  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. We elucidate this dependence by systematically varying the spacing
between pore constrictions in a model porous medium. We find that when the pore
spacing is large, unstable eddies form upstream of each pore, similar to
observations of an isolated pore. By contrast, when the pore spacing is
sufficiently small, the flow exhibits a surprising bistability, stochastically
switching between two distinct unstable flow states. We hypothesize that this
unusual behavior arises from the interplay between flow-induced polymer
elongation and relaxation of polymers as they are advected through the porous
medium. Consistent with this idea, we find that the flow state in a given pore
persists for long times. Moreover, we find that the flow state is correlated
between neighboring pores; however, these correlations do not persist
long-range. Our results thus help to elucidate the rich array of flow behaviors
that can arise in polymer solution flow through porous media.
