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

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Abstract
In multispecies electrolyte solutions, each individual species can migrate according to its specific ionic properties. This process is called electrochemical migration or electro-diffusion and is well-described by the Nernst–Planck equation. The common approach for solving the corresponding mathematical system is based on the null current (NC) assumption, which expresses the electric potential in terms of charges and concentrations of chemical components. This assumption has a great advantage as it eliminates the electric potential from the Nernst–Planck equation. However, the NC assumption has limited capacities in describing electro-diffusion processes when the domain is subjected to an external electric field. The validity of the NC assumption could be questionable, even in the absence of an external electric field. This topic has never been investigated in the past. The main goal of this work is to evaluate the validity of the NC assumption and to understand its effect on the model outputs. Thus, we present a new reactive transport model that allows for a reliable representation of the electrochemical migration process. This model is based on the Nernst–Planck and Poisson (NPP) equations which are solved together. We also implement a model based on the NC assumption. Both models have been validated by comparison with CrunchFlow, based on several benchmarks. The results show that in the case of high sorptivity, the NC assumption is no longer valid. Therefore, in the case of sorption processes, the NPP should be used to simulate coulombic interactions.

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