Viscous flow of polymers and viscous electron current in graphene

A minute addition of long-chain, flexible, polymer molecules to Newtonian fluid strongly affects both laminar and turbulent flows. Polymers being stretched by a velocity gradient, particularly in a flow with curvilinear streamlines, engender elastic (hoop) stress that modifies the flow via a feedback mechanism. It results in pure elastic instabilities and elastic turbulence (ET), observed at Reynolds number Re  1 and Weissenberg number Wi  1.  I will discuss a sequence of elastic instabilities and ET observed in a wake between two widely-spaced obstacles, hindering the channel flow. Further, I will present first quantitative evidence of elastic waves in ET.

In the second part of my talk, I will discuss viscous electron flow in graphene and our analogous experiments with Newtonian fluid. Electron transport in two-dimensional conducting materials, with dominant electron-electron interaction, exhibits unusual current vortices that result in negative resistance (nonlocal current-field relation). The transport behavior of these materials is best described by low Reynolds number hydrodynamics, where constitutive pressure-speed relation is the Stoke's law. I will present evidence of such vortices in a flow of viscous Newtonian fluid in a microfluidic device-analogous to the electronic system.