Elastic instabilities between two cylinders confined in a channel

Abstract

Polymeric flow through porous media is relevant in industrial applications, such as enhanced oil recovery, microbial mining, and groundwater remediation. Biological processes, such as drug delivery and the transport of cells and particles in the body, also depend on the viscoelastic flow through the porous matrix. Large elastic stresses induced due to confined geometries can lead to elastic instability for the viscoelastic fluid flow through porous media. We have numerically studied viscoelastic flow through a channel having two closely placed cylinders to investigate pore scale elastic instabilities. We have discovered three distinct flow states in the region between the cylinders. These flow states are closely coupled with the topology of the polymeric stress field. The transition between the flow states can be identified with two critical Weissenberg numbers (Wicr1 and Wicr2), where the Weissenberg number (Wi) is the ratio of elastic to viscous forces. At Wi<Wicr1, the flow is stable, symmetric, and eddy free. For Wicr1<Wi<Wicr2, eddies form in the region between the cylinders. We have measured the area occupied by the eddies for different flow conditions and fluid rheological parameters. At Wi>Wicr2, the eddy disappears and the flow around the cylinders becomes asymmetric. We have quantified the flow asymmetry around the cylinders for different flow rates and fluid rheology. We have also studied the effect of the cylinders' diameter and separation on the eddies' size (Wicr1<Wi<Wicr2) and flow asymmetry (Wi>Wicr2). We have also investigated the effect of fluid rheology and cylinders' diameter and separation on the value of critical Weissenberg numbers.

Bifurcations in flows of complex fluids around microfluidic cylinders

“…The onset of asymmetric flows around two aligned cylindrical posts has also been reported in recent simulations using the FENE-P constitutive model. 147 In that study, varying the degree of shear-thinning, dumbbell extensibility, and channel blockage ratio all had effects consistent with the predictions of our proposed mechanism.…”

Lagrangian stretching reveals stress topology in viscoelastic flows

“…Beyond the exact analytical correspondence between stress and stretching for weakly unsteady viscoelastic flows (Eqs. 15, 18, and 19), strong nonlinearities yield complex and timedependent flow structures that emerge at large Weissenberg number [13,17,18]. To illustrate the persistent concordance between the polymeric stress and stretching field topologies, viscoelastic flows are numerically simulated through various geometries at large Weissenberg numbers (Wi 1).…”

“…Intricate flow geometries -for example in porous media [8] -increase the complexity of instabilities leading to multi-stable and strongly time-dependent flow structures [17,18,49].…”

“…The onset of these phenomena are captured by the Weissenberg number (Wi), representing the ratio of elastic to viscous stress: Wi = λ γ, where λ and γ are the polymeric relaxation time and deformation rate, respectively. Importantly, the topology of the polymeric stress field has been shown to regulate flow structure, whereby streaks of high polymeric stress lead to separation and act as a barrier to flow [17,18]. Determining the topology of the stress field and its relationship to flow kinematics are fundamental to understanding and predicting dynamic flow patterns and ultimately, material transport in complex flows.…”

Characterizing elastic turbulence in the three-dimensional von Karman swirling flow using the Oldroyd-B model

“…Numerical work has demonstrated elastic instabilities in similar geometries as the ones explored in the experiments but limited to two-dimensional flows. This includes the cross-slot geometry 12,36,37 , sudden-expansion flow in widening channels 38 , serpentine channels 39 , two cylinders confined in a channel 40 , two lateral side-by-side cylinders in a channel 41 , and the Taylor-Couette geometry 42 . Recent nu-merical work has demonstrated the elastic instability in the von Kármán swirling flow 43 .…”