Bistability in the unstable flow of polymer solutions through pore constriction arrays

Polymer solutions are often injected in porous media for applications such as oil recovery and groundwater remediation. As the fluid navigates the tortuous pore space, elastic stresses build up, causing the flow to become unstable at sufficiently large injection rates. However, it is poorly understood how the spatial and temporal characteristics of this unstable flow depend on pore space geometry, which can vary widely between different porous media. We investigate this dependence by systematically varying the spacing between pore constrictions in a one-dimensional ordered array. We find that when the pore spacing is large, unstable eddies form upstream of each constriction, similar to observations of an isolated constriction. By contrast, when the pore spacing is sufficiently small, the flow in the different pores exhibits a surprising bistability, stochastically switching between two distinct unstable flow states. We hypothesize that this unusual behaviour arises from the interplay between elongation and relaxation of polymers as they are advected through the pore space. Consistent with this idea, we find that the flow state in a given pore persists for long times; moreover, flow states are strongly correlated between neighbouring pores. Thus, the characteristics of unstable flow are not determined just by injection conditions and the geometry of the individual pores, but also depend on the spacing between pores. Ultimately, these results help to elucidate the rich array of behaviours that can arise in polymer solution flow through porous media.