The flow thickens: predicting macroscopic flow resistance of viscoelastic fluid flow in porous media

Flows of viscoelastic polymer solutions in porous media are ubiquitous in industrial and environmental applications. Despite their shear thinning nature in bulk rheology, these fluids can exhibit anomalous flow thickening above a threshold flow rate in porous media, marked by a drastic increase in flow resistance. The precise mechanisms for flow thickening have remained a puzzle since the first reports in the 1960s. Previous studies have suggested mechanisms including extensional viscosity, added viscous dissipation associated with elastic instabilities, and chemical adsorption or pore clogging; however, direct quantification of these mechanisms remains lacking. Here, we show that a mechanical power balance incorporating the added viscous dissipation arising from the onset of an elastic flow instability coupled with resistance from extensional viscosity can capture the macroscopic flow resistance of polymer solution flow in 2-D and 3-D ordered porous media. Our model directly links pore-scale flow fields obtained using confocal microscopy to the macroscopic flow resistance with no additional fitting parameters. Further, we find that stagnation point-driven extensional flows can be well-captured by a resistance-per-stagnation point in ordered geometries. Our work thus improves understanding into the mechanisms driving flow thickening and provides guidelines towards controlling macroscopic flow resistance in applications.