Derivation of an effective dispersion model for electro-osmotic flow involving free boundaries in a thin strip
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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.
KeywordsElectrodispersion 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.
- 1.Acar YB, Gale RJ, Alshawabkeh AN, Marks RE, Puppala S, Bricka M, Parker R (1995) Electrokinetic remediation: basics and technology status. J Hazard Mater 40(2):117–137. Soil Remediation: Application of Innovative and Standard TechnologiesGoogle Scholar
- 2.Jacob H, S.B. Masliyah (2006) Electrokinetic and colloid transport phenomena. Wiley, New YorkGoogle Scholar
- 3.Jamshidi-Zanjani A, Khodadadi Darban A (2017) A review on enhancement techniques of electrokinetic soil remediation. Pollution 3(1):157–166Google Scholar
- 4.Xuan X: Recent advances in direct current electrokinetic manipulation of particles for microfluidic applications. Electrophoresis 40(18–19):2484–2513Google Scholar
- 9.van Noorden TL, Pop IS, Ebigbo A, Helmig R (2010) An upscaled model for biofilm growth in a thin strip. Water Resour Res 46(6):W06505Google Scholar
- 32.van Duijn C, Mikelić A, Pop I, Rosier C (2008) Chapter 1 effective dispersion equations for reactive flows with dominant Péclet and damkohler numbers. In: Guy DW, Marin B, Yablonsky GS (eds) Advances in chemical engineering mathematics in chemical kinetics and engineering, vol 34. Advances in Chemical Engineering. Academic Press, New York, pp 1–45CrossRefGoogle Scholar
- 41.Ray N, Schulz R (2017) Derivation of an effective dispersion model for electroosmotic flow involving free boundaries in a thin strip. Tech. Rep. 398, Preprint Series Angewante Mathematik, Universität Erlangen-NürnbergGoogle Scholar