero and R becomes
one. Such an assumption is often made for anionic and neutral tracers such as
chloride, bromide, and tritium, among others. In some cases R may become less
than one, indicating that only a fraction of the soil solution phase participates in
the transport process. This may be the case when the solute is subject to signifi-
cant anion exclusion or when relatively immobile water regions are present, for
example, inside dense aggregates that do not contribute to convective transport.
Van Genuchten and Weirenga (1986) suggested that, in case of anion exclusion,
(1 − R ) may be viewed as the relative anion exclusion volume. However, for
most reactive chemicals in soils, nonlinear isotherms are expected:

b

S= K C

(3.38) f