Transport Processes in Submerged Soils - The Biogeochemistry of Submerged Soils - page 21

percolation in puddled submerged soils are generally less than a few mmday − 1 ,
that is ≤ 2 × 10 − 7 dm s − 1 . Solute diffusion coefficients in submerged soils are
of the order of 5 × 10 − 8 dm 2 s − 1 (next section). Therefore the time taken for the
distance moved by mass flow to exceed the mean distance moved by diffusion
would be 14 days.

2.2 DIFFUSION

The rates of many important processes in submerged soils are governed by rates
of diffusion. A comprehensive theory of diffusion in soils exists, allowing the
development of mechanistic models of soil processes involving diffusion. I briefly
describe this theory in this section; more complete treatments are given in Nye
(1979) and Tinker and Nye (2000).
Diffusion results from the random thermal motion of particles. If there is a
concentration gradient of a substance through a medium in which it is mobile,
the net amount of substance crossing a unit section in unit time is given by Fick's
first law (Equation 2.3):

=− D d C
d x

F ( 2 . 16 )

where F is the flux of the substance, d C /d x is its concentration gradient across
the section, and D is the diffusion coefficient, which is defined by this relation.

2.2.1 DIFFUSION COEFFICIENTS IN SOIL

In submerged soils there is no continuous gas phase through which volatile solutes
can diffuse. Hence we are mainly concerned with the liquid and solid phases.
If the concentration of a volatile solute in the liquid becomes sufficiently large
for an appreciable amount to come out of solution, the resulting gas bubbles
will rise through the soil by the process of ebullition, partly becoming entrapped
beneath soil particles until they are dislodged by mechanical forces. Ebullition is
discussed in Section 2.3. For diffusion in the liquid and solid phases, the same
principles apply as for non-submerged soils though there are some additional
effects, which I shall describe.
Most solutes in soils are to some extent adsorbed on the soil solid; only a
small fraction is in the solution in the pores. However some adsorbed solutes,
particularly exchangeable cations, can have considerable mobility on soil surfaces
(see below), so it is important to consider the solid phase pathway as well as
the solution. Because the diffusing solute passes rapidly between the solid and
solution, the two pathways partly act in series. In such a heterogeneous medium
as soil it is not realistic to account for the mobilities and concentration gradients
of solutes in all the constituent parts. But if the soil volumes and reaction times