On N. Park's Analytical solution for steady state density‐ and mixing regime—dependent solute transport in a vertical soil column

Abstract

Recently, Park [1996] presented an analytical solution for stationary one‐dimensional solute transport in a variable‐density fluid flow through a vertical soil column. He used the widespread Bear‐Scheidegger dispersion model describing solute mixing as a sum of molecular diffusion and velocity‐proportional mechanical dispersion effects. His closed‐form implicit concentration and pressure distributions thus allow for a discussion of the combined impact of molecular diffusion and mechanical dispersion in a variable‐density environment. Whereas Park only considered the example of vanishing molecular diffusion in detail, both phenomena are taken into account simultaneously in the present study in order to elucidate their different influences on concentration distribution characteristics. The boundary value problem dealt with herein is based on an upward inflow of high‐density fluid of constant solute concentration and corresponding outflow of a lower constant concentration fluid at the upper end of the column when dispersivity does not change along the flow path. The thickness of the transition zone between the two fluids appeared to strongly depend on the prevailing share of the molecular diffusion and mechanical dispersion mechanisms. The latter can be characterized by a molecular Peclet number Pe, which here is defined as the ratio of the column outflow velocity multiplied by a characteristic pore size and the molecular diffusion coefficient. For very small values of Pe, when molecular diffusion represents the exclusive mixing process, density differences have no impact on transition zone thicknesses. A relative density‐;dependent thickness increases with flow velocities (increasing Pe values) very rapidly compared to the density‐independent case, and after having passed a maximum decreases asymptotically to a constant value for the large Peclet number limit when mechanical dispersion is the only mixing mechanism. Hence the special transport problem analyzed gives further evidence for the importance of simultaneously considering molecular diffusion and mechanical dispersion in gravity‐affected solute transport in porous media.