On the Validity of the Null Current Assumption for Modeling Sorptive Reactive Transport and Electro-Diffusion in Porous Media

Tabrizinejadas, Sara; Carrayrou, Jérôme; Saaltink, Maarten W.; Baalousha, Husam Musa; Fahs, Marwan

doi:10.3390/w13162221

Cited by 3 publications

(1 citation statement)

References 31 publications

(48 reference statements)

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“…which is used commonly in the literature when there is no external electric field (Ben-Yaakov 1972;Gupta et al 2019;Tournassat, Steefel & Gimmi 2020;Tabrizinejadas et al 2021). Moreover, for the electroneutrality initial data, the zero electric current condition ensures that the electroneutrality condition is always true (see Boudreau, Meysman & Middelburg 2004).…”

Section: Advection Nernst-planck Equationmentioning

confidence: 99%

Shear dispersion of multispecies electrolyte solutions in the channel domain

Ding

2023

J. Fluid Mech.

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In multispecies electrolyte solutions, even in the absence of an external electric field, differences in ion diffusivities induce an electric potential and generate additional fluxes for each species. This electro-diffusion process is well-described by the advection Nernst–Planck equation. This study aims to analyse the long-time behaviour of the governing equation under electroneutrality and zero current conditions, and to investigate how the diffusion-induced electric potential and shear flow enhance the effective diffusion coefficients of each species in channel domains. The exact solutions of the effective equation with certain special parameters, as well as the asymptotic analyses for ions with large diffusivity discrepancies, are presented. Furthermore, there are several interesting properties of the effective equation. First, it is a generalization of the Taylor dispersion, with a nonlinear diffusion tensor replacing the scalar diffusion coefficient. Second, the effective equation exhibits a scaling relation, revealing that the system with a weak flow is equivalent to the system with a strong flow under scaled physical parameters. Third, in the case of injecting an electrolyte solution into a channel containing well-mixed buffer solutions or electrolyte solutions with the same ion species, if the concentration of the injected solution is lower than that of the pre-existing solution, then the effective equation simplifies to a multi-dimensional diffusion equation. However, when introducing the electrolyte solution into a channel filled with deionized water, the ion–electric interaction results in several phenomena not present in the advection–diffusion equation, including upstream migration of some species, spontaneous separation of ions, and non-monotonic dependence of the effective diffusivity on Péclet numbers. Finally, the dependence of effective diffusivity on concentration and ion diffusivity suggests a method to infer the concentration ratio of each component and ion diffusivity by measuring the effective diffusivity.

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Section: Advection Nernst-planck Equationmentioning

confidence: 99%

Shear dispersion of multispecies electrolyte solutions in the channel domain

Ding

2023

J. Fluid Mech.

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Applied Groundwater Modelling for Water Resource Management and Protection

Baalousha

Lowry

2022

Water

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Validating the Nernst–Planck transport model under reaction-driven flow conditions using RetroPy v1.0

Huang,

Flemisch,

Qin

et al. 2023

Geosci. Model Dev.

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Abstract. Reactive transport processes in natural environments often involve many ionic species. The diffusivities of ionic species vary. Since assigning different diffusivities in the advection–diffusion equation leads to charge imbalance, a single diffusivity is usually used for all species. In this work, we apply the Nernst–Planck equation, which resolves unequal diffusivities of the species in an electroneutral manner, to model reactive transport. To demonstrate the advantages of the Nernst–Planck model, we compare the simulation results of transport under reaction-driven flow conditions using the Nernst–Planck model with those of the commonly used single-diffusivity model. All simulations are also compared to well-defined experiments on the scale of centimeters. Our results show that the Nernst–Planck model is valid and particularly relevant for modeling reactive transport processes with an intricate interplay among diffusion, reaction, electromigration, and density-driven convection.

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On the Validity of the Null Current Assumption for Modeling Sorptive Reactive Transport and Electro-Diffusion in Porous Media

Cited by 3 publications

References 31 publications

Shear dispersion of multispecies electrolyte solutions in the channel domain

Shear dispersion of multispecies electrolyte solutions in the channel domain

Applied Groundwater Modelling for Water Resource Management and Protection

Validating the Nernst–Planck transport model under reaction-driven flow conditions using RetroPy v1.0

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