Taylor Dispersion and Anomalous Diffusion

Abstract

Diffusion is a very rich phenomenon which goes beyond the classical simple description in quiescent systems. On the one side, inhomogeneities in the flow velocity exert a deep influence on the behaviour of diffusion and have enormous environmental and industrial importance, as for instance in the transport of pollutants or in the functioning of chemical reactors under continuous flow. Furthermore, the exponents characterizing the temporal behaviour of diffusion are drastically altered in the presence of velocity gradients. Indeed, the presence of a simple shear changes the usual behaviour áx ²ñ ~ t to áx ²ñ ~ t ³, with x the displacement of the solute particles with respect to the moving solvent in the direction of the flow. This implies an enormous enhancement of diffusion along this direction. Note that an exponent 3 for time also appears in diffusion in turbulent situations (Ichisenko 1992).