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

• Published in: Journal of engineering mathematics 2019-12, Vol.119 (1), p.167-197
• Main Authors: Ray, Nadja, Schulz, Raphael
• Format: Article
• Language: English
• Subjects: Applications of Mathematics; Computational Mathematics and Numerical Analysis; Cross coupling; Debye length; Dispersion; Electroosmosis; Evolution; Free boundaries; Ion transport; Mathematical and Computational Engineering; Mathematical Modeling and Industrial Mathematics; Mathematical models; Mathematics; Mathematics and Statistics; Organic chemistry; Partial differential equations; Peclet number; Strip; Theoretical and Applied Mechanics; Thickness; Transport phenomena; Zeta potential
• ISSN: 0022-0833; 1573-2703
• DOI: 10.1007/s10665-019-10024-8

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.