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We measured the effective diffusion coefficient in regions of microfluidicnetworks of controlled geometry using the FRAP (Fluorescence Recovery AfterPhotobleaching) technique. The geometry of the networks was based on Voronoitessellations, and had varying characteristic length scale and porosity. For afixed network, FRAP experiments were performed in regions of increasing size.Our results indicate that the boundary of the bleached region, and inparticular the cumulative area of the channels that connect the bleached regionto the rest of the network, are important in the measured value of theeffective diffusion coefficient. We found that the statistical geometricalvariations between different regions of the network decrease with the size ofthe bleached region as a power law, meaning that the statistical error ofeffective medium approximations decrease with the size of the studied medium,although no characteristic length scale could be defined over which the porousmedium is equivalent to an effective medium.

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