Effects of fluid rheology and geometric disorder on the enhanced resistance of viscoelastic flows through porous media

Recent works have highlighted the importance of chaotic flow fluctuations as a mechanism for the enhanced resistance observed in viscoelastic porous media flows, and have also shown that chaotic fluctuations can be either enhanced or suppressed by the structural disorder of porous media. We seek further insight into the mechanisms of flow resistance enhancement in porous media by performing pressure drop measurements and flow velocimetry on two viscoelastic fluids of contrasting rheology (one with near-constant viscosity, the other strongly shear thinning) in inertialess flow through microfluidic post arrays. Ordered hexagonal arrays have nearest neighbour posts either “staggered” or “aligned” along the mean flow direction. Increasing disorder is applied to each configuration by randomly displacing each post within a progressively large area about its initial location. Both shear thinning and constant viscosity dilute polymer solutions show the expected increase in flow resistance for Weissenberg numbers, Wi ≳ 1 . In both cases, the flow resistance enhancement increases significantly with the geometric disorder in aligned arrays, but is independent of disorder in staggered arrays. At sufficient randomisation, aligned and staggered arrays become indistinguishable, as expected. Flow velocimetry performed in selected geometries over a range of Wi reveals no sign of chaotic fluctuations for the constant viscosity fluid. Instead the observation of elastic wakes between the stagnation points of the posts evokes the coil-stretch transition and implicates the extensional viscosity as the cause of the enhanced flow resistance. In contrast, the shear thinning fluid does show chaotic fluctuations for Wi > 1 , which are enhanced by disorder in aligned arrays and independent of disorder in staggered arrays (correlating with the flow resistance in this case). We further show that the first normal stress difference is insufficient to account for the flow resistance observed for the constant viscosity fluid, but may account for the resistance observed in the shear thinning case. Our results suggest that there may not be one universal cause for the enhanced pressure drop in viscoelastic porous media flows. Rather, the dominant mechanism may emerge depending on the specific combination of fluid rheology and geometric complexity.