Geometry dependence of viscoelastic instabilities through porous media

Abstract

Viscoelastic instabilities are notoriously sensitive to their geometrical environment. Consequently, understanding the onset and general behavior of viscoelastic instabilities in geometrically complex applications where viscoelastic fluids naturally occur, such as porous media, is far from a trivial task. To this aim, this study numerically investigates the geometrical dependence of viscoelastic instabilities through confined one-dimensional channel arrays of circular pore contractions of ideal (i.e., symmetrical) and non-ideal (i.e., asymmetrical) pore configurations. At low elasticity, we demonstrate that the viscoelastic instability behavior in all geometries is the same as it was previously reported in ideal pore geometries, which can be characterized by a gradual loss of the well-defined symmetry in the velocity streamline plots, as well as the buildup of secondary vortices. However, at higher elasticity, we observe the transition into strong transient behavior, whereby the flow in all pore geometries experiences the multistability phenomenon reported by Kumar et al. [“Numerical investigation of multistability in the unstable flow of a polymer solution through porous media,” Phys. Rev. Fluids 6, 033304 (2021)]. Interestingly, it is shown that the viscoelastic instability response is the strongest for the most non-ideal pore geometry, which not only has the fastest transition time but also produces the most chaotic flow fluctuations, characterized by a broadband spectrum. Ultimately, we demonstrate that the viscoelastic instability response in each pore geometry adheres to the Pakdel–McKinley criterion for elastic instability, specifically the streamline curvature and elastic stress anisotropy.