Polymer extension at stagnation points governs flow thickening of polymer solutions in ordered porous media

Polymer solutions exhibit anomalous flow thickening -- marked by an abrupt increase in the macroscopic flow resistance -- above a threshold flow rate in a porous medium, but not in bulk solution. This phenomenon has evaded a mechanistic description for over half a century. Here, we develop a model that quantitatively links pore-scale flow fields and fluid rheology to macroscopic flow thickening, and validate it in experiments in two- and three-dimensional (2D and 3D) porous media. We find that flow thickening in ordered media is governed by polymer extension at stagnation points -- in contrast to disordered media, where viscous dissipation by unsteady flow fluctuations also contributes substantially. Our results provide a foundation to predict and control such flows in energy, environmental, industrial, and microfluidic applications.