Bistability in the Unstable Flow of Polymer Solutions Through Porous Media

Abstract: 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.