Universal electro-osmosis formulae for porous media

Approximate analytical formulae valid for any porous media with elongated pores are derived for the electro-osmotic coefficient α   and for the average ionic concentration n¯. A macroscopic Debye–Hückel length κ¯−1 based on n¯ is introduced. Simultaneously, the electro-osmotic coefficient α   is systematically calculated for various media, zeta potentials and electrolyte concentrations by solving the local equations. Numerical results show that κ¯−1 and α follow universal curves valid whatever the porous medium; these curves can be approximated by the analytical formulae previously derived. These formulae can be used to provide a priori estimates of the electro-osmotic coefficient.

Graphical abstractElectro-osmotic coefficients calculated for any porous media, any zeta potentials and any electrolyte concentrations are shown to follow a universal curve when the macroscopic Debye–Hückel length based on the average concentration is used.Figure optionsDownload full-size imageDownload as PowerPoint slide