The first open channel for yield-stress fluids in porous media

The prediction of the first fluidized path of yield-stress fluids in complex porous media is a challenging yet 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 porous medium. For porous media made of non-overlapping discs, we find that the pressure drop required to open the first channel for a given yield stress depends on both the relative discs size to the macroscopic length of the system and the packing fraction. The non-dimensional pressure gradient (i.e. the critical yield number), however, depends on the packing fraction only, leading to a mastercurve for all examined ratios of. In the case of non-overlapping discs, we find. We also report the statistics on the arclength of the first open path. Finally, we discuss the implication of our results for the design of porous media used in energy storage applications.