Patches of patches: Spatial fluctuations of elastic turbulence in 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 flow rates—a phenomenon often known as “elastic turbulence”. However, what physical factors determine the onset of this instability, and what its spatial and temporal characteristics are, remain unknown. In this talk, I describe some of our work using direct visualization in model porous media to address this gap in knowledge. First, we show that the spacing between pores strongly influences the flow: when the pore spacing is sufficiently small, the unstable flow in the different pores exhibits a surprising bistability due to the interplay between elongation and relaxation of polymers as they are advected through the pore space (Browne et al., J. Fluid Mech. 2020). Second, using experiments in full three-dimensional porous media, we show that the onset of unstable flow in each pore is akin to a second-order phase transition, arising due to the persistence of discrete patches of instability. Thus, unstable flow is patchy across the different pores of the medium. Guided by these findings, we directly link the energy dissipated by pore-scale fluctuations to the flow resistance through the entire medium, enabling prediction of the macroscopic transport behavior (Browne and Datta, Science Advances 2021). Together, these results reveal the rich array of behaviors that can arise during the unstable flow of polymer solutions through porous media, and provide a general framework by which flow fluctuations can be predicted and controlled.