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

TL;DR

This study investigates how fluid rheology and structural disorder influence flow resistance in viscoelastic porous media, revealing that resistance enhancement depends on fluid properties and media geometry, with chaotic fluctuations playing a key role.

Contribution

It provides new insights into the combined effects of fluid rheology and geometric disorder on flow resistance, highlighting different mechanisms in constant viscosity and shear thinning fluids.

Findings

Flow resistance increases with Weissenberg number for both fluids.

Disorder amplifies resistance in aligned arrays but not in staggered arrays.

Chaotic fluctuations are observed only in shear thinning fluids at Wi > 1.

Abstract

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.