Anomalous percolation flow transition of yield stress fluids in porous media

Yield stress fluid (YSF) flows through porous materials are fundamental to biological, industrial, and geophysical processes, from blood and mucus transport to enhanced oil recovery. Despite their widely recognized importance across scales, the emergent transport properties of YSFs in porous environments remain poorly understood due to the nonlinear interplay between complex fluid rheology and pore microstructure. Here, we combine microfluidic experiments and nonlinear network theory to uncover an anomalous, hierarchical yielding process in the fluidization transition of a generic YSF flowing through a random medium. Percolation of a single fluidized filament gives way to pathways that branch and merge to form a complex flow network within the saturated porous medium. The evolution of the fluidized network with the flowing fraction of YSF results in a highly nonlinear flow conductivity and reveals a novel dispersion mechanism, resulting from the rerouting of fluid streamlines. The identified flow percolation phenomenon has broad implications for YSF transport in natural and engineered systems, and provides a tractable archetype for a diverse class of breakdown phenomena.