Universal electro-osmosis formulae for porous media

Understanding fluid transport in porous structures is central to many engineering and scientific applications. Prior research has shown that electro-osmosis, a process where fluid moves due to an electric field, is influenced by pore geometry and ionic concentration. However, predicting electro-osmotic behavior across diverse porous media remains challenging. Existing models often assume idealized pore shapes, limiting their applicability. This gap motivated the search for a more general approach. No prior work had resolved how to unify electro-osmotic predictions across arbitrary pore geometries. The need for a predictive framework that avoids numerical simulations is clear. This paper's contribution lies in deriving analytical expressions that apply broadly. The study addresses the lack of a unified model for electro-osmotic transport in complex media.

This work aims to derive analytical expressions for electro-osmotic transport in porous media with arbitrary pore geometries. The specific problem involves predicting the electro-osmotic coefficient and ionic concentration without relying on numerical simulations. The motivation stems from the limitations of existing models, which are often geometry-specific. The study seeks to provide a universal framework applicable to any elongated pore structure. The authors propose a method that combines macroscopic parameters with local equations. This approach allows for a priori estimation of electro-osmotic behavior. The goal is to simplify the prediction of fluid transport in heterogeneous media. The study bridges the gap between theoretical models and practical applications.

The study derives analytical formulae by considering elongated pores in porous media. A macroscopic Debye-Hückel length is defined based on average ionic concentration. Local equations are solved numerically for various media and zeta potentials. The electro-osmotic coefficient is calculated systematically across different conditions. The analytical and numerical results are compared to assess universality. The pore geometry is not restricted to any specific shape in the derivation. The approach combines theoretical analysis with numerical validation. The method ensures that the derived formulae are broadly applicable.

The derived formulae accurately predict the electro-osmotic coefficient across diverse porous media. Numerical simulations confirm the universality of the analytical expressions. The macroscopic Debye-Hückel length correlates strongly with the coefficient. The results show that the coefficient follows a consistent trend regardless of pore geometry. The average ionic concentration is also well described by the analytical model. The study demonstrates that the formulae can be used for a priori estimation. The agreement between analytical and numerical results is robust. The findings suggest that the formulae are reliable for practical applications.

The authors propose that the derived formulae provide a universal framework for electro-osmotic transport. The study shows that the electro-osmotic coefficient can be predicted without detailed pore geometry. The analytical expressions are validated through numerical simulations. The universality of the results is supported by consistent trends across different media. The study does not claim that the formulae are the only valid approach. The authors suggest that the expressions are useful for a priori estimation. The findings do not imply that all pore geometries behave identically. The study emphasizes the predictive power of the derived formulae.