Dispersion of multiple charged species in an axially symmetric slowly varying channel

TL;DR

This paper develops a macroscopic model for the dispersion of multiple charged ions in axially symmetric channels, revealing how channel geometry influences ionic separation efficiency.

Contribution

It combines lubrication approximation and homogenization theory to derive an effective transport equation for charged species in varying channels, highlighting geometry effects.

Findings

Channel geometry can be tuned to enhance ionic separation.

Geometry-induced electro-diffusive coupling can inhibit dispersion.

Non-monotonic NTP observed depending on channel shape.

Abstract

The transport and dispersion of multiple species of charged ions are central to many biological and physical processes, including electrokinetic ion separation. However, most theoretical studies of dispersion in channels have focused on neutral solutes, leaving the transport of multiple charged species comparatively unexplored. Differences in ionic diffusivities in a multispecies electrolyte solution generate an self-induced electric fields that drive electromigration. To capture these effects at the macroscopic scale, we combine the lubrication approximation with homogenization theory, under electroneutrality and zero-current constraints, to derive an effective transport equation governing the cross-sectionally averaged concentrations. We apply our model framework to a range of channel geometries and compute the resulting effective dispersion coefficients. Finally, we investigate how channel geometry can be tuned to enhance ionic separation. We observe a geometry-induced electro-diffusive coupling that inhibits solute dispersion in certain channels, leading to a non-monotonic Number of Theoretical Plates (NTP) and making such channels ideal for separation processes.