About diffusion in porous medium: the role of the correlation length

TL;DR

This paper develops a model to understand diffusion in porous media, emphasizing the effects of pore geometry and flux fluctuations, and compares theoretical predictions with experimental data from electrochemical systems.

Contribution

The paper introduces a novel model that decouples geometry from reaction-diffusion processes to analyze diffusion fading in porous media, incorporating flux heterogeneity and reactive effects.

Findings

Model accurately predicts current transients in electrochemical porous systems.

Flux heterogeneity significantly impacts diffusion behavior.

Comparison with experimental data validates the model's relevance.

Abstract

In this paper we develop a model to describe the diffusion process in a porous medium. For the observed decrease in current yield, we propose other causes than difference in diffusivity, which we consider unaltered by the porous medium. The physical situation we try to model consists of systems of reduced dimensions (~0.001-1.0 cm^3) with pores of sub micrometric dimension. This is particularly suitable to represent organic structures or special cells in electrochemical devices. We try to explore two basic contributions as an answer for diffusion fading in porous medium, namely, the effect of the void geometry and a dissipative process as well. This dissipative process is in the kernel of our analysis and it is related to the heterogeneous fluctuations of the flux lines occurring at the border among pores. To mimic biophysical and electrochemical conditions we also include in our model a reactive process, such migration of species do not need, necessarily, a pressure gradient because of the reaction diffusion process. As usual, the mathematical description of the phenomenon is introduced through the prescription of boundary and initial conditions for a transport equation, however here we decouple the geometry from the reaction-diffusion-convection problem examining a unitary conduct, in which the fluid flows and that, replicated in the space, is able to generate the entire system. We estimate the current transient provided by our model and compare it to the one obtained by the process of controlled growth of metallic inverse opals prepared by electrochemical crystallization of matter, so the theoretical results can be compared with experimental data.