Stagnation points at grain contacts generate an elastic flow instability in 3-D porous media

Many environmental, energy and industrial processes involve the flow of viscoelastic polymer solutions in three-dimensional (3-D) porous media where fluid is confined to navigate through complex pore space geometries. As polymers are transported through the tortuous pore space, elastic stresses accumulate, leading to the onset of unsteady, time-dependent flow fluctuations above a threshold flow rate. How does pore space geometry influence the development and features of this elastic instability? Here, we address this question by directly imaging polymer solution flow in microfabricated 3-D ordered porous media with precisely controlled geometries consisting of simple-cubic (SC) or body-centred cuboid (BC) arrays of spherical grains. In both cases, we find that the flow instability is generated at stagnation points arising at the contacts between grains rather than at the polar upstream/downstream grain surfaces, as is the case for flow around a single grain. The characteristics of the flow instability are strongly dependent on the unit cell geometry: in SC packings, the instability manifests through the formation of time-dependent, fluctuating 3-D eddies; whereas in BC packings, it manifests as continual fluctuating ‘wobbles’ and crossing in the flow pathlines. Despite this difference, we find that characteristics of the transition from steady to unsteady flow with increasing flow rate have commonalities across geometries. Moreover, for both packing geometries, our data indicate that extensional flow-induced polymeric stresses generated by contact-associated stagnation points are the primary contributor to the macroscopic resistance to flow across the entire medium. Altogether, our work highlights the pivotal role of inter-grain contacts – which are typically idealised as discrete points and therefore overlooked, but are inherent in most natural and engineered media – in shaping elastic instabilities in porous media.