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

Abstract

AbstractThe need to distinguish between volume‐averaged or resident concentrations (cr) and flux‐averaged or flowing concentrations (cf) 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, cf is equivalent to cr 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, cf can be both negative or much greater than the initial concentration of cr, especially during the early stages of solute displacement. This physically odd situation results from the fact that cf 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 cf for a semi‐infinite system when the column Peclet number is greater than ≈ 5. However, if the initial distribution involves a high gradient in cr near the exit, cr values for finite and semi‐infinite systems at the exit can be very different, similarly as those for cr, because of the adoption of different outlet conditions.