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Analytical Solutions for Solute Transport in Finite Soil Columns with Arbitrary Initial Distributions

U.S. Salinity Lab., USDA-ARS, 450 West Big Springs Road, Riverside, CA 92507

Nobuo Toride

Dep. of Agricultural Sciences, Saga Univ., Saga 840, Japan

*Corresponding author (fleij{at}ussl.ars.usda.gov).

ABSTRACT

Analytical expressions were derived for the solute concentration in soils with a nonuniform initial distribution and a finite outlet condition assuming a zero gradient at the soil outlet. The advection-dispersion equation (ADE) was solved by successively using a Laplace transform with respect to time, variation of parameters, and two different inversion procedures. Solutions for two resident concentrations and a flux-averaged concentration were derived for arbitrary and pulse-type initial distributions. The solutions are applicable for a wide range of conditions. Particular attention was paid to cases involving small Peclet numbers and large dispersive fluxes associated with steep fronts in the initial distribution. Flux-averaged concentrations may become negative or exceed the initial concentration, while solutions for the resident concentration, derived for first- and third-type inlet conditions, can predict a substantial amount of upstream solute transport due to dispersion. This suggests that the conventional ADE is not always suitable to describe initial value problems where travel times are typically short and large concentration gradients may occur.

Received for publication July 9, 1997.

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