Analysis of vortices in viscoelastic fluid flow through confined geometries at low Reynolds numbers

Understanding the behavior of viscoelastic (VE) fluids in confined geometries is crucial for applications in biologic systems, heat transfer devices, enhanced oil recovery, and many others. Here, we perform a systematic steady-state simulation of a VE fluid at low Reynolds numbers through a channel with successive smooth contractions and expansions. We analyze the hydrodynamic performance of the fluid with particular attention to vortex patterns that develop downstream of the contractions. We show that elastic vortices form at higher contraction ratios and that there are critical Weissenberg numbers (Wic) unique to each contraction ratio where the flow shifts from non-vortical to vortical. This Wic increases with an increasing contraction length. The coexistence of elongational-, shear-, and rotational-flow is essential for vortex development and evolution. We also analyzed the effect of the Deborah number (De) on the vortex pattern in a multiple contraction system and observed that the vortex area significantly depends on the distance between the contractions. We show that there are three distinctly different regions in De, in which the flow characteristics change in successive contractions. For high De, the flow in the downstream contraction is significantly affected by the upstream contraction. Our results have implications for the use of VE fluids with various VE properties in different types of porous media.