Patchy elastic turbulence generates anomalous flow resistance in porous media

Diverse applications rely on the viscous-dominated flow of polymer solutions through disordered porous media. For many polymers, the macroscopic flow resistance abruptly increases above a threshold flow rate in a porous medium, but not in bulk solution. The reason for this anomalous increase has remained a puzzle ever since it was first reported over half a century ago. Here, by directly visualizing the flow in a transparent 3D porous medium, we demonstrate that this anomalous increase is due to the added dissipation arising from an elastic instability in which the flow exhibits strong spatio-temporal fluctuations reminiscent of inertial turbulence, despite the vanishingly small Reynolds number. We find that the transition to unstable flow in each pore is akin to a universal second-order phase transition, arising due to the increased persistence of discrete patches of instability above an onset flow rate; however, this onset varies from pore to pore. Thus, unstable flow is patchy across the different pores of the medium. Guided by these findings, we directly link the energy dissipated by patchy pore-scale fluctuations to the anomalous increase in flow resistance through the entire medium. Our work thus helps to resolve the long-standing puzzle of why polymer solutions exhibit an anomalous increase in macroscopic flow resistance in porous media and provides guidelines for predicting and controlling these flows.