Electro-hydrodynamic transport in porous materials

Depending on the permeability of porous materials, different mass transport mechanisms have to be distinguished. Whereas mass transport through porous media characterized by low permeabilities is governed by diffusion, mass transport through highly permeable materials is governed by advection. Additionally a large number of porous materials are characterized by the presence of surface charge which affects the permeability of the porous medium. Depending on the ion transport mechanism various phenomena such co-ion exclusion, development of diffusion-exclusion potentials, and streaming potentials may be encountered. Whereas these various phenomena are commonly described by means of different transport models, a unified description of these phenomena can be made within the framework of electro-hydrodynamics.

In this paper the fundamental equations describing micro-scale multi-ion transport are given. These equations comprise the generalized Nernst-Planck equation, the Poisson equation of electrostatics, and the Navier-Stokes equation. Various phenomena such as the development of exclusion potentials, diffusion-exclusion potentials, and streaming potentials are investigated. Furthermore, the influence of the surface charge on permeability and ion transport are studied in detail for various problems using numerical simulation tools. The nanoscale findings provide insight into events observed at the macroscale in clay soils.

• Introduction

• Transport equations for diffusion-advection at the micro-scale

• Mass transport through a charged slit opening

• Summary and Conclusions

• Acknowledgments

• References