Exact moment analysis of transient/asymptotic dispersion properties in periodic media with adsorbing/desorbing walls

The paper develops a robust and computationally efficient homogenization approach, grounded on exact local and integral moments, to investigate the temporal evolution of effective dispersion properties of solute particles in periodic media possessing absorbing/desorbing walls. Adsorption onto and desorption from active walls allow linear and reversible mass transfer between the solid surface and the fluid phase. The transient analysis reveals some important features of the dispersion process that cannot be captured by asymptotic approaches aimed at determining exclusively the long-range/large-distance dispersion properties. Two case studies are considered: the dispersion of an analyte in a sinusoidal channel with adsorbing/desorbing walls and the retentive pillar array column for liquid chromatography. For both systems, the transient analysis shows how the tortuous fluid motion induced by the sinusoidal walls or by the presence of pillars induces wide and persistent temporal oscillations of the effective velocity and dispersion coefficient even for a steady (non-pulsating) Stokes flow. The adsorption/desorption process strongly amplifies the phenomenon of the overshoot for the effective dispersion coefficient that, on short/intermediate time scales, reaches values significantly larger than the asymptotic one. Moreover, the method proposed allows a detailed analysis of the temporal evolution of the skewness of the marginal distribution of the analyte along the main stream direction. It clearly shows that the time scale for achieving the macro-transport regime, which implies a Gaussian (symmetric) marginal pdf, is largely underestimated if one bases the analysis on the attainment of constant asymptotic values for the effective velocity and for the dispersion coefficient.