ANALYTICAL SOLUTIONS FOR SOLUTE TRANSPORT IN FINITE SOIL COLUMNS WITHARBITRARY INITIAL DISTRIBUTIONS

Analytical expressions were derived for the solute concentration in so ils with a nonuniform initial distribution and a finite outlet conditi on assuming a zero gradient at the soil outlet. The advection-dispersi on equation (ADE) was solved by successively using a Laplace transform with respect to time, variation of parameters, and two different inve rsion procedures. Solutions for two resident concentrations and a flux -averaged concentration were derived for arbitrary and pulse-type init ial distributions. The solutions are applicable for a wide range of co nditions. Particular attention was paid to cases involving small Pecle t numbers and large dispersive fluxes associated with steep fronts in the initial distribution. Flux-averaged concentrations may become nega tive or exceed the initial concentration, while solutions for the resi dent 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 sui table to describe initial value problems where travel times are typica lly short and large concentration gradients may occur.