Agriculture Reference
In-Depth Information
2 Transport Processes
in Submerged Soils
The properties of submerged soils are, to a large extent, determined by transport
processes controlling the fluxes of solutes and gases through the soil or through
plants growing in it. For example, the reason the soil rapidly becomes anoxic
following submergence is the much slower transport of oxygen through the water-
filled pores of submerged soil than through the air spaces of well-drained soil.
Diffusion coefficients in the liquid phase are four orders of magnitude smaller
than those in the gas phase. It therefore makes sense to start with an account of the
various transport processes that operate in submerged soils. Transport processes
in plants are considered in Chapter 6.
Because of the central importance of transport, and because there is a well-
established theory and mathematics of transport processes in soils, submerged
soils lend themselves well to mathematical modelling. Models necessarily give
only a crude picture, particularly of the biological processes. But some form of
modelling is essential to unravel the complex interactions taking place. Most mod-
els involving transport processes in soils are based on the 'continuity equation'
which relates the change in mass of a substance in a small volume of soil over a
small time to the fluxes of the substance into and out of the volume. I here explain
the basis of the continuity equation and then describe the transport equations
derived from it that are used later in the topic. For an introduction to the mathe-
matics of transport processes in environmental systems see Crank
et al
. (1981).
Considering the mass balance of a solute moving in soil between two planes
of unit cross-section at distances
x
and
x
+
δx
, the rate of change in mass is
equal to the rate of entry across the plane at
x
less the rate of removal across the
plane at
x
+
δx
. Hence
δx
∂C
∂t
x
≈
(F
x
−
F
x
+
δx
)
t
≈−
δx
∂F
(
2
.
1
)
∂x
t
where
F
x
and
F
x
+
δx
are the fluxes across
x
and
x
+
δx
and
C
is the amount of
solute per unit volume of soil. In the limit
δx
→
0,
∂C
∂t
∂F
∂x
x
=
−
(
2
.
2
)
t
This is the continuity equation in one dimension.
