Taylor-Aris dispersion for N-zone and continuous systems with variable sorption strength – extending Aris’s approach

Abstract

It is shown Aris’ general solution method for the asymptotic axial dispersion in nested two-layer systems with a radial distribution of the axial velocity and with different diffusion and sorption properties in each layer can be generalized to nested and distributed N-zone systems and systems with continuously varying sorption strength by introducing a generalized flux expression J = −D.K.∇(C/K). In this expression, the local diffusion coefficient D and the local sorption constant K can be either piecewise constant (N-zone system) or continuous functions of the radial space coordinates (continuous system). After a mathematically sound derivation of the general solution, it is validated by comparing the resulting expressions for Dax with either existing literature expressions or with the dispersion coefficient found by numerically solving the complete, time-dependent advection–diffusion mass balance for a number of selected examples. Applications can be found in continuous flow membrane separations, chromatography, and flows through extruded mesoporous ceramic beds.