A Consistance Model for Anion Exclusion and Surface Diffusion
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ABSTRACT A decomposition of the diffusion flux equation for an electrostatically bound and mobile hydrated ion into two components is proposed. The first component includes the effects arising solely from the irregular pore shape and increase in solvent viscosity in the proximity of negatively charged pore walls. Apart from these effects, the second flux component includes an additional contribution from an increased (decreased) concentration for cations (anions) close to the pore walls. Defining the distribution coefficient, Kd, in a fashion that allows negative values for co-ions readily accounts for their exclusion without the need to introduce somewhat artificial quantities like the "effective co-ion porosity". In this study, it is thus possible to retain the purely volumetric meaning of the porosity and to maintain consistency throughout the conceptualization for anions, cations and electrically neutral species. Furthermore, the decomposition of the flux equation provides support for surface diffusion, a subject of great controversy and lively debate in the literature. In this connection, the role of concentration to regulate the diffusive flux for ions in relation to neutral species is emphasized. Implications for the theoretical apparent and effective diffusivities in compacted montmorillonite clay are also discussed and a modified form of the macroscopic theory is proposed.
INTRODUCTION The process of surface diffusion can be understood as the transport of cations compensating for the negative surface charge of the clay. The cations residing in the whole of the electric double layer (EDL) can thus be viewed as participating in this process. Similarly, the cations outside the influence of the diffuse layer are thought of as free cations to which pore fluid diffusivities can be assigned. This conceptual division affords a plausible explanation as to why the suggested surface diffusion becomes more pronounced upon compaction and, consequently, upon the increase in EDL interpenetration. That is to say, the percentage of cations transported by surface diffusion increases in relation to their pore fluid diffusion. The objective of this study is to gain insight into the origin of the surface diffusion term in the flux equation and to rectify some fairly common misconceptions about surface diffusion in compact clays. From the mathematical and phenomenological standpoints, the decomposition of the diffusion flux stemming from the EDL theory can be shown to justify the surface diffusion term. An interesting outcome of the flux decomposition is that the surface diffusion, as understood in the context of EDLs, becomes an anion property, too. This is perfectly logical since there is no reason as to why anions could not diffuse in the EDL although their concentrations there are very low.
THEORY Microscopic model Following the EDL theorization in [1] (and the tacit assumptions therein) for the microscopic-level diffusive transport of ions in slit-like channels and correcting the diffusivities for
E-mail: Jarmo.Lehikoin
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