Taylor dispersion in a two-zone packed tube

Heterogeneity of media distribution in a packed tube plays an important role on scalar dispersion by enhancing the transverse non-uniformity of the flow velocity. Presented in this paper is a theoretical analysis for an instantaneous release of scalar substance into a fully developed flow through a long tube of two zones distinctively packed with porous media. The velocity distribution of the flow through the tube is derived, with the known solution for a single zone tube flow included as a special case. Mei’s perturbation analysis for scalar dispersion in a single phase fluid flow is rigorously generalized for the two-zone case of a tube flow to develop a dispersion model by averaging the concentration transport equation. Corresponding dispersivity is analytically determined, and Taylor’s well-known result for a single-zone tube flow is recovered by setting corresponding parameters as unity. The enhancement of the dispersion by the heterogeneity and the dependence of the enhanced dispersion on the tube radius are illustrated and characterized by relevant dimensionless parameters.