Non-monotonic variations in pressure drop and chaos in viscoelastic fluid flows through an ordered microporous medium

Abstract

Several recent experimental studies have revealed non-monotonic variations in elastic turbulence-induced chaotic flow behaviour and pressure drop during the flow of viscoelastic fluids through a microporous medium. The present numerical study aims to investigate and hypothesise about the physical mechanisms governing these complex flow behaviours in an ordered microporous medium consisting of cylindrical micropillars arranged in a staggered configuration. We propose that birefringent strands of high elastic stress, generated by the stretching and alignment of polymer molecules within the porous structure, play the dominant role in controlling the non-monotonic variations in chaos and pressure drop. At low Weissenberg numbers, these stress strands develop gradually, mainly downstream of the micropillars, whereas beyond a critical Weissenberg number, they begin to fluctuate strongly, leading to chaotic flow dynamics. However, at even higher Weissenberg numbers, the strands become larger and stronger, eventually interconnecting between neighbouring micropillars, causing the flow to reorganise into a nearly steady, ordered state similar to that observed at low Weissenberg numbers. On the other hand, the pressure drop in the system consists of a mean contribution, obtained from statistically stationary flow quantities, and a fluctuating contribution. While the mean component increases monotonically with the Weissenberg number, the fluctuating component varies non-monotonically, leading to a similar trend in the total pressure drop. Moreover, the non-monotonic chaotic behaviour strongly depends on the solid volume fraction of the porous medium, which alters both the critical Weissenberg number for instability onset and the range over which the non-monotonic behaviour persists.