Effect of geometric disorder on chaotic viscoelastic porous media flows

Abstract

Many practical applications, such as enhanced oil recovery or groundwater remediation, encounter the flow of viscoelastic fluids in porous media. Once the flow rate exceeds a critical value in such flows, an elastic instability with a fluctuating flow field is observed, which ultimately transits to a more chaotic and turbulence-like flow structure as the flow rate further increases. In this study, we present an extensive numerical investigation of the viscoelastic fluid flows in a model porous media consisting of a microchannel with many micropillars placed in it by considering both their initial staggered and aligned configurations. Within the present range of conditions encompassed in this study, we find that the geometric disorder always increases the chaotic fluctuations irrespective of the initial arrangement of micropillars. We propose that it is due to the formation of preferential paths or lanes and the formation of highly curved streamlines, which results in the local stretching of polymer molecules and, hence, significant origin in the local elastic stresses. We further show that this chaotic flow behavior strongly depends on the competitive influence between the strain-hardening and shear-thinning behaviors of a viscoelastic fluid, which again strongly depends on the polymer extensibility parameter, polymer viscosity ratio, and geometric disorder parameter. In particular, we show that the strain-hardening behavior of a viscoelastic fluid promotes these chaotic fluctuations, whereas the shear-thinning behavior tends to suppress these. Therefore, it is not a general phenomenon that can always be seen in the flows of a viscoelastic fluid in porous media.