Viscoelastic instabilities in micro-scale flows

Abstract

Many artificial and natural fluids contain macromolecules, particles or droplets that impart complex flowbehavior 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 anideal 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 wherechaotic advection is unfeasible. Flows of viscoelastic fluids are characterized by the Weissenberg (Wi) andReynolds (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 extensionalcomponent, including: flow through a hyperbolic contraction followed by a sudden expansion; flow ina microfluidic diode and in a flow focusing device; flow around a confined cylinder; flow through porousmedia and simplified porous media analogs. These flows exhibit different types of flow transitionsdepending on geometry, Wi and Re, including: transition from a steady symmetric to a steady asymmetricflow, often followed by a second transition to unsteady flow at high Wi; direct transition between steadysymmetric and unsteady flows.