Elastic turbulence in porous media

Abstract

Polymer additives have potential as a key engineering tool for modifying environmental, industrial, energy, and microfluidic flows. In many cases, polymer elasticity can drive unstable, chaotic flow fluctuations in many ways reminiscent of turbulence, despite the absence of inertia that is typically requisite. While this unstable flow is well-studied in unconfined settings, it remains poorly understood how---or even if---this instability arises in complex, tortuous porous media, which are characteristic of environmental, industrial, energy, and microfluidic applications. In this dissertation, we address this gap in knowledge by fabricating transparent porous media of controlled geometries and directly imaging the flow in situ. First, using 1D pore arrays, we demonstrate that polymers accumulate memory along the successive expansions and contractions of a porous medium, and produce a surprising bistability in the stationary pore-scale flow state. Next, using 3D bead packings, we demonstrate for the first time that elastic turbulence can arise in disordered 3D porous media at flow conditions relevant to industrial applications. Leveraging this new knowledge of the underlying flow, we develop a theoretical model for the macroscopic flow resistance at varying flow rate, providing the first quantitative link between microscopic fluctuations and macroscopic transport of polymer solutions in porous media, resolving an over-50-year-old puzzle. We then extend this model to stratified porous media characteristic of many environmental applications. We demonstrate that elastic turbulence arises at distinct macroscopic flow rates in individual strata, allowing design of flow conditions that leverage the concomitant increase in flow resistance to redirect flow to low permeability strata and homogenize the flow across strata. Our ongoing work indicates these findings can be generalized to other polymer solutions, and leveraged for new applications, like enhanced mixing under confinement. These results suggest that many modeling approaches from inertial turbulence can be adapted for elastic turbulence---thus providing new avenues to understand, control, and engineer chaotic flows in confined spaces.