Elastic flow instability enhances solute mixing in 3D porous media

Polymer solutions are often injected in porous media for applications such as groundwater remediation, column chromatography, or packed bed reactions. In these settings, it is often important to mix solutes in initially separated streams. For Newtonian fluids, the flow is typically laminar, limiting mixing to the dispersion inherent to the disordered pore space. However, it remains unknown how polymer solutions modify this mixing. Here, we directly visualize the mixing of two fluorescently dyed streams within a transparent 3D porous medium. We find that, above a threshold flow rate, the mixing rate increases above the expected laminar dispersion. By imaging the pore-scale velocity field, we demonstrate that the increase in solute mixing rate is concomitant with the onset of an elastic instability in which the flow exhibits strong spatio-temporal fluctuations reminiscent of inertial turbulence, despite the vanishingly small Reynolds number. This elastic instability produces a spectrum of solute concentration fluctuations that follow power-law scalings consistent with Batchelor mixing. Thus, by linking macro-scale mixing to the pore-scale unstable flow, our work provides generally-applicable guidelines to control mixing of passive scalars in disordered porous media.