Deformation and transport of an elastic fiber in a viscous cellular flow & Elastic flow instabilities in curved microchannels

1) The interaction of a deformable body with a viscous flow is found in a wide range of situations, ranking from biology to polymer science. Here we address the fundamental question of the modification of the transport of an object induced by its deformation in a viscous flow as studied by Young et al [Young and Shelley, Phys. Rev. Lett.,99, 058303 (2007)].
In this context, we experimentally study the deformation and transport of an isolated elastic fiber in a viscous cellular flow at low Reynolds number, namely a lattice of counter-rotative vortices. We show that the fiber can buckle when approaching a stagnation point. By tuning either the flow or the fiber properties, we measure the onset of this buckling instability. The buckling threshold is determined by the relative intensity of viscous and elastic forces, the elasto-viscous number Sp. We directly compare our experimental results to theoretical predictions by Young et al. Moreover we show that flexible fibers escape faster from a vortex (formed by closed streamlines) compared to rigid ones. As a consequence, the deformation of the fiber changes its transport properties in the cellular flow.

2) Purely elastic instabilities are known to occur in flows with curved streamlines in viscoelastic fluids at low Reynolds numbers. They have recently attracted renewed interest as they have been shown to increase mixing in wavy microchannels [1]. The onset of instability has been proposed to be a function of the balance between curvature and normal stress effects [2], but the exact form of this relation is scarcely studied, in particularly for channel flow. Here we report the results of a combined experimental and numerical investigation of variation of the instability threshold with the channel curvature.

[1] A. Groisman and V. Steinberg. Elastic Turbulence in curvilinear flows of polymer solutions, New J. Phys. 6, 29 (2004).

[2] P. Pakdel and G. H. McKinley. Elastic instability and curved streamlines. Physical Review Letters, 77(12):2459-2462, 1996.