Application of the Convection‐Dispersion Model to Solute Transport in Finite Soil Columns

The one‐dimensional convection‐dispersion model is investigated with respect to the proper boundary conditions to impose in applications to tracer movement in freely draining soil columns. It is shown that the model can be interpreted probabilistically and that this interpretation leads to physical restrictions on solute molecule transport through the inlet and exit boundaries of a soil column. These constraints, in turn, show that the correct exit boundary condition for a freely draining soil column is zero resident concentration or, equivalently, zero gradient in the flux concentration. This boundary constraint is combined with conditions appropriate to either an open or a closed inlet boundary to derive a variety of mass‐conserving solutions (some apparently new) to the convection‐dispersion model for both resident and flux concentrations. In particular, a new solution is presented for the resident concentration under a closed inlet boundary. The corresponding flux concentration solution for a constant solute flux at the inlet is shown to be the same as a solution first obtained by R.W. Cleary and D.D. Adrian (1973).