# Surface permeability and surface flow tortuosity of particulate porous media

## TL;DR

This paper develops a numerical approach to determine surface permeability and flow tortuosity in particulate porous media, enhancing the understanding of dispersion processes at low saturation levels.

## Contribution

It extends the Laplace-Beltrami boundary-value problem methodology to interconnected particle ensembles using surface finite element techniques.

## Key findings

- Accurate estimation of surface permeability in particle ensembles.
- Quantitative analysis of flow tortuosity effects.
- Validation of the numerical approach for complex geometries.

## Abstract

The dispersion process in particulate porous media at low saturation levels takes place over the surface elements of constituent particles and, as we have found previously by comparison with experiments, can be accurately described by super-fast non-linear diffusion partial differential equations. To enhance the predictive power of the mathematical model in practical applications, one requires the knowledge of the effective surface permeability of the particle-in-contact ensemble, which can be directly related with the macroscopic permeability of the particulate media. We have shown previously that permeability of a single particulate element can be accurately determined through the solution of the Laplace-Beltrami Dirichlet boundary-value problem. Here, we demonstrate how that methodology can be applied to study permeability of a randomly packed ensemble of interconnected particles. Using surface finite element techniques we examine numerical solutions to the Laplace-Beltrami problem set in the multiply-connected domains of interconnected particles. We are able to rigorously estimate tortuosity effects of the surface flows in a particle ensemble setting.