# Homogenization based two-scale modelling of ionic transport in fluid saturated deformable porous media

## TL;DR

This paper develops a homogenized two-scale model for ionic transport in deformable porous media, capturing electrochemical interactions and fluid-structure coupling, with numerical implementation demonstrating microstructure influence on effective properties.

## Contribution

It introduces a homogenization approach for coupled ionic transport and deformation in porous media, including a numerical implementation in finite element software.

## Key findings

- Homogenized coefficients depend on microstructure porosity.
- The model separates electrolyte flow from solid deformation.
- Microscopic responses can be reconstructed from macroscopic solutions.

## Abstract

The paper deals with the homogenization of deformable porous media saturated by two-component electrolytes. The model relevant to the microscopic scale describes steady states of the medium while reflecting essential physical phenomena, namely electrochemical interactions in a dilute Newtonian solvent under assumptions of a small external electrostatic field and slow flow. The homogenization is applied to a linearized micromodel, whereby the thermodynamic equilibrium represents the reference state. Due to the dimensional analysis, scaling of the viscosity and electric permitivity is introduced, so that the limit model retains the characteristic length associated with the pore size and the electric double layer thickness. The homogenized model consists of two weakly coupled parts: the flow of the electrolyte can be solved in terms of a global pressure and streaming potentials of the two ions, independently of then the solid phase deformations which is computed afterwards for the fluid stress acting on pore walls. The two-scale model has been implemented in the SfePy finite element software. The numerical results show dependence of the homogenized coefficients on the microstructure porosity. By virtue of the corrector result of the homogenization, microscopic responses in a local representative cell can be reconstructed from the macroscopic solutions.