Tristability in confined viscoelastic flow*

Viscoelastic flows through confined geometries are relevant in enhanced oil recovery, microbial mining, environmental remediation, and targeted drug delivery. The confinement induces large elastic stresses in viscoelastic flow, which leads to purely elastic instability of the flow. We have numerically investigated viscoelastic instabilities between two cylinders located in the streamwise direction in a channel. We have discovered the tristability of the flow states in the region between the cylinders induced by the formation of streaks characterized by high polymeric stress. The streaks formed by high polymeric stress act as a barrier for the flow crossing the regions, which leads to flow separation and the formation of multiple flow states inside the channel. We have investigated the criteria of viscoelastic instability and discovered that the criterion of purely elastic instability can be used to forecast the type and location of instability after the transition. We also explored the effect of fluid rheology and cylinders’ size and separation on the flow instabilities.