Disorder, dispersion, and stretching in viscoelastic flows through porous media

Viscoelastic flows through porous media transition from steady to time dependent and chaotic dynamics under critical flow conditions. However, the implications of the microstructured geometry for flow stability and transport in these systems were largely unknown. Recently, we measured the onset of spatiotemporal velocity fluctuations for a viscoelastic flow through microfluidic pillar arrays and found that increasing the degree of disorder delays the transition to chaos. The existence of preferential flow paths in disordered media promote shear over extensional deformation and consequently enhance global flow stability by locally reducing polymer stretching. Combined experiments and simulations show that preferential paths enhance longitudinal dispersion in porous media, and consequently, suppressed velocity fluctuations reduce transverse dispersion. Finally, we show that features of the dispersion can be understood through analysis of Lagrangian stretching manifolds, which act as transport barriers and guide material along preferential paths. The observed stretching manifolds strongly correlate with the polymeric stress field topology, providing a link between stress, stretching, and transport properties in these viscoelastic flows.