Measured Lagrangian stretching reveals stress topology and transport barriers in viscoelastic flows

Viscoelastic flows through confined geometries cause large polymeric stresses and elastic instabilities at large Weissenberg number (Wi), which lead to chaotic flow and enhanced mixing in a multitude of natural and industrial processes. Determining the polymeric stress distribution is key to understanding the onset of instabilities and material transport in these systems, but direct measurements remain challenging. In this work, we experimentally demonstrate that the Lagrangian stretching field of viscoelastic flows strongly correlates with the polymeric stress field. The stretching field is quantified from micro-PIV measurements of viscoelastic flows through a host of canonical microfluidic geometries for a broad range of Wi. Across both steady and unstable flow regimes, we show that the measured stretching field topology mirrors the polymeric stress field, determined from simulations. Furthermore, we investigate the mixing properties of these flows across a range of Wi and Peclet numbers, and show that the regions of high stress serve as local transport barriers. This work helps to establish a new Lagrangian framework to analyze viscoelastic flows and directly illustrates the link between stress, stretching, and transport.