A solution of the differential equation of longitudinal dispersion in porous media

Abstract

Published papers indicate that most investigators use the coordinate transformation (x ut) in order to solve the equation tor dispersion of a moving fluid in porous media. Further, the boundary conditions O=0 at x=> and 0=00 at x= > for Z>0 are used, which results in a symmetrical concentration distribution. This paper presents a solution of the differential equation that avoids this transformation, thus giving rise to an asymmetrical concentration distribution. It is then shown that this solution approaches that given by symmetrical boundary conditions, provided the dispersion coefficient D is small and the region near the source is not considered.