Concentration distribution in the wake of a sphere buried in a granular bed through which fluid flows

Abstract

The concentration distribution in the wake of a soluble sphere immersed in a granular bed of inert particles, through which fluid flows with “uniform velocity”, has been obtained numerically, for solute transport by both advection and diffusion/dispersion. Fluid flow in the granular bed around the sphere was assumed to follow Darcy’s law and, at each point, dispersion of solute was considered in both the cross-stream and streamwise directions. The elliptic PDE equation, resulting from a differential material balance on the solute, was solved numerically over a wide range of values of the relevant parameters (Peclet number and Schmidt number). The solution gives the concentration contour plots and, for each concentration level, the width and downstream length of the corresponding contour surface were determined. General expressions are presented to predict contaminant “plume” size downstream of the polluting source.