Investigations of effective dispersion models for electroosmotic flow with rigid and free boundaries in a thin strip

Reactive flow and transport in porous media is topic of intense research since decades. 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 investigate novel effective di...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2024-01, Vol.47 (1), p.206-228
Main Authors: Schulz, Raphael, Gärttner, Stephan, Ray, Nadja
Format: Article
Language:English
Subjects:
Cross coupling
Diffusion layers
Dispersion
electrodispersion
Electroosmosis
Evolution
evolving microstructure
existence
Free boundaries
Geometry
Investigations
Mathematical models
Modelling
Molecular diffusion
numerical simulations
Parameters
Porous media
Strip
Taylor dispersion
Thickness
Transport phenomena
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Summary:Reactive flow and transport in porous media is topic of intense research since decades. 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 investigate novel effective dispersion models for reactive transport of electrically charged chemical species in a thin, potentially evolving strip taking into account Taylor–Aris and electroosmotic‐induced dispersion as well as their cross‐coupling effects. We prove positivity of the dispersion coefficient and the existence and uniqueness of strong solutions in the fixed geometry setting. Moreover, we numerically investigate scenarios for both the fixed and evolving geometry situation. The simulation results illustrate the possibility of separating charged species, such that the findings of this study can lead to a better understanding of mixing and separation processes of charged solutes and an improved prediction of breakthrough curves. Finally, we study the limits of vanishing channel width, precipitation layer thickness, and molecular diffusion. We show convergence of the solutions to the corresponding limit cases such as a hyperbolic model or the fixed geometry case. From these results, we can rate the impact of distinct dispersion mechanisms and evaluate the necessity of a detailed modeling for different parameter regimes.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.9651