First‐ and third‐type boundary conditions in two‐dimensional solute transport modeling

This paper presents a general analytical solution for convective‐dispersive solute transport in a two‐dimensional, semiinfinite porous medium. The solute is assumed to be subject to linear equilibrium sorption and first‐order decay. Solutions are derived for several third‐type (Cauchy) or flux‐type boundary conditions at the input surface. After presenting a generally applicable solution a special solution is given for a strip‐type solute source. It is shown that the third‐type boundary condition correctly conserves mass in the two‐dimensional system and that the first‐type (Dirichlet) or concentration‐type boundary condition corresponds to a situation that the solute flux at the source decreases with time and at large time approaches to the solute flux of the third‐type boundary condition. This can lead to significant discrepancies in the calculated concentrations, especially near the source boundaries.