Mobile, Immobile, and Multiflow Domain Approaches - Transport and Fate of Chemicals in Soils: Principles and Applications - page 266

As a result, a more general formulation for estimating α c is

nD (1 −Θ F )

e

α=

(8.16)

c

2

a

e

where n is a geometry factor and a is an average effective diffusion length.
Details can be found in van Genuchten and Dalton (1986) and van Genuchten
(1985). Equation 8.14 has been used to estimate solute transport in porous
media (Selim and Gaston, 1990; Goltz and Roberts, 1988).

8.3.3 Estimation of Θ m and Θ im

A common way of estimating the mobile and immobile water content is by
use of curve fitting of tracer breakthrough results (Li and Ghodrati, 1994;
van Genuchten and Wierenga, 1977). De Smedt and Wierenga (1984) found
Θ im = 0.8530 is applicable for unsaturated glass beads with diameters in the
neighborhood of 100 μm. Alternatively, a direct method of estimating Θ m
and Θ im is by measuring the soil water content at some arbitrary water ten-
sion (ψ). Smettem and Kirkby (1990) used water content at ψ = 14 cm as the
matching point between the interaggregate (macro-) and the intraaggregate
(micro-) porosity by examining the ψ - Θ soil moisture characteristic curve.
Jarvis, Bergstrom, and Dik (1991) estimated macroporosity from specific
yield under water tension of 100 cm. Other water tensions used to differenti-
ate macropores from micropores are 3 cm (Luxmoore, 1981), l0 cm (Wilson,
Jardine, and Gwo, 1992), 20 cm (Selim, Schulin, and Flühler, 1987), and 80 cm
(Nkedi-Kizza et al., 1982). A list of water tensions used by different authors
was provided by Chen and Wagenet (1992). The equivalent diameters at these
water tensions range from 10 to 10,000 μm. Another experimental measure-
ment of Θ im is based on the following mass balance equation:

Θ R = Θ m R m + Θ im C im (8.17)

When α is small enough to assume C im = 0 and C o (input concentration) at
certain infiltration time t , the approximate equation is obtained:

C
C

C
C

m

Θ=Θ=Θ

(8.18) m

o

Applications of this method can be found in Clothier, Kirkham, and Mclean
(1992) and Jaynes et al. (1995). By assuming that a tracer concentration in the
mobile water phase ( C m ) equals input solution concentration ( C o ), Jaynes et al.
(1995) derived the following formula from Equations 8.2 and 8.18:

im

C
C

=− α

t Θ

Θ

ln 1 − + ln

(8.l9)

im

Θ

o