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

Abstract

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.

Structured microgroove columns as a potential solution to obtain perfectly ordered particle beds

“…Knowing from earlier work on pillar array columns that the kinetic performance of columns composed of a parallel bundle of interconnected channels is quasi-independent of the degree of channel tortuosity [31], and invoking Brenner's dispersion theory [29,30], the unit cell can be limited to a single pocket (Fig. S-2).…”

“…Based on this velocity field and a range of dimensionless velocities, the so-called B-field from the Brenner dispersion theory [29] was calculated. This led to the effective axial dispersion coefficient D ax [30], from which the reduced plate height could be calculated. The appropriateness of the Brenner dispersion theory to calculate chromatographic data was validated in-house, and resulted in a perfect agreement of the obtained plate height values compared to those described in literature CFD studies [9].…”

An In-Depth Investigation of Micropillar Array Columns for the Separation of Finite-Sized Particles by Hydrodynamic Chromatography

“…Equations – are valid for a tracer particle as well, although they strongly simplify by enforcing w 0 = 1/Vol­(Ω) . The advantage of eq has already been extensively exploted for the analysis of dispersion properties in partition and adsorption chromatography. − The velocity field, the stationary pdf w 0 , and the b-field in the unit cell are obtained by the Finite Element Method in Comsol Multiphysics. Numerical details are listed in the SI.…”

Nonadditivity and Nonlinearity of Mobile and Stationary Zone Mass Transfer Resistances in Chromatography

“…An alternative to moment analysis is the method of volume-averaging, which has previously been applied to study the dispersion in porous media. − However, recent developments in moment analysis have demonstrated some of its advantages, such as its near-endless generalizability and its applicability to both transient and steady-state processes. − …”