Enhanced dispersion by elastic turbulence in porous media

Abstract

-We experimentally investigate hydrodynamic dispersion in elastic turbulent flows of a semi-dilute aqueous polymer solution within a periodic porous structure at ultra-low Reynolds numbers < 10 −3 by particle tracking velocimetry. Our results indicate that elastic turbulence can be characterized by an effective dispersion coefficient which exceeds that of Newtonian liquids by several orders of magnitude and grows non-linearly with the Weissenberg number Wi. Contrary to laminar flow conditions, the velocity field, and thus the shear rate, is not proportional to the flow rate and becomes asymmetric at high Wi.Introduction. -Turbulent flow is characterized by unsteady velocity fields which suddenly vary in space and time. For Newtonian liquids, this regime is reached for high Reynolds numbers Re, where inertial effects dominate over viscous forces. In contrast, for viscoelastic fluids, turbulent flow at arbitrarily small Re numbers, usually referred to as elastic turbulence [1], can be observed. Such fluids are characterized by an elastic response, e.g. due to the entanglement and the dynamics of polymer chains [2]. The degree of elastic effects can be described by the dimensionless Weissenberg number Wi = λ ·γ, which quantifies the anisotropic polymer alignment in the presence of shear [3]. Here, λ is the equilibrium polymer relaxation time andγ the shear rate of the flow. Accordingly, for Wi → 0 the response of the fluid to a sudden stress is purely viscous while for Wi > 0 an elastic short-time response is obtained. Since the polymer alignment not only depends on the instantaneous but also on the previous shear, this explains why a highly non-linear flow dependence on the shear strength is observed [2]. It has been experimentally demonstrated that above a critical Weissenberg number Wi c 1, elastic turbulence occurs [4]. Similar to inertial turbulence, this regime is characterized by an enhanced flow resistance and a power-law decay of the spectral power density [1,5,6]. This effect can be exploited to dramatically increase the mixing efficiency at small length scales and small Reynolds numbers (Re < 10 −4 ) in microfluidic devices [7,8].

Pore‐Scale Flow Characterization of Polymer Solutions in Microfluidic Porous Media

“…[188,[218][219][220] Mixing and Solute Transport: The velocity fluctuations that characterize unstable flow of polymer solutions can also enhance mixing and solute dispersion on mesoscopic scales. [22,160,[221][222][223][224][225] This enhanced mixing could improve EOR and groundwater remediation efforts by improving the transport of key additives like surfactants, colloids, and oxidants. However, systematic tests of this behavior are lacking.…”

Extra dissipation and flow uniformization due to elastic instabilities of shear-thinning polymer solutions in model porous media

“…14 Recently, direct observations of elastic instabilities in two-dimensional models of porous media made using microfluidics have been reported. 15,16 It is shown in these works that the streamlines exhibit fluctuations at high enough flow rates. Above the threshold, the apparent diffusion coefficient is greatly enhanced, 16 the apparent viscosity is increased, 15,17 and some a) Electronic mail: hugues.bodiguel@univ-grenoble-alpes.fr trapped oil droplets are mobilized.…”

“…15,16 It is shown in these works that the streamlines exhibit fluctuations at high enough flow rates. Above the threshold, the apparent diffusion coefficient is greatly enhanced, 16 the apparent viscosity is increased, 15,17 and some a) Electronic mail: hugues.bodiguel@univ-grenoble-alpes.fr trapped oil droplets are mobilized. 15,18 This last consequence is likely to be related to oil field results in Wang,19,20 where additional oil has been recovered using polymer flooding in the semi-dilute regime.…”

Disorder Suppresses Chaos in Viscoelastic Flows

“…This condition is often characterized by a Weissenberg number, Wi = τγ > Wi cr ∼ 1, wherė γ is the typical shear rate and τ is the fluid relaxation time [2]. Purely elastic instabilities manifest as spatiotemporal chaotic flow and elastic turbulence [3,4] in a wide range of natural and industrial applications: Elasticity generates secondary flows of DNA and blood suspensions in biological systems [5,6], hydrodynamic resistance increases [7] along with power consumption and cost in polymer processing, and elastic instabilities enhance mixing and dispersion in microfluidic and porous media flows [8][9][10]. Experimental [11][12][13][14][15] and numerical [16][17][18] efforts have characterized the onset and impact of elastic instabilities in well-defined geometries including cross slot [13,17], Couette [19,20], Poiseuille [8,21], and ordered pillar array flows [12,22,23].…”

“…The stabilizing effect of disorder is attributed to a shift in the flow type history of the viscoelastic fluid, which evolves from extensional and unstable in ordered systems to shear-dominated and stable in disordered systems. We expect that the transport properties of these transitional flows will likewise be sensitive to disorder due to temporal fluctuations, which are important for extraction, remediation, and other industrial processes in porous media flows [9,10]. More broadly, coupled systems often exhibit chaotic dynamics under sufficient forcing, where only a few examples have thus far demonstrated the counterintuitive restoration of synchrony or stability by disorder [30]: Arrays of forced, coupled pendula desynchronize, but introducing disorder among their natural frequencies suppresses chaotic oscillations and recovers periodicity [28,31].…”