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

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 D_ax 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.