Mobile, Immobile, and Multiflow Domain Approaches - Transport and Fate of Chemicals in Soils: Principles and Applications - page 291

velocity ( q A , q B ), porosity (Θ A , Θ B ), solute concentration ( C A , C B ), and disper-
sion coefficient ( D A , D B ). The two flow domains are related by an interaction
term Γ such that:

Γ=α− ( C AB )

(8.72)

where α is the mass transfer coefficient between the two flow domains.
This two-domain model reduces to a capillary bundle model when α = 0
and it approaches the classic one-domain convective-dispersion equation as
α increases. The two-flow domain model can also be reduced to a mobile-
immobile model when V B equals zero. The convective-dispersion equation
in each flow domain can be written as (Skopp, Gardner, and Tyler, 1981):

∂ C

t

2

C
x

∂
∂

C
x

α
Θ

∂
∂

A A A

= D − v − ( CC − )

(8.73)

A A AB

∂

2

A

∂
∂

C
t

2

C
x

∂
∂

C
x

− α
Θ

∂
∂

B B B

= D − v ( CC − )

(8.74) B B B A

2

B

The corresponding initial and boundary conditions associated with each
flow domain ( i ) can be expressed as:

C i = 0 ( t = 0, 0 < x < L ) (8.75)

∂
∂

C
x

i

vC = Θ vC D ( xt =< , t )

(8.76)

i o i i i p

∂
∂

C
x

i

0 = Θ vC D ( xt => 0, t )

(8.77)

i i i p

∂
∂

C
x

i

= 0( xLt = , ≥ )

(8.78)

These conditions are similar to those described earlier for the transport of
a solute pulse (input) having a concentration C o in a uniform soil having a
finite length L where a steady water flux v was maintained constant.

8.6.1 Experimental Evidence

The two-flow domain model, which may be referred to as a dual-porosity
concept, has been used in the solute transport literature to account for the