Geoscience Reference
In-Depth Information
steadily spreads into the corridor and other rooms where connecting doors are open,
but all windows remain closed. The air in your apartment is stagnant, i.e., there is no
draft, convection, or movement of air. Yet, in spite of the stagnant air, molecules of
stink readily extend the undesirable stench throughout the apartment. The fl ux of
those molecules is called diffusion - you observe the same process after you slowly
place a spoon with salt into a glass of water. After a time all of the water will be salty
without having mixed or stirred the salt and water together with the spoon. The
physical explanation is based upon the natural-occurring thermal, never-ending
vibrations of all molecules that cause them to diffuse and redistribute from locations
of higher to lower or nil concentrations. In the above examples, the high concentra-
tion of stinking odiferous molecules from the overcooked chicken originating in the
kitchen diffuses throughout the apartment, and the salt contained in the spoon ini-
tially dissolves and diffuses within the water to eventually make all of the water in
the entire glass salty and have the same concentration.
Diffusion was fi rst described by the equation known today as Fick's second law.
Because its diffusion coeffi cient was often not a constant, the equation was modifi ed
and became the Fokker Planck equation. Since a nonconstant diffusion coeffi cient
was uniquely comparable to our nonconstant unsaturated hydraulic conductivity
function, the utility of a diffusion-type format to describe unsaturated soil water
fl ow was an emerging possibility at the beginning of the twentieth century. Early
formulations were initiated by physicists at the American school of Utah State
University. It was not just by chance that the fi rst steps were done in the arid, some-
what hostile Utah environment where most farming is realized with irrigation often
using poor-quality slightly saline water. The economic use of sparse water as well
as preventing harmful salt accumulation in the topsoil required experimental and
theoretical research to derive an adequate theory and to prepare optimal instructions
for farmers. Lorenzo (“Ren”) Adolph Richards, a student at USU, extended what he
learned from his physics professors with his own research to complete and publish
his Ph.D. dissertation, “Capillary conduction of liquids through porous mediums,”
in 1931. Ren completed at that time the Buckingham's revolutionary act of
shifting soil physics from empirical observation toward the exact language of
Newtonian physics.
Even with the availability of Richards' equation, the 1930s through most of the
1950s remained uneventful regarding the application of theoretical equations to
describe unsaturated water movement. This period of more than 20 years occurred
partly due to the fact that Richards did not attract a group of students eager to extend
and actually to try to fi nd solutions of their teacher's equations. Additionally, the
equation resembling the various diffusion equations (and even in a more compli-
cated form) was not suffi ciently applicable to observations of unsaturated water
fl ow in fi eld soils. The situation was also diffi cult due to the impossibility to mea-
sure soil water content without disturbing the soil or an ideal homogeneous soil
column in the laboratory. It was so until the application of neutron probe method.
Starting from the 1950s in the twentieth century, the mathematics of diffusion was
extended and immediately the procedures leading to analytical and semi-analytical
solutions were applied in studies on practical tasks on water fl ow in soils not fully
