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Journal of Porous Media
インパクトファクター: 1.752 5年インパクトファクター: 1.487 SJR: 0.43 SNIP: 0.762 CiteScore™: 2.3

ISSN 印刷: 1091-028X
ISSN オンライン: 1934-0508

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Journal of Porous Media

DOI: 10.1615/JPorMedia.v12.i2.10
pages 101-118

Electrodiffusive Transport in Charged Porous Media: From the Particle-Level Scale to the Macroscopic Scale Using Volume Averaging

Peter Pivonka
Department of Civil and Environmental Engineering, The University of Melbourne, VIC 3010, Australia
Guillermo A. Narsilio
Department of Civil and Environmental Engineering, The University of Melbourne, VIC 3010, Australia
Renmin Li
Institute of Geotechnical Engineering, Southeast University, Nanjing, Jiangsu, China
David W. Smith
Department of Civil and Environmental Engineering, The University of Melbourne, VIC 3010, Australia
Bruce Gardiner
Department of Civil and Environmental Engineering, The University of Melbourne, VIC 3010, Australia

要約

The Poisson-Nernst-Planck (PNP) system of equations can be used to describe electro-diffusive multi-ion transport through uncharged porous materials. Phenomenological formulations have been proposed for charged porous media (e.g. clays), usually disregarding links to the particle level scale. However using volume averaging of microscale governing equations, we derive a new set of up-scaled generalized (macroscopic) PNP equations that are valid for both charged and uncharged porous materials. These equations consistently account for non-homogeneous ionic distributions at the microscale, but reduce standard phenomenological PNP equations for the special case of uncharged porous materials. With this approach we can estimate macroscopic parameters such as effective diffusion coefficients for individual charged species, and the effective fixed charge concentration, based on microscale quantities. It is shown that effective ion diffusion coefficients are functions of ion self-diffusion coefficients, the tortuosity of the porous material, and effective concentrations, which depend on surface charge density and concentration of background electrolyte. We apply the proposed method to electro-diffusive transport of a binary electrolyte through a thin charged porous membrane containing cylindrical pores. This allows estimation of the derived generalized effective diffusion coefficient in two ways, i.e., based on the derived formula and from the ion flux equations.


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