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metal breakthrough curves were observed for the four undisturbed soil col-
umns, reflecting different preferential flow paths. Similarly, Corwin, David,
and Goldberg (1999) demonstrated with a lysimeter column study that with-
out accounting for preferential flow, 100% of the applied As was isolated in
the top 0.75 m over a 2.5-year period. However, when preferential flow was
considered and a representative bypass coefficient was used, about 0.59% of
applied As moved beyond 1.5 m. Han et al. (2000) quantified the distribution
of several heavy metals in a clay soil grown to pasture which had received
poultry waste applications over 25 years. They found significant concentra-
tion for Zn up to 1 m when compared to nonamended soil.
8.3 Mobile-Immobile or Two-Region
One of the most popular mechanistic models that is currently used to model
the physical nonequilibrium that results from either the presence of aggre-
gates or macropores was presented by van Genuchten and Wierenga (1976),
which was based on the scheme developed in petroleum engineering by
Coats and Smith (1964). The great simplicity of this model is that one frac-
tion of the soil water Θ im is considered, for transport purposes, to be stag-
nant. This immobile water may be residing in the intra-aggregate domain,
or within the micropores of the matrix. Furthermore, mobile soil water Θ m
may be regarded as water residing between the aggregates or flowing in
the macropores. This arbitrary division of mobile and immobile soil water
fractions is not realistic. Nevertheless, because of its simplicity it provides
a convenient analytical tool to assess the influence of mobile-immobile on
preferential flow (Clothier, Kirkham, and Mclean, 1992).
For soils dominated by macropores that are connected within a micro-
porous matrix, an earlier-than-expected arrival of solute will occur due
to preferential transport along the larger and multiconnected macroporcs
(Figure  8.1). This higher velocity transport, coupled with mechanical mix-
ing between the variously sized macropore networks, will result in a break-
through of inert solute in which the smearing is dominated by hydrodynamic
dispersion. The relative role of diffusion from the macropores will depend
on the comparative size of the macropores. In the lower limit the pore sizes
will be of the same order, and the flow will become uniform since local equi-
librium will prevail.
As stated earlier, several experimental studies showed evidence of early
breakthrough results and tailing with nonsymmetrical concentration distri-
butions of effluent breakthrough curves (BTCs). Discrepancies from symmet-
rical or ideal behavior for several solutes led to the concept of solute transfer
between mobile and immobile waters. It is commonly postulated that tailing
under unsaturated conditions was perhaps due to the fact that larger pores
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