Viscoelastic instabilities in microscale flows

Many artificial and natural fluids contain macromolecules, particles or droplets that impart complex flow behavior to the fluid. This complex behavior results in a non-linear relationship between stress and deformation standing in between Newton’s law of viscosity for an ideal viscous liquid and Hooke’s law for an ideal elastic material. Such non-linear viscoelastic behavior breaks down flow reversibility under creeping flow conditions, as encountered at the micro-scale, and can lead to flow instabilities. These instabilities offer an alternative to the development of systems requiring unstable flows under conditions where chaotic advection is unfeasible. Flows of viscoelastic fluids are characterized by the Weissenberg (Wi) and Reynolds (Re) numbers, and at the micro-scale flow instabilities occur in regions in the Wi–Re space typically unreachable at the macro-scale, namely high Wi and low Re. In this paper, we review recent experimental work by the authors on the topic of elastic instabilities in flows having a strong extensional component, including: flow through a hyperbolic contraction followed by a sudden expansion; flow in a microfluidic diode and in a flow focusing device; flow around a confined cylinder; flow through porous media and simplified porous media analogs. These flows exhibit different types of flow transitions depending on geometry, Wi and Re, including: transition from a steady symmetric to a steady asymmetric flow, often followed by a second transition to unsteady flow at high Wi; direct transition between steady symmetric and unsteady flows.