FLUX-AVERAGED CONCENTRATIONS FOR TRANSPORT IN SOILS HAVING NONUNIFORMINITIAL SOLUTE DISTRIBUTIONS

The need to distinguish between volume-averaged or resident concentrat ions (c(r)) and flux-averaged or flowing concentrations (c(r)) is now widely accepted. Flux-averaged concentrations associated with the conv ection-dispersion equation (CDE) have been mostly used for solute tran sport problems involving uniform initial distributions. We present flu x-averaged concentrations for nonuniform initial distributions using a nalytical solution methods for a semi-infinite soil system and numeric al methods for a finite system. Mathematically, c(r) 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 i nitial conditions. We show that, for a stepwise initial distribution, c(r) can be both negative or much greater than the initial concentrati on of c(r) especially during the early stages of solute displacement. This physically odd situation results from the fact that c(r) represen ts a solute Our rather than a directly measurable volumetric concentra tion. Flux-averaged concentrations at the exit of a finite soil column with a uniform initial distribution are nearly identical to c(r) for a semi-infinite system when the column Peclet number is greater than a pproximate to 5. However, if the initial distribution involves a high gradient in c(r) near the exit, c(r) values for finite and semi-infini te systems at the exit can be very different, similarly as those for c (r) because of the adoption of different outlet conditions.