A mathematical analysis is presented of the phenomenon of simultaneous dispersion and adsorption of a solute in porous media flow. Mathematical solutions are given that refer to the case of dispersion without adsorption and to the case of adsorption without dispersion. Numerous experiments were conducted in a lucite column containing 3 mm or 5 mm diameter glass beads; water was the fluid and methylene blue dye the solute in all experiments. The Reynolds number range extended from 6.6 to 280. It was found that the rate constants, introduced in the expression for solute transfer from the fluid phase to the solid phase, correlated fairly well with the Reynolds number. A dimensionless plot of all concentration data was obtained; the coordinates of this plot were predicted from the mathematical analysis. This work relates to some aspects of soil leaching and salinity intrusion problems.