Justification of a new original homogenized model for ionic diffusion in porous media.

IF 2.6 4区 工程技术 Q2 MECHANICS
M. K. Bourbatache, O. Millet, G. Gagneux
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引用次数: 0

Abstract

In this work, a new original justification of an homogenized model for ionic diffusion in porous media is proposed. The approach used enables to specify clearly the domain of validity of this homogenized model, involving a source term characterizing the electrical double layer effect at the macroscale. This homogenized model is obtained from the formal periodic homogenization of Nernst-Planck-Poisson system at the pore scale accounting for conductivity of the solid phase which is generally neglected. The Poisson equation is defined in both fluid and solid phases and the discontinuity of fluxes at the solid-fluid interface is modeled by a jump of the electrical field, linked to the surface electrical charge of the solid interface. Numerical simulations are carried out at the scale of the unit cell to underscore the influence of the contrast on the electrical permittivity between fluid and solid phases. The comparison of the concentrations and the electrical potential given at the macro-scale by the homogenized model and by a direct pore scale model reveals the accuracy of the homogenized model which is very simple to use.
多孔介质中离子扩散的一种新的原始均匀化模型的证明。
在这项工作中,为离子在多孔介质中的均匀扩散模型提出了一个新的原始理由。所使用的方法能够清楚地指定这种均匀化模型的有效域,包括在宏观尺度上表征电双层效应的源项。该均匀化模型是从孔尺度上的能斯特-普朗克-泊松系统的形式周期均匀化获得的,考虑到固相的电导率,而固相的电导率通常被忽略。泊松方程在液相和固相中都有定义,并且通过与固体界面的表面电荷相关的电场跳跃来模拟固体-流体界面处通量的不连续性。在晶胞的尺度上进行了数值模拟,以强调对比度对液相和固相之间的介电常数的影响。均化模型和直接孔尺度模型在宏观尺度上给出的浓度和电势的比较揭示了使用非常简单的均化模型的准确性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
4.80
自引率
3.80%
发文量
95
审稿时长
5.8 months
期刊介绍: All areas of theoretical and applied mechanics including, but not limited to: Aerodynamics; Aeroelasticity; Biomechanics; Boundary layers; Composite materials; Computational mechanics; Constitutive modeling of materials; Dynamics; Elasticity; Experimental mechanics; Flow and fracture; Heat transport in fluid flows; Hydraulics; Impact; Internal flow; Mechanical properties of materials; Mechanics of shocks; Micromechanics; Nanomechanics; Plasticity; Stress analysis; Structures; Thermodynamics of materials and in flowing fluids; Thermo-mechanics; Turbulence; Vibration; Wave propagation
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