Tortuosity-porosity relation in the porous media flow

TL;DR

This study numerically investigates the tortuosity-porosity relation in porous media, highlighting the importance of finite-size effects and proposing a simple calculation method that aligns well with empirical data.

Contribution

It introduces a straightforward tortuosity calculation method and clarifies the impact of finite-size effects on previous underestimations, confirming the empirical tortuosity-porosity relation.

Findings

Finite-size effects significantly affect tortuosity estimates.

The proposed method simplifies tortuosity calculation.

Numerical results agree with empirical $T-1\,\propto\,\ln\phi$ relation.

Abstract

We study numerically the tortuosity--porosity relation in a microscopic model of a porous medium arranged as a collectin of freely overlapping squares. It is demonstrated that the finite-size effects and the discretization errors, which were ignored in previous studies, may cause significant underestimation of tortuosity. The simple tortuosity calculation method proposed here eliminates the need for using complicated, weighted averages. The numerical results presented here are in good agreement with an empirical relation between tortuosity ($T$) and porosity ($\phi$) given by $T-1\propto \ln\phi$, that was found by others experimentally in granule packings and sediments. This relation can be also written as $T-1\propto R S/\phi$ with $R$ and $S$ denoting the hydraulic radius of granules and the specific surface area, respectively.