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

Recent works reveal the importance of chaotic flow fluctuations as a mechanism for the enhanced resistance observed in viscoelastic porous media flows, and also show how chaotic fluctuations are affected by the structural disorder of porous media. We seek further insight by performing pressure drop measurements and flow velocimetry on two viscoelastic fluids of contrasting rheology (one with constant viscosity, another strongly shear thinning) in flow through microfluidic post arrays. Ordered hexagonal arrays have posts either staggered'' or aligned’’ along the mean flow direction and disorder is applied to each configuration by randomly displacing each post about its initial location. Both polymer solutions show the expected increase in flow resistance for Weissenberg numbers, Wi > 1. In both cases, the flow resistance enhancement increases with the geometric disorder in aligned arrays, but is independent of disorder in staggered arrays. At sufficient randomisation, aligned and staggered arrays become indistinguishable. Flow velocimetry performed over a range of Wi reveals no sign of chaotic fluctuations for the constant viscosity fluid. In this case, 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. For the shear thinning fluid chaotic fluctuations are observed for Wi > 1, which broadly correlate with the flow resistance in this case. We also show that the first normal stress 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 the dominant mechanism for resistance enhancement in viscoelastic porous media flow may emerge depending on the specific combination of fluid rheology and geometric complexity.

💡 Research Summary

This study investigates the origins of the anomalously high pressure drop observed when viscoelastic polymer solutions flow through porous media. Two dilute polymer solutions were examined: (i) a high‑molecular‑weight polyacrylamide (PAA) that exhibits essentially constant shear viscosity, and (ii) a partially hydrolyzed polyacrylamide (HP‑AA) that is strongly shear‑thinning. Both fluids display nonlinear elasticity, as quantified by the first normal stress difference N₁, but the shear‑thinning fluid has a much larger N₁ magnitude.

Microfluidic channels (2.4 mm × 1 mm × 25 mm) were fabricated in fused silica with arrays of cylindrical posts (R = 50 µm, lattice spacing S = 240 µm). Two lattice orientations were used: “aligned” (a₁ vector parallel to the mean flow) and “staggered” (a₁ at 30° to the flow). Geometric disorder was introduced by randomly displacing each post within a circle of radius βS, with β ranging from 0.05 to 0.4. The porosity of all arrays was ≈0.84.

Pressure‑drop measurements were performed while varying the flow rate to span Weissenberg numbers Wi = λ · ε̇ from ≈0.1 to >10. For both fluids, a marked increase in flow resistance occurs once Wi > 1, confirming that elastic effects dominate the resistance. However, the dependence on disorder differs dramatically between the two lattice orientations. In aligned arrays, increasing β leads to a strong, monotonic rise in the normalized pressure drop; at β ≈ 0.3–0.4 the resistance of aligned and staggered arrays becomes indistinguishable. In staggered arrays, disorder has essentially no effect on the pressure drop. This behavior is interpreted as follows: disorder in aligned arrays creates additional stagnation points and blocks preferential flow channels, thereby enhancing extensional deformation; in staggered arrays the number of stagnation points is already high, so further disorder does not significantly alter the flow topology.

Time‑resolved micro‑particle image velocimetry (µ‑PIV) was used to probe the flow field. For the constant‑viscosity PAA solution, even at Wi > 1 the flow remains steady; however, elastic wakes develop downstream of each post, and the fluid stretches between successive stagnation points. These observations are consistent with a coil‑stretch transition that dramatically raises the extensional viscosity and thus the macroscopic pressure drop. No chaotic velocity fluctuations are detected.

In contrast, the shear‑thinning HP‑AA solution exhibits strong, time‑dependent velocity fluctuations for Wi > 1. The fluctuations are spatially heterogeneous, become more intense with increasing disorder in aligned arrays, and are essentially unchanged in staggered arrays—mirroring the pressure‑drop trends. Quantitative analysis shows that the extra viscous dissipation associated with these fluctuations accounts for most of the observed pressure‑drop increase. Moreover, the product N₁·Wi correlates well with the resistance for the shear‑thinning fluid, suggesting that the first normal stress contributes significantly to the extra drag. For the constant‑viscosity fluid, N₁ alone cannot explain the resistance increase, reinforcing the conclusion that extensional effects dominate.

Overall, the work demonstrates that there is no single universal mechanism for resistance enhancement in viscoelastic porous‑media flow. When the fluid’s shear viscosity is nearly constant, the coil‑stretch transition and the associated rise in extensional viscosity (elastic wakes) are the primary drivers. When the fluid is strongly shear‑thinning, elastic turbulence—manifested as chaotic velocity fluctuations—and the resulting additional viscous dissipation, together with normal‑stress effects, dominate. Geometric disorder modulates which mechanism is active, especially in aligned lattices where it can either suppress or amplify chaotic fluctuations. The findings imply that predictive models for polymer‑enhanced oil recovery, groundwater remediation, or filtration must account for the combined influence of fluid rheology (shear‑thinning, normal stress, extensional viscosity) and pore‑scale geometry (orientation, disorder) to accurately capture the pressure‑drop behavior.