Journal of Engineering Mathematics

, Volume 119, Issue 1, pp 167–197 | Cite as

Derivation of an effective dispersion model for electro-osmotic flow involving free boundaries in a thin strip

  • Nadja RayEmail author
  • Raphael Schulz


Since dispersion is one of the key parameters in solute transport, its accurate modeling is essential to avoid wrong predictions of flow and transport behavior. In this research, we derive new effective dispersion models which are valid also in evolving geometries. To this end, we consider reactive ion transport under dominate flow conditions (i.e. for high Peclet number) in a thin, potentially evolving strip. Electric charges and the induced electric potential (the zeta potential) give rise to electro-osmotic flow in addition to pressure-driven flow. At the pore-scale a mathematical model in terms of coupled partial differential equations is introduced. If applicable, the free boundary, i.e. the interface between an attached layer of immobile chemical species and the fluid is taken into account via the thickness of the layer. To this model, a formal limiting procedure is applied and the resulting upscaled models are investigated for dispersive effects. In doing so, we emphasize the cross-coupling effects of hydrodynamic dispersion (Taylor–Aris dispersion) and dispersion created by electro-osmotic flow. Moreover, we study the limit of small and large Debye length. Our results improve the understanding of fundamentals of flow and transport processes, since we can now explicitly calculate the dispersion coefficient even in evolving geometries. Further research may certainly address the situation of clogging by means of numerical studies. Finally, improved predictions of breakthrough curves as well as facilitated modeling of mixing and separation processes are possible.


Electrodispersion Electro-osmosis Evolving microstructure Taylor dispersion Upscaling 



This research was inspired by fruitful discussions with Kundan Kumar, University of Bergen, Norway. The personal exchange was kindly supported by the German Academic Exchange Service in the framework of the German–Norwegian collaborative research support scheme 2016.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of MathematicsFriedrich–Alexander University of Erlangen–NürnbergErlangenGermany

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