Signature of elastic turbulence of viscoelastic fluid flow in a single pore throat

Abstract

When a viscoelastic fluid, such as an aqueous polymer solution, flows through a porous medium, the fluid undergoes a repetitive expansion and contraction as it passes from one pore to the next. Above a critical flow rate, the interaction between the viscoelastic nature of the polymer and the pore configuration results in spatial and temporal flow instabilities reminiscent of turbulentlike behavior, even though the Reynolds number Re 1. To investigate whether this is caused by many repeated pore body-pore throat sequences, or simply a consequence of the converging (diverging) nature present in a single pore throat, we performed experiments using anionic hydrolyzed polyacrylamide (HPAM) in a microfluidic flow geometry representing a single pore throat. This allows the viscoelastic fluid to be characterized at increasing flow rates using microparticle image velocimetry in combination with pressure drop measurements. The key finding is that the effect, popularly known as "elastic turbulence," occurs already in a single pore throat geometry. The critical Deborah number at which the transition in rheological flow behavior from pseudoplastic (shear thinning) to dilatant (shear thickening) strongly depends on the ionic strength, the type of cation in the anionic HPAM solution, and the nature of pore configuration. The transition towards the elastic turbulence regime was found to directly correlate with an increase in normal stresses. The topology parameter, Q f , computed from the velocity distribution, suggests that the "shear thickening" regime, where much of the elastic turbulence occurs in a single pore throat, is a consequence of viscoelastic normal stresses that cause a complex flow field. This flow field consists of extensional, shear, and rotational features around the constriction, as well as upstream and downstream of the constriction. Furthermore, this elastic turbulence regime, has high-pressure fluctuations, with a power-law decay exponent of up to |−2.1| which is higher than the Kolmogorov value for turbulence of |−5/3|.

Stagnation points control chaotic fluctuations in viscoelastic porous media flow

“…The PSD is shifted to higher frequencies than at and decays with an exponent of . The power law decays in the power spectra of the fluctuating signals indicate that the fluctuations are aperiodic, and the slopes are consistent with values reported in studies of elastic turbulence ( 7 , 21 , 26 – 28 ).…”

“…Elastic tensile stresses due to stretching on curvilinear streamlines (as through porous media) are conditions well established to lead to linear instabilities in viscoelastic fluids ( 16 – 19 ), which can be precursors to elastic turbulence as is further increased ( 7 , 20 – 23 ). The chaotic fluctuations that result are expected to greatly enhance the pressure loss and the dispersion in porous media, with positive impacts on, for example, removing oil ganglia from the pore space in EOR or improving the distribution of drugs throughout a tumor ( 24 – 27 ).…”

Viscous flow through microfabricated axisymmetric contraction/expansion geometries

“…A planar hyperbolic contraction/expansion geometry has since been commercialized as a high deformation rate extensional viscometer rheometer on-a-chip device (the e-VROC TM , Rheosense Inc., CA, see e.g., Pipe et al 2008;Ober et al 2013;Keshavarz and McKinley 2016;Garcia and Saraji 2019;Zografos et al 2020). Similar microfluidic hyperbolic converging channels have also been employed to simulate blood flows in stenoses (Sousa et al 2011), to measure the deformation of white blood cells (Rodrigues et al 2015) and single DNA molecules (Larson et al 2006), to study the deformation and breakup of droplets (Mulligan and Rothstein 2011), and to examine elastic turbulence of viscoelastic fluids (Groisman and Steinberg 2000;Ekanem et al 2020). Some of the most recent developments in this area have involved "fine-tuning" the hyperbolic wall profile of the planar converging/ diverging geometry by an iterative numerical optimization procedure to further improve the homogeneity of the flow field (Zografos et al 2016).…”

A pore network modelling approach to investigate the interplay between local and Darcy viscosities during the flow of shear-thinning fluids in porous media

“…Such stretching makes the flow unstable and causes irregular secondary flow resulting in elastic turbulence [54]. By means of particle image velocimetry experiments performed in a microfluidic device, Ekanem et al [55] showed that the elastic turbulence effect occurs within a single pore throat with no flow history. Also, Browne et al [56] proved that unstable eddies form upstream of pore constrictions when the pore spacing is large, while switching between two distinct unstable flow states occur when pore spacing is sufficiently small.…”