The role of molecular diffusion in dispersion theory

Abstract

The analytic derivations of the equations governing dispersive flow assume that different solutions entering an interstitial flow channel are completely mixed at the exit node of the flow channel. The physical mechanisms which can effect this mixing are turbulence and molecular diffusion between the solutions in the channel. We have examined these mechanisms and find for the interstitial velocities ordinarily encountered in groundwater flow that turbulence is not effective as a mixing mechanism whereas molecular diffusion is. For molecular diffusion to be efficient as a mixing mechanism the interstitial velocities should be less than: u < 2.25 ks h 2 where k is the diffusion coefficient of the salt solution; s the mean length of the interstitial channels and h the channel diameter. This velocity places an upper limit to the range of validity of the equations of dispersion theory as presently developed.