# Impact of Network Heterogenity on Nonlinear Electrokinetic Transport in Porous Media

## TL;DR

This study uses numerical simulations to explore how heterogeneity in porous media affects nonlinear electrokinetic transport, revealing the dominance of electroconvection in certain conditions and highlighting the limitations of homogenized models.

## Contribution

It introduces a detailed numerical framework to analyze the impact of pore network topology on electrokinetic phenomena, emphasizing the role of heterogeneity and flow loops.

## Key findings

- Electroconvection dominates in large potential regimes for weak surface conduction.
- Heterogeneous pore networks exhibit different transport behaviors compared to homogenized models.
- The framework can inform design of porous media for water purification applications.

## Abstract

We present a numerical study of nonlinear electrokinetic transport in porous media, focusing on the role of heterogeneity in a porous microstructure on ion concentration polarization and over-limiting current. For simplicity, the porous medium is modeled as a network of long, thin charged cylindrical pores, each governed by one-dimensional effective transport equations. For weak surface conduction, when sufficiently large potential is applied, we demonstrate that electrokinetic transport in a porous network can be dominated by electroconvection via internally induced flow loops, which is not properly captured by existing homogenized models. We systematically vary the topology and "accessivity" of the pore network and compare with simulations of traditional homogenized parallel-pore (capillary-bundle) models, in order to reveal the effects of regular and hierarchical connectivity. Our computational framework sheds light on the complex physics of nonlinear electrokinetic phenomena in microstructures and may be used to design porous media for applications, such as water desalination and purification by shock electrodialysis.