Geoscience Reference
In-Depth Information
which provides an alternative expression for the sorptivity. A second point of interest
is that the form of Equations (9.17), (9.18) and (9.19) is already suggestive of a way to
scale the variables that govern the sorption phenomenon. Indeed, because
f
has the same
dimensions as the hydraulic conductivity, it is only natural to make it dimensionless with
that variable; with (9.19) this produces then immediately a dimensionless time variable,
as well. Thus one can construct the following dimensionless variables
k
0
t
f
k
0
,
k
0
F
A
0
f
+
=
t
+
=
A
0
,
and
F
+
=
(9.21)
Over the years, the sorptivity has come to be considered as one of the more funda-
mental flow properties of a soil whose relevance extends well beyond the phenomenon
of sorption. As will become clear later in this chapter, the sorptivity also arises naturally
in the formulation of vertical infiltration capacity and in the formulation of different
facets of rainfall infiltration. Methods have been developed to measure the sorptivity in
the field (see Talsma, 1969; Talsma and Parlange, 1972; Clothier and White, 1981; Cook
and Broeren, 1994). It has also been used by White and Perroux (1987) to derive other
field soil hydraulic properties such as the diffusivity
D
w
(
θ
), the hydraulic conductivity
k
(
). As an illustration of the orders of magnitude
of this quantity, the following values (in cm min
−
1
/
2
) were measured by Talsma and
Parlange (1972) in the field: 0.97 (Bungendore sand), 0.08 (Pialligo sand), 0.17 (Barton
clay loam); the respective satiated hydraulic conductivities,
k
0
were 0.092, 1.08 and
0.093 cm min
−
1
.
θ
) and the soil water characteristic
H
(
θ
Wetting front
In certain applications it is of interest to determine the position of the wetting front. The
position of this front can be defined as the value of
x
=
x
f
, where the water content assumes
a certain value
>θ
i
). Experimentally, this water content may be taken as the value
at which the soil changes color as the water infiltrates. Mathematically, because the front
can be quite sharp in many soils, it is often convenient to assume simply that it is located
where the water content approaches
θ
=
θ
i
,or
S
n
=
0. Since
φ
is a function of
θ
, it is clear
in light of Equation (9.11), that the position of the wetting front is directly proportional
to
t
1
/
2
,or
θ
=
θ
f
(
x
f
=
φ
f
t
1
/
2
(9.22)
in which
φ
f
=
φ
(
θ
f
) is a constant for a given choice of
θ
f
. An experimental illustration of
Equation (9.22) is shown in Figure 9.5.
9.2.2
Some applications of the first integration
Equation (9.13) can be integrated once, subject to the first of (9.14), to yield immediately
θ
2
D
w
d
θ
d
φ
−
=
φ
(
y
)
dy
(9.23)
θ
i
