The progress of the interface between an invasive fluid and a defending mixture of granular material together with a second fluid, immiscible with the invading phase, has recently been used to form complex patterns in both Hele-Shaw cells or millifluidic confinements. These are the result of the deformation of a confined porous material, made of an homogeneous granular phase, into an heterogeneous structure exhibiting various sizes and permeabilities at different scales. A labyrinthine pattern can then be obtained after the withdraw of a liquid phase containing glass beads and confined in an horizontal Hele-Shaw cell, see Knudsen et al., PRE 77, 021301 (2008). What are then the transport properties within such a geometrical structure? The geometrical constraints with dead-ends are limiting the transport of diffusing species from a central entry point towards the edges of the labyrinth. A transient subdiffusive transport can be obtained over a time scale determined by the wavelength of the pattern.
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