Transport - Transport and Fate of Chemicals in Soils: Principles and Applications - page 72

flow, when a solute, if dispersion is ignored, moves in a porous medium or
is displaced through the soil like a piston. Dispersion is a passive process
in response to water flow. Therefore, dispersion is effective only during
fluid flow, so that for a static water condition or when water flow is near
zero, molecular diffusion is the dominant mixing process for solute trans-
port in soils. A longitudinal dispersion coefficient ( D L ) and transverse dis-
persion coefficients ( D T ) are needed to describe the dispersion mechanism.
Longitudinal dispersion refers to that in the direction of water flow and ( D T )
refers to dispersion in directions perpendicular or transverse to the direc-
tion of flow. Longitudinal dispersive transport can be described by an equa-
tion similar to Equation 3.14 for diffusion:

∂
∂

C
z

= −Θ (3.23)

U D

m L

Separate studies investigated the effects of the soil water content Θ (Laryea
et al., 1982; Smiles and Philip, 1978; Smiles et al., 1978) and the water flux q
(Smiles and Gardiner, 1982; De Smedt and Wierenga, 1984) on D L . A linear
relationship between unique D L and v , where v is referred to as the pore-
water velocity and is given by ( q /Θ), is commonly used:

D =D o +λ

v (3.24)

L

where D o is the molecular diffusion coefficient in water. The term λ is a
characteristic property of porous media known as the dispersivity (cm).
Dispersivity values λ vary from a few centimeters for uniformly packed (dis-
turbed) laboratory soil columns to several meters for field-scale experiments.
Large values of λ are also reported for well-aggregated soils. In practice, an
empirical parameter D rather than D L is often introduced to simplify the flux
equation (Boast, 1973). Moreover, because D o << D L , D L or simply D = λν, or a
more general formula (see Bear, 1972):

DD =

λ

n

(3.25)

= v

L

is often used, where n is an empirical constant with a common range of 1.0 to
1.2 (Yasuda et al., 1994; Montero et al., 1994; Jaynes, Bowman, and Rice, 1988).
Therefore, D versus ν may not be strictly linear and the dispersivity λ is not
velocity dependent (Gerritse and Singh, 1988).
Several modifications of D vs. ν are found in the literature by introducing
the tortuosity coefficient τ of Equation (3.17), including that by Brusseau (1993):

D= D τ+λ

n

(3.26)

v

o