Viscoelasticity based droplet migration and sorting.

We experimentally elucidate the cross-stream migration behavior of viscoelastic Polydimethylsiloxane (PDMS) droplets in the non-inertial Poiseuille flow of constant viscosity aqueous viscoelastic solution of Polyvinylpyrrolidone (PVP) in straight rectangular microchannels. We investigate the complex interaction among deformability induced non-inertial lift force, viscoelastic lift force due to matrix viscoelasticity, and viscoelastic lift force due to droplet viscoelasticity and propose a new droplet migration regime. We vary the drop-to-medium viscosity ratio (k) by varying the PVP concentration and demonstrate center-ward droplet migration for k \textless 18.52 and \textgreater 3.72 respectively, while droplets stay near the wall for 3.72$\le $ k $\le $18.52, contrary to Chan and Leal's prediction with second-order fluids. We observe that for k $=$ 12, Newtonian castor oil (viscosity 650 mPa-s, relaxation time $=$ 0) droplets migrate to center while PDMS (average viscosity 666 mPa-s, relaxation time $=$ 0.001) droplets stay near the wall. Finally, we demonstrate viscoelasticity based sorting of castor and PDMS droplets.