Elastic instabilities between two cylinders confined in a channel

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 (Wi(cr1) and Wi(cr2)), where the Weissenberg number (Wi) is the ratio of elastic to viscous forces. At Wi < Wi(cr1), the flow is stable, symmetric, and eddy free. For Wi(cr1) < Wi < Wi(cr2), 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 > Wi(cr2), 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 (Wi(cr1) < Wi < Wi(cr2)) and flow asymmetry (Wi > Wi(cr2)). We have also investigated the effect of fluid rheology and cylinders' diameter and separation on the value of critical Weissenberg numbers. Published under an exclusive license by AIP Publishing.

Automated summary

The study explores the flow of polymers in porous media and identifies three distinct flow states between two closely placed cylinders, each associated with different characteristics and the topology of the polymeric stress field. Different stages of Weissenberg numbers correspond to different flow behaviors, including stability, symmetry, and the formation of eddies. The research also investigates the effects of cylinder diameter and separation on flow characteristics and eddies.