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The first open channel for a yield-stress fluid in complex porous media

The prediction of the first fluidized path of a yield-stress fluid in complex porous media is a challenging yet an important task to understand the fundamentals of fluid flow in several industrial and biological processes. In most cases, the conditions that open this first path are known either through experiments or expensive computations. Here, we present a simple network model to predict the first open channel for a yield-stress fluid in a complex porous medium. For porous media made of non-overlapping disks, we find that the pressure drop required to open the first channel for given yield stress depends on both the relative disks size to the macroscopic length of the system and the packing fraction. We also report the statistics on the arc-length of the first open path. Finally, we discuss the implication of our results on the design of porous media used in energy storage applications.