The Yielding Network

Push a Newtonian fluid through a disordered pore network and the flow scales smoothly with pressure. The disorder averages out. The network’s randomness is an inconvenience, not a structural feature.

Push a yield-stress fluid through the same network and the behavior splits in two. Abitbol, Hansen, Rosso, and Talon show that above the percolation threshold, the flow curve is governed by deterministic critical pressure values with quantifiable fluctuations — predictable, reproducible. At the percolation threshold itself, the flow becomes non-self-averaging: repeated experiments on the same-sized system give different results, and the scaling is governed entirely by the geometry of the percolation backbone.

The through-claim: the yield stress couples the flow physics to the network topology in a way that Newtonian fluids cannot. A Newtonian fluid flows wherever there’s a path. A Bingham fluid flows only where the local stress exceeds the yield threshold, which means the effective flow network is a subset of the geometric network — and that subset depends on the applied pressure. The fluid selects its own pathway.

At percolation threshold, this selection becomes critical. The backbone — the minimal set of paths carrying flow — dominates, and its fractal geometry determines the transport scaling. The pore size distribution becomes irrelevant; only the topology matters.

The fluid and the network cannot be separated. The flow defines the network it flows through.