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Flux-Averaged Concentrations for Transport in Soils Having Nonuniform Initial Solute Distributions

U.S. Salinity Lab., USDA-ARS, 4500 Glenwood Drive, Riverside, CA 92501

*Corresponding author.

ABSTRACT

The need to distinguish between volume-averaged or resident concentrations (c_r) and flux-averaged or flowing concentrations (c_f) is now widely accepted. Flux-averaged concentrations associated with the convection-dispersion equation (CDE) have been mostly used for solute transport problems involving uniform initial distributions. We present flux-averaged concentrations for nonuniform initial distributions using analytical solution methods for a semi-infinite soil system and numerical methods for a finite system. Mathematically, c_f is equivalent to c_r associated with a first-type inlet condition (rather than a third-type condition) only for semi-infinite soil profiles having uniform initial conditions. We show that, for a stepwise initial distribution, c_f can be both negative or much greater than the initial concentration of c_r, especially during the early stages of solute displacement. This physically odd situation results from the fact that c_f represents a solute flux rather than a directly measurable volumetric concentration. Flux-averaged concentrations at the exit of a finite soil column with a uniform initial distribution are nearly identical to c_f for a semi-infinite system when the column Peclet number is greater than 5. However, if the initial distribution involves a high gradient in c_r near the exit, c_r values for finite and semi-infinite systems at the exit can be very different, similarly as those for c_r, because of the adoption of different outlet conditions.

Received for publication November 30, 1992.