Agriculture Reference
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an adaptation of the traveling wave solution. Wu, Kool, and Huyakorn (1997)
developed another analytical model for nonlinear adsorptive transport
through layered soils ignoring the effects of dispersion. In addition, Guo et
al. (1997) showed that the transfer function approach was a very powerful
tool to describe the nonequilibrium transport of reactive solutes through lay-
ered soil profiles with depth-dependent adsorption.
When we study transport processes of dissolved chemicals in layered
soils, it is of interest to investigate whether soil layering affects solute
breakthrough. When flow remains one-dimensionally vertical, which is
the case when horizontal stratification is dominant, it is of interest whether
the layering order affects breakthrough results at the groundwater level
(van der Zee, 1994). The early results from Shamir and Harleman (1967)
showed that the order of layering did not affect breakthrough significantly.
This interesting result was further elaborated upon by Barry and Parker
(1987) based on various analytical approaches. Results from various linear
and nonlinear numerical simulations for several sorption model types also
supported this conclusion (Selim, Davidson, and Rao, 1977). Furthermore,
Selim, Davidson, and Rao (1977) concluded that layering order was also
unimportant for Freundlich adsorption. Their experimental results also
supported this conclusion. However, van der Zee (1994) attributed the
results attained by Selim and coworkers (1977) to the small Peclet number
assumed for the nonlinear layer, which prevents nonlinearity effects from
being clearly manifested. Van der Zee (1994) used a hypothetical result to
illustrate that layering sequence should have an effect. However, what van
der Zee (1994) used to support his conclusion was the traveling wave, which
was the curve of concentration versus depth at different times, that is, the
concentration profile. More recently, Zhou and Selim (2001) accounted
for several nonlinear and kinetic retention mechanisms for multilayered
soils. For individual soil layers, Zhou and Selim (2001) considered solute
retention mechanisms of the nonlinear (Freundlich), Langmuir, first- and
nth-order kinetic, second-order kinetic, and irreversible reactions. For all
retention mechanisms used, their simulation results indicated that sol-
ute breakthrough curves (BTCs) were similar regardless of the layering
sequence in a soil profile. This finding is consistent with the earlier finding
of Selim, Davidson, and Rao (1977) and contrary to that of Bosma and van
der Zee (1992) for nonlinear adsorption.
In the next sections, we present general equations for solute transport
in multilayered systems followed by a discussion of the various choices of
boundary conditions at the interface between layers. We further present
selected case studies of linear and nonlinear adsorption mechanisms in lay-
ered soil systems based on numerical simulations for a range of soil proper-
ties and fluxes (or Brenner numbers). Experimental BTCs based on miscible
displacements from a packed sand-clay soil column for a tracer (tritium) and
for reactive solutes (Ca and Mg) are subsequently presented in support of
theoretical findings.
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