# Local details versus effective medium approximation: A study of diffusion in microfluidic random networks made from Voronoi tessellations

## TL;DR

This study investigates how local geometric details influence effective diffusion measurements in microfluidic networks with Voronoi tessellation, revealing that boundary effects and network size impact the validity of effective medium approximations.

## Contribution

It demonstrates that boundary effects significantly affect diffusion measurements and that statistical errors decrease with region size, challenging the existence of a characteristic length scale for effective medium equivalence.

## Key findings

- Boundary of bleached region influences diffusion coefficient
- Statistical error decreases with region size as a power law
- No characteristic length scale for effective medium equivalence

## Abstract

We measured the effective diffusion coefficient in regions of microfluidic networks of controlled geometry using the FRAP (Fluorescence Recovery After Photobleaching) technique. The geometry of the networks was based on Voronoi tessellations, and had varying characteristic length scale and porosity. For a fixed network, FRAP experiments were performed in regions of increasing size. Our results indicate that the boundary of the bleached region, and in particular the cumulative area of the channels that connect the bleached region to the rest of the network, are important in the measured value of the effective diffusion coefficient. We found that the statistical geometrical variations between different regions of the network decrease with the size of the bleached region as a power law, meaning that the statistical error of effective medium approximations decrease with the size of the studied medium, although no characteristic length scale could be defined over which the porous medium is equivalent to an effective medium.