Mobile, Immobile, and Multiflow Domain Approaches - Transport and Fate of Chemicals in Soils: Principles and Applications - page 261

Local non-equilibrium Tr ansport

C i C i

C o C o

Intra-aggregate
diffusion

Macroporous
dispersion

FIGURE 8.1
Local nonequilibrium transport through an aggregated soil where preferential flow is domi-
nated by intraaggregate diffusion (left) and in a macroporous soil where solute breakthrough
is controlled by hydrodynamic dispersion. (From B. E. Clothier, M. B. Kirkham, and J . E.
Mclean. 1992. Soil Sci. Soc. Am. J . 56: 733-736. With permission.)

are eliminated for transport and the proportion of the water that does not
readily move within the soil increased. This fraction of water was referred
to as stagnant or immobile water. A decrease in water content increases the
fraction of air-filled macropores resulting in the creation of additional dead
end pores which depend on diffusion processes to attain equilibrium with a
displacing solution. However, the conceptual approach of mobile-immobile
or two-region behavior is perhaps more intuitively applicable for well-struc-
tured or aggregated soils under either saturated or unsaturated flow.

8.3.1 General Formulation

The equations describing the movement for a nonreactive solute through a
porous medium having mobile and immobile water fractions are:

∂
∂

m 2 m

−νΘ ∂
∂

m

C
t

∂
∂

C
x

C
x

m m mm mim

Θ = Θ D −α ( CC − ) (8.1)

2

and

∂

im

C
t

im mim

Θ =α − ( CC )

(8.2)

∂

Equation 8.1 is a modified version of the convection-dispersion equation
where D is the hydrodynamic dispersion coefficient in the mobile water region
(cm 2 h -1 ), Θ m and Θ im are mobile and immobile water fractions (cm 3 cm -3 ),